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Abstract

The parameters of a complex, nonlinear, time-varying system are estimated from missing system output measurements. [Solution] The estimator includes a two-step process for accurately estimating the time-varying parameters of a time-varying system based on input and output samples of the time-varying system. First, multiple filters in a high-frequency processing loop operate to process input and output samples of the time-varying system independently and concurrently to generate a hypersurface containing time-series objects. Each filter is restricted to adapt only a subset of the modeled time-varying parameters. The hypersurface containing the time-series objects is aggregated through multiple iterations of the high-frequency processing loop. Second, the hypersurface passes through a neural network in a low-frequency processing loop to infer estimates of the time-varying system parameters.

Description

Technical Field

[0001] Cross - reference to related applications

[0001] This application claims priority under 35 U.S.C. § 119 to U.S. Provisional Patent Application No. 63 / 456,527, filed Apr. 2, 2023, and U.S. Provisional Patent Application No. 63 / 627,066, filed Jan. 31, 2024, which are hereby incorporated by reference in their entirety.

[0002]

[0002] The present disclosure generally relates to inferential sensing applied to the input and output behavior of a time - varying system to notify a control system, an anomaly detection system, and a decision - making system of the behavior of time - varying system parameters and states. In particular, the present disclosure relates to using neural - network - based adaptive inferential sensing to provide real - time estimates of parameters and state behavior governing a non - linear time - varying system to control, detect, and decision - making systems.

Background Art

[0003]

[0003] Conventional inferential sensing (i.e., adaptive estimation) methods are used in adaptive control systems. Conventional inferential sensing is applied to system inputs and outputs to estimate the time - varying parameters and state behavior of a system that are not directly sensed, and to provide such information to a control system to update an implicit or explicit reference model incorporated in the system. Such time - varying system parameters may be physical characteristics that define or govern the behavior of the system, but for the purposes of an inferential sensor (i.e., an adaptive estimator), may also include the operating regime of the system, system disturbances from the environment, unknown control inputs, stochastic elements, and time.

[0004]

[0004] Conventional inference sensors (e.g., variations of Kalman filters) provide support for generalized state and parameter estimation for time-varying systems that can be represented by a set of linearizable state-space equations, in which case there are only a few independent time-varying parameters, generally less than or equal to the number of independent measurement system outputs or the number of state-space equations. However, time-varying systems that are highly nonlinear and have a very large number of potential time-varying parameters, leading the estimation problem into a state of under-constrained conditions, have traditionally been supported by specialized ad-hoc methods that can provide adaptive control solutions within a limited range. Furthermore, the physical properties of modern complex operating systems are increasingly being represented using computational models (e.g., computational fluid dynamics). These representations lack both conventional state-space representations and the high-precision, low-dimensional models necessary to provide parameter estimations within a limited range for adaptive control purposes. In addition, the lack of generalized parameter estimation methods applicable to highly nonlinear time-varying systems and the problems with under-constrained estimation applications limit the feasibility of inference sensing in a large class of estimation problems related to the autonomy of machines and robots, such as autonomous navigation, rendezvous, docking, and collision avoidance by spacecraft.

[0005]

[0005] Consequently, there is a need for a widely applicable inference sensing method that can estimate the time-varying parameters of a time-varying system, which are necessary for the effective operation and performance of a control system for a complex nonlinear time-varying system. [Overview of the Initiative] [Means for solving the problem]

[0006]

[0006] Non-limiting embodiments relate to novel state and parameter filtering using a two-step process to accurately estimate the time-varying parameters of a nonlinear dynamic time-varying system based on its input and output behavior, which is underconstrained.

[0007]

[0007] In the first stage, this process utilizes filters (described later), but incorporates them into a multiple simultaneous filtering methodology that includes P filters (where P is the number of time-varying system parameters), while operating the filters in failure mode 2 (see Table 1). This process uses each filter to process the same input and output observations from the target system independently and concurrently. However, the i-th filter is assigned to adapt only a subset p of available parameters, and the parameter vector of the i-th filter

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[0008]

[0008] In the second stage, the hypersurface component outputs of the filter bank are aggregated to generate hypersurfaces corresponding to the system time-varying parameter errors associated with the input and output samples. To ensure the uniqueness and predictive ability of the hypersurfaces, each filter can perform multiple iterations on the input and output samples to generate a series of outputs, which are also aggregated into the hypersurfaces. Furthermore, to improve predictive ability, the hypersurfaces generated over multiple past time steps (i.e., past sequences of input and output samples) can be concatenated into a final hypersurface. The auxiliary neural network then uses this hypersurface to infer accurate estimates of the relevant time-varying system parameters. As a result of this two-stage operation, the number of parameters that can be estimated becomes unlimited, eliminating the limiting relationship with the number of system outputs. This unlimited parameter estimation provides novel performance opportunities and new operational purposes for highly nonlinear time-varying systems, including applications such as fault management, autonomy of systems interacting with time-varying environments, and supervision of strong artificial intelligence.

[0009]

[0009] In the case of fault management, the systems and methods described herein enable a system to optionally perform comprehensive fault detection and fault tolerance control by estimating a comprehensive range of potential time-varying parameters that define the system under consideration, regardless of the expectation of degradation or failure. This approach significantly eliminates significant unexpected events and associated risks, facilitates real-time decisions (e.g., diagnosis and prognosis) at the system and subsystem levels, and allows for fine-tuning of control responses to degradation and failure. Furthermore, such systems and methods have the potential to facilitate systematized and reproducible fault management techniques that can be generalized, controlled, and edited across systems, missions, and the entire mission lifecycle, representing the complex fault management capabilities that are highly sought after by modern engineering organizations, including the National Aeronautics and Space Administration (NASA). Applications of fault detection and management include essentially all complex systems and systems of systems that experience deviations and failures, including physical structures, machinery, pipelines, engines, turbomechanical systems, biological systems, electromagnetic systems, mechanical systems, fluid systems, chemical systems, nuclear systems, and artificial intelligence systems.

[0010]

[0010] One example of the advantages of high autonomy is the autonomous rendezvous, docking, and collision avoidance of a spacecraft. In such cases, a great many time-varying parameters that define the dominant orbital dynamics solution may include the behavior of the gravitational field, the orbit of external objects, the intrinsic and extrinsic motion, position and acceleration of the spacecraft, and the spacecraft propulsion performance. Generally, a suitable orbital dynamics solution and orbital design are achieved by ground control on Earth and performed by the spacecraft in a planned phase (including long waiting periods). However, the systems and methods described herein facilitate the continuous, real-time, ad-hoc generation of spacecraft autonomous control behavior (including propulsion response) corresponding to the estimated dominant orbital dynamics to achieve the desired spacecraft motion, position, and propellant-saving objectives. Other examples of applications include general autonomous transportation systems (e.g., aircraft, automobiles, ships), tracking systems (e.g., for power radio transmission, line-of-sight communication), and robotic services (i.e., construction, repair, surgery).

[0011]

[0011] With regard to supervising strong artificial intelligence, the systems and methods described herein generally enable the dynamic specification of large-scale, appropriate weak or strong artificial intelligence system parameters in response to missing probabilistic and dynamic observational datasets. Superintelligence (i.e., strong artificial intelligence that far exceeds human intelligence, and by extension, human predictive, inferential, and control capabilities) is predicted to be achieved within about 10 years. Superalignment (i.e., weaker artificial intelligence that supervises artificial superintelligence) is considered critical to human safety. However, how superalignment can be implemented is currently unknown. Related artificial intelligence systems in the form of large-scale language models are likely to be precursors to artificial superintelligence, and these models may contain billions of parameters. Furthermore, the time-varying parameter space defining the behavior of such models may include millions of external information disturbances, as well as millions of embeddings and other dynamic information patterns originating from within and outside the core artificial superintelligence. The systems and methods described herein enable rapid management of such large parameters in response to relatively rare system output behaviors that may indicate a relative threat or adverse impact to human safety, allowing for a transition to a safer configuration. [Brief explanation of the drawing]

[0012] Brief explanation of the drawing [Figure 1]

[0012] This is a block diagram of a fault management system for a time-varying system according to various aspects of the present disclosure. [Figure 2]

[0013] These are block diagrams of adaptive states and parameter estimators according to various aspects of this disclosure. [Figure 3]

[0014] This is a block diagram of a filtering process according to various aspects of this disclosure. [Figure 4]

[0015] This is a schematic diagram of a filter according to various aspects of this disclosure. [Figure 5A]

[0016] This is a schematic diagram of state and output predictor and estimator neural network configurations according to various aspects of this disclosure. [Figure 5B]

[0016] This is a schematic diagram of a state and output predictor and estimator neural network configuration according to various aspects of the present disclosure. [Figure 6A]

[0017] These are schematic diagrams of state and parameter estimators according to various aspects of this disclosure. [Figure 6B]

[0017] This is a schematic diagram of a state and parameter estimator according to various aspects of the present disclosure. [Figure 7]

[0018] This is a simplified block diagram of a network system suitable for implementing a fault management system for time-varying systems, according to various aspects of this disclosure. [Figure 8]

[0019] This is an illustrative flowchart of a method for estimating the state and parameters of a time-varying system according to various aspects of the present disclosure. [Figure 9]

[0020] This is an illustrative flowchart of the filtering process in a filter of a high-frequency processing loop according to various aspects of the present disclosure. [Figure 10]

[0021] This is an illustrative flowchart of a low-frequency processing loop according to various aspects of the present disclosure. [Figure 11]

[0022] This is a block diagram of a computer system suitable for implementation in various methods and devices according to various aspects of this disclosure. [Figure 12]

[0023] This is a block diagram of an autonomous navigation system for time-varying systems according to various aspects of the present disclosure. [Figure 13]

[0024] This is a block diagram of an artificial intelligence super-alignment system for time-varying artificial intelligence, according to various aspects of this disclosure. [Figure 14]

[0025] This is a block diagram of a time-varying distributed system comprising multiple time-varying subsystems, each having subsystem-specific adaptive states and parameter estimators, according to various aspects of the present disclosure. [Figure 15A]

[0026] This is a simplified schematic block diagram of a liquid propulsion rocket engine according to various aspects of this disclosure. [Figure 15B]

[0027] This is a block diagram of an exemplary time-varying liquid propulsion rocket engine, including several interrelated time-varying subsystems, according to various aspects of the present disclosure. [Figure 16]

[0028] Figure 15B is an exemplary block diagram of a time-varying liquid propulsion rocket engine, including adaptive state and parameter estimators for the interrelated time-varying subsystems of the liquid propulsion rocket engine, according to various aspects of the present disclosure. [Figure 17]

[0029] These are exemplary pseudocode implementations of adaptive control for liquid propulsion rocket engines according to various aspects of this disclosure. [Modes for carrying out the invention]

[0013]

[0030] The aspects of this disclosure and its merits will be best understood by referring to the detailed description below. Similar reference numbers have been used to identify similar elements shown in one or more figures, and it should be understood that these references are for illustrative purposes only and not to limit the disclosure.

[0014] Detailed explanation

[0031] It should be understood that the following disclosure provides many different aspects or embodiments for implementing different features of the disclosure. For the sake of brevity, specific examples of components and arrangements are described below. Naturally, these are merely examples and not intended to be limiting. For brevity and clarity, various features may be depicted at arbitrary different scales.

[0015]

[0032] Some embodiments incorporate filters described by the following equations (i~iii).

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[0016]

[0033] Equations i to iii describe the process for estimating the nonlinear system state and parameters, in which, function f RNN () represents the recurrent neural network model of the target nonlinear system.

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[0017]

[0034] In the equation, y is a vector of independent system outputs, and this filter is f RNN (iv) A nonlinear system that is sufficiently accurately modeled by () y(k+1)=Sys(x(k),q(k),u(k)) (iv) Assuming that such a condition exists, this corresponds to the case where the system parameters are equal to the estimated parameters, i.e., the following equation (v) holds.

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[0018]

[0035] Furthermore, this assumption is,

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[0019]

[0036] Therefore, filters (i~iii) have two main independent failure modes, which are described in Table I below.

[0020] [Table 1]

[0021]

[0037] This disclosure relates to a system and method for estimating dynamic states and parameters in time-varying systems, which are applied to improve the ability of control systems or decision systems (e.g., artificial intelligence systems) to adapt to time-varying systems and domains. The method for estimating states and parameters is achieved at least in part using machine learning (including machine learning models and neural networks). Machine learning relates to a paradigm for determining an embedding function based on a dataset containing inputs and corresponding outputs, which is trained on the inputs and generates corresponding outputs.

[0022]

[0038] This disclosure further relates to estimating many system parameters in a complex, time-varying dynamic system and providing such estimates to a control or decision system to improve the ability to adapt to or control the time-varying system. Embodiments can estimate dynamic system parameters in a variety of scenarios, including when there are insufficient available measured system outputs. Embodiments implicitly extend the dimension of the insufficient system outputs to satisfy the requirement of a general solution having a sufficient number of independent output behaviors to match the number of independent system parameters to be estimated. Thus, embodiments provide the ability to estimate an infinite number of independent time-varying system parameters, regardless of the number of contributing system outputs. In other words, for a vector q(.) of system time-varying parameters having size P≧1 and a vector y(.) of measured independent system outputs having size M≧1, embodiments estimate system parameters having size N=P, regardless of the number of system outputs M.

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[0023]

[0039] The diagrams in this disclosure include specific notations, which are often used to describe the flow of discrete-time control and estimation systems, but are not typically seen in descriptions of continuous-time systems. In particular, these concepts include three types of notations corresponding to the indices of relative time, relative delay, and estimation dependency (with respect to time). Relative time is denoted, for example, by k+1, k, k-1, etc. In the case of the information sequence {y(.)}, y(k) precedes y(k+1) in time, and y(k-1) precedes y(k) in time. In the case of delay notation, the symbol z is used for some integer n. -n The symbol z is used. Relative delay notation is used to explicitly indicate the relative timing of recursion and the signals resulting from such recursion in the flowchart. -n This affects the relative time of the signal, and the signal y(k) is represented as z -nIt is input into a block containing the symbol, and output from the block with the symbol updated to y(kn).

[0024]

[0040] For example, in the case of a simple (i.e., immediate) feedback loop, n=1 and z -1 Or it can simply be denoted as z. In the case of a feedback loop with different frequencies, the period of the simple feedback (or 1-unit delay) of the low-frequency loop is normalized with respect to the period of the high-frequency loop, and z -n This is shown, where n is the number of feedback cycles (i.e., periods) that the high-frequency loop performs to correspond to a single feedback cycle of the low-frequency loop.

[0025]

[0041] The estimation dependency is the estimated value

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[0026]

[0042] Figure 1 is a block diagram 100 of an environment in which an adaptive state and parameter system may be implemented according to aspects of the present disclosure. Figure 1 shows the environment 100, which includes a time-varying system 105, a control system 110, and an adaptive state and parameter estimator 130, all of which can be implemented in hardware, software, or a combination thereof. The adaptive state and parameter estimator 130 includes sufficient mechanical and electronic functions to receive, transmit, and convert information to support interaction with other parts of the environment 100. The adaptive state and parameter estimator 130 estimates specific parameters and states of the time-varying system 105 and notifies the control system 110 of the correct parameters and states to form the basis for a control response to achieve its purpose. In non-limiting embodiments, the time-varying system 105 may be a stochastic nonlinear dynamical system such as a space propulsion system, a space environment (including stars, planets, spacecraft, and gravitational fields), an external collision threat, artificial intelligence, a quantum computer, an autonomous vehicle, or a densely populated urban environment. In non-limiting embodiments, the control system 110 may be a control system, detection system, anomaly detection system, or decision system for the time-varying system 105. In some non-limiting embodiments, the “control system” may include conventional control systems as well as adaptive control and reconfiguration systems (including, but not limited to, electronic, electromagnetic, and mechanical implementations), decision systems (including, but not limited to, expert systems and artificial intelligence), logs, monitors (including, but not limited to, human-readable displays), communication systems (including, but not limited to, audio, visual, kinesthetic, chemical alarms and indicators), and humans (including, but not limited to, audio, sound, kinesthetic, and biofeedback via various forms of feedback).

[0027]

[0043] Furthermore, the environment 100 also includes signal conversion blocks 140 and 150. Although depicted outside the time-varying system 105, the control system 110, and the adaptive state and parameter estimator 130, the signal conversion blocks 140 and 150 may also be incorporated into the time-varying system 105, the control system 110, and the adaptive state and parameter estimator 130. Moreover, the embodiment is not limited to signal conversion blocks 140 and 150, and any number of signal conversion blocks may be included to achieve connectivity and interaction of the environment 100. In some embodiments, the adaptive state and parameter estimator 130 may be combined with or incorporated into the control system 110.

[0028]

[0044] The time-varying system 105 may be a system that experiences degradation or failure. Examples include pressure loss or unwanted vibration in a mechanical system such as an engine. The time-varying system 105 can receive a known input, denoted as system input u(.)155, and an output, denoted as system output y(.)160. System input 155 and output 160 are vector functions of discrete-time variables, which may correspond to clock ticks, as implemented in software or hardware. If no variables appear in the function arguments (i.e., the use of a single period), the function generally refers to an arbitrary time step, rather than a specific time step (specified using parameters such as k). Unless otherwise stated, where k appears in the function arguments, it indicates the function at the k-th time step, which may be specified in milliseconds, seconds, minutes, and similar units. Consequently, k+1 in the function arguments means the function at the time step immediately following the k-th time step. System input u(.)155 may contain instructions or objectives that the time-varying system 105 should achieve by manipulating the degrees of freedom available to it. The system output y(.)160 may correspond to sensor readings (power consumption, temperature, direction, position, altitude, speed, etc.) associated with the time-varying system 105. The system output y(.)160 can be acquired by the adaptive state and parameter estimator 130 by any sensing means, including radar, cameras (e.g., machine vision), thermocouples, accelerometers, microphones, etc. The time-varying system 105 may also have unknown (e.g., unmeasured) system states x(.) and unknown system parameters q(.). Examples of system states x(.) include power consumption or temperature of a particular system component. Unknown system parameters q(.) may reflect degradation of the time-varying system 105 (e.g., fluid leakage, internal mechanical vibration, stress, and friction in the fuel supply subsystem), and may also reflect time, ideas, abstract concepts, disturbances, unexplained control inputs, and other quantifiable information associated with the behavior of the time-varying system.

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[0029]

[0045] The control system 110 can provide commands and / or information in the system input u(.)155 to the time-varying system 105. The commands and / or information include the system output y(.)160 received from the time-varying system 105, and the system state estimates from the adaptive state and parameter estimator 130.

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[0030]

[0046] The adaptive state and parameter estimator 130 can receive system input u(.)155 and system output y(.)160 from the time-varying system 105. The adaptive state and parameter estimator 130 estimates the system state of the time-varying system 105.

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[0031]

[0047] Figure 2 is a block diagram 200 of an adaptive state parameter estimator according to several embodiments of the present disclosure. The adaptive state and parameter estimator 130 includes a multiplex filter system 205, a state and parameter estimator 210, and a state and parameter updater 215. The multiplex filter system 205, the state and parameter estimator 210, and the state and parameter updater 215 can be contained within two processing loops, namely a high-frequency inner loop (HFIL) 220 and a low-frequency outer loop (LFOL) 225 (also called the high-frequency processing loop and the low-frequency processing loop, respectively). The HFIL 220 and LFOL 225 can work together to estimate the parameters and states of a time-varying system 105. In non-limiting embodiments, the multiplex filter system 205 includes a plurality of filters 205A-C. Filters 205A-C are described in more detail below in Figure 3. The HFIL 220 uses the multiplex filter system 205 to generate an information-rich hypersurface. The LFOL 225 estimates accurate parameter values ​​based on these hypersurfaces. The hypersurfaces represent the unknown system state x(.) or the estimated error of the unknown system parameters.

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[0032]

[0048] HFIL 220 can execute operations at a frequency higher than the sampling frequency of the control system 110 of a target system such as the time-varying system 105. The plurality of filters 205A-C of the multi-filter system 205 process the system output y(.)160 and the system input u(.)155 of the time-varying system 105 in parallel. For each of the filters 205A-C of the multi-filter system 205, HFIL 220 collects a sequence of prediction errors and corresponding estimated system parameters, as well as other corresponding data, into a moving window object of width w≧n, where n is the operation period of LFOL 225, which in some embodiments is greater than or equal to the sampling period of the control system. In some aspects, collecting the sequence provides a hyper-surface that can be used to infer accurate parameter estimates at time step k+n. For example, assume that the HFIL frequency f HFIL is normalized such that f HFIL =1. In this case, the basic time step available for use in the embodiment is 1. Thus, the filtered estimates and their aggregation described and shown in FIGS. 3-5 are performed by HFIL 220 at time steps k = 1, 2, 3,....

[0033]

[0049] FIG. 2 shows the filters 205A-C, but the multi-filter system 205 can include a variable number of filters, such as N filters, where N is an integer value. The multi-filter system 205 receives filtered estimated system parameters from the state and parameter updater 215

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[0034]

[0050] The data sequence is aggregated from each filter of the multiple filter system 205 by the multiple filter system 205 within a moving time window of time step width w (for some values, w ≥ n, which can be set based on various tests, where n is the LFOL period). For the i-th filter, the sequence of prediction errors defined by the moving time window (k, kw) of width w ≥ n at time step k is given by equation 1 below:

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[0035]

[0051] Similarly, filtered estimated system parameters up to time step k

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[0036]

[0052] The aggregated sequence data for the i-th filter is:

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[0037]

[0053] Object {v i (.)}260 is the filtered estimated system parameter of LFOL 225.

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[0038]

[0054] Moving on to LFOL 225, LFOL 225 can perform operations every n time steps, where the value of period n can be an integer multiple of the period of HFIL 220. The value of period n can be based on a test, such as n ≥ τ, where τ is the period of HFIL 220. LFOL 225 performs inference operations every n time steps, i.e., at time steps k = n, 2n, 3n…, and obtains objects {v} from HFIL 220 at such k intervals. i Infer parameter estimates based on (.)}260.

[0039]

[0055] In some embodiments, LFOL 225 includes a state and parameter estimator 210. The state and parameter estimator 210 is an object {v i Receive the output from HFIL 220, which may be a multidimensional hypersurface having (.)}260. Object {v i (.)}260 is all objects {v i It can be a set of (.)}(i=1, N). The state and parameter estimator 210 is an object {v i (.)}260 can be preprocessed. The Sample() function processes each of the N objects {v i Extract a subset of the time series data within (.)} and use a properly pre-trained neural network g NN (.) provides the extracted subset in some combination (for example, a mathematical combination). As will be described later, the neural network g NN (.) indicates the estimated system parameter.

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[0040]

[0056] The Sample() function handles each object {v i (.)}260 extracts at least one time-series data and supplies the output of the Sample() function as input to the state and parameter estimator 210. In some embodiments, the state and parameter estimator 210 is a feedforward neural network g NN This may include neural networks such as (.). In some embodiments, the Sample() function takes all aggregated time series data {v} developed by each of the N filters of the multifilter system 205. i (.)}260 can be extracted as a complete dataset. In addition, the input to the state and parameter estimator 210 at time step k+1 is the previous system parameter estimate at k.

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[0041]

[0057] Alternatively, the state and parameter estimator 210 can determine the estimated value by inferring the parameter adjustment amount Δq(k+n) and adding the adjustment amount to past values ​​(i.e.,

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[0042]

[0058]

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[0043]

[0059] As LFOL 225 performs calculations, the i-th filtered estimated system parameter

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[0044]

[0060] Next, the process returns to HFIL 220, and the process is effectively restarted at time step k+1. The signal converter 230 can shift the estimated parameters 245 and state 270 at time step k+1 to the estimated parameters and state at time step k, and then the estimated parameters

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[0045]

[0061] The control system 110 uses filtered system parameter estimates.

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[0046]

[0062] An additional advantage of the embodiments discussed herein is that the updated output prediction error makes the relative accuracy of the state and parameter estimates observable. For the purpose of such observability, the inferred system parameter estimates

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[0047]

[0063] The errors in the state and parameter estimates can be defined by the following equations (9) and (10).

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[0048]

[0064] These error values ​​may be unknown when estimates of the time-varying system 105 are provided by the adaptive state and parameter estimator 130. However, if a correlation can be established between the prediction error (equation 8) and the estimation error (equations 9 and 10) during the training and validation of the neural network model, the error values ​​are known, for example, the output prediction error.

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[0049]

[0065] The value of delta (Δ) is determined empirically and set to a predefined value. The value of delta (Δ) can also be determined during the training and validation of the neural network. Similarly, δ x and δ q The value of can also be determined from the training and validation of the neural network. In some embodiments, the neural network g in the state and parameter estimator 210 NN (.) is the time series data {v} defined by the Sample(.) function. i A subset of (k+1) (i=1, 2, ..., N) is obtained from the previous filtered system parameter estimates.

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[0050]

[0066] Figure 3 is a block diagram 300 of a multiplex filter system 205 according to an aspect of the present disclosure. The multiplex filter system 205 receives the system output y(.)160 from the time-varying system 105, the system input u(k)155, and the previously filtered estimated system parameter values.

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[0051]

[0067] To generate an error surface suitable for the applications described herein, several variations and embodiments of the multi-model method may exist, including neural and non-neural network models, software and hardware implementations, and various algorithms for updating estimated parameter estimates (including gradient descent, heuristic methods, stochastic methods, and genetic algorithms). The best performance is achieved by the system parameter estimates.

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[0052]

[0068] The maximum number of parameters that can be updated by one of filters 205A~C is η. max is, η max ≤ M, where M is the size of the output prediction error vector e(.).

[0053]

[0069] In some embodiments, filters 205A-C represent a neural network, other empirical structures, first-principles models, hardware structures, or a set of estimated system parameters.

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[0054]

[0070] Since the multiplex filter system 205 may require a minimum level of excitation at the output of the time-varying system 105, the dynamics of the time-varying system 105 are excited by the input from the dither signal 305, as shown in Figure 3. The dither signal 305 can be a randomized signal added to the system input u 155. If the natural dynamics and process noise of the time-varying system 105 do not provide enough excitation for the multiplex filter system 205 to correctly interpret the behavior of the time-varying system 105, a dither signal 305 with appropriately defined amplitude and frequency can be incorporated.

[0055]

[0071] Figure 4 is a schematic diagram of a filter contributing to several aspects of this disclosure. Figure 4 shows a filter adapted to the requirements of the i-th filter of a multiplex filter system 205 according to several aspects of this disclosure. Filter 405 may be one of filters 205A to C in the multiplex filter system 205 discussed above. Filter 405 may include one or more neural networks, such as neural network state predictors 410A, 410B, neural network output estimator 415, and function module 420. Also, Figure 4 shows the system input u 155, system output y 160, and predicted system output

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[0056]

[0072] Filter 405 can be constructed from pre-trained neural network state predictors 410A, 410B and output estimator 415. Neural network state predictors 410A, 410B are recurrent neural networks f RNN () and the output estimator 415 is the neural network h NN () is possible. The neural network state predictor 410A filters the estimated system parameters

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[0057]

[0073] The neural network state predictor 410B uses filtered estimated system parameters

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[0058]

[0074] The output estimator 415 receives the predicted system state

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[0059]

[0075] In some embodiments, the filter 405 may include an output prediction error cost function 460. The output prediction error cost function 460 can determine the output prediction error e from the system output y(k) 160 and the predicted system output

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[0060]

[0076] The function module 420 receives the filtered estimated system parameters

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[0061]

[0077] Filter 405 re-introduces the updated smoothed estimated system parameter 445F into the neural network state predictor 410B(f RNN ()) to determine the filtered estimated system state

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[0062]

[0078] In some embodiments, the vectors

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[0063]

[0079] Figure 5A is a block diagram of a neural network state predictor and output estimator according to an aspect of the present disclosure. Figure 5A shows a neural network state predictor f implemented by 410A and 410B. RNN (.), and the output estimator h implemented by 415 NN We show a generalization of (.). Also, due to the flexibility of neural networks, the estimator f RNN (.) and h NN It should be noted that (.) can be incorporated into a single neural network. RNN (.) and h NN The separate descriptions in (.) are used to clarify functional behavior and are not intended to restrict the architecture of the neural network or neural network system.

[0064]

[0080] Neural network state predictor 410A(f RNN (.)) is the control input vector which is the system input u 155, and the filtered estimated system parameters

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[0065]

[0081] In some embodiments, the input to the neural network state predictor 410A may be transformed using signal converter blocks 505A~F to generate a delayed input. For example, the system input u 155 can pass through signal converter blocks 505A, 505B before being supplied to the neural network state predictor 410A. In another example, the input

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[0066]

[0082] In some embodiments, the input to the output estimator 415 may be transformed using signal converter blocks 510A and 510B to generate a delayed input. For example, filtered estimated system parameters

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[0067]

[0083] Figure 5B is a block diagram of a generalized neural network output predictor according to an aspect of the present disclosure. Figure 5B shows a neural network state predictor and a separate output estimator as the output predictor f RNN An embodiment in which (.) 550 is replaced is shown. This can occur when access to sufficient states for the development of the training dataset is not possible, or when the system output is explicitly also a system state. In such cases, the predictive estimated system output 435 may also function as a predictive system state and a filtered estimated system state, often supporting an increase in the level of recursion in the system output (as a delayed input). The output recursion used in Figure 5B is as shown, i.e., the true system output y(.) or the recursive predictive system output estimate.

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[0068]

[0084] In some embodiments, the neural network output predictor 550 takes the system input u(k) 155 and filtered estimated system parameters.

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[0069]

[0085] In some embodiments, the input to the neural network state predictor 550 may be transformed using signal converter blocks 515A-F to generate a delayed input. For example, the system input u(k) 155 can pass through signal converter blocks 515A, 515B before being supplied to the neural network state predictor 410B. In another example, the input

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[0070]

[0086] In some embodiments, the neural network state predictor 410A may be a recurrent neural network (RNN), but its implementation is not limited to this embodiment. The output estimator 415 may utilize a feedforward neural network (NN), but its implementation is not limited to this embodiment. In some embodiments, other architectures can be used for the neural network. The neural network can be replaced with other structures, which may be implemented in hardware or software, and may utilize empirical, first-principles, or hybrid formulations. Also, if the state estimate is also the (measured) system output, the output estimator can be omitted because the neural network output predictor (e.g., 550) can directly estimate such values ​​(e.g., as shown in Figure 5B). When using the output estimator 415 as shown in Figure 5A, the filtered estimated system parameters are optionally

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[0071]

[0087] Neural network predictors 410A, 410B, 550(f RNN ()) and output estimator 415(h NN Before incorporating ()) into the filtering process, neural network predictors 410A, 410B, 550(f RNN ()) and output estimator 415(hNN ()) can be trained. In some embodiments, neural network predictors 410A, 410B, 550(f RNN ()) and output estimator 415(h NN ()) can be trained using supervised training and data generated from a first-principles software model of the target system, a highly instrumented testbed version or prototype of the actual target system, or any combination of these methods. The objective of training the neural network is to predict the system state.

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[0072]

[0088] Figure 6A is a block diagram of the state and parameter estimator 210 in several embodiments. As discussed above, the state and parameter estimator 210 can perform parameter estimation during LFOL 225. The state and parameter estimator 210 may include a parameter estimator 610 and a state filter 620. The parameter estimator 610 uses a signal transformation block 615 to shift filtered system parameter estimates.

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[0073]

[0089] In some embodiments, the parameter estimator g NN The 610 training data are objects v generated by filters 205A~C of the multi-filter system 205. i Such sampled components may be included and applied to first-principles models, appropriately instrumented testbeds or system prototypes, or other suitable data sources. The attributes of such models, testbeds, prototypes, and data sources may include system parameters q(.), which are known as long as the input u(.) of the target system is sufficiently rich and vary in rich patterns. Many neural network architectures (including feedforward, recurrent, convolution, etc.), suitable transformation functions (including linear and nonlinear functions, empirical and first-principles), training methods (e.g., supervised learning, reinforcement learning, generative learning, etc.), and N objects v are available to create a sufficient mapping from the developed time-series data to the time-varying system parameters q(k). i There are several combinations of data included in (.). State filter 620 is the smoothed system parameter estimate.

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[0074]

[0090] Figure 6B is a block diagram of another state and parameter estimator 120 according to several embodiments. The state and parameter estimator 210 may include a parameter estimator 610 and a state filter 620. The parameter estimator 610 uses a signal transformation block 615 to shift system parameter estimates.

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[0075]

[0091] Figure 7 is a simplified block diagram of a network system 700 suitable for implementing the state and parameter estimation frameworks of Figures 1-6. In one embodiment, the system 700 includes a user device 710 that can be operated by a user 740, a server 720, and other forms of devices, servers, and / or software components that operate to perform various methodologies according to the embodiments described. Symbolic devices and servers may include devices, standalone, and enterprise-class servers running MICROSOFT® OS, UNIX® OS, LINUX® OS, or other suitable device and / or server-based OSs. It will be understood that the devices and / or servers shown in Figure 7 can be deployed in other ways, and that the operations performed and / or services provided by such devices and / or servers can be combined or separated for a given embodiment, and can be performed by more or fewer devices and / or servers. One or more devices and / or servers may be operated and / or maintained by the same or different entities.

[0076]

[0092] In addition, the network system 700 may include a control system 110 and a time-varying system 105. The exemplary control system 110 may be an onboard computer capable of relaying instructions for reconfiguring the target system discussed above. The exemplary time-varying system 105 may be the target system.

[0077]

[0093] The user device 710, server 720, control system 110, and time-shifting system 105 may be connected by a network 760. Network 760 may be implemented as a single network or as a combination of multiple networks. For example, in various embodiments, network 760 may include the Internet or one or more intranets, fixed telephone networks, wireless networks, and / or other suitable types of networks. Thus, network 760 may correspond to small-scale communication networks such as private or local area networks, or large-scale networks such as wide area networks or the Internet, which are accessible to various components of system 700.

[0078]

[0094] The user device 710 and the server 720 can communicate with each other over the network 760. The user device 710 can access various functions available on the user device 710, including processes and / or applications associated with the server 720 that are used by the user 740 (e.g., drivers, system administrators, etc.).

[0079]

[0095] Each user device 710 may include one or more processors, memory, and other suitable components for executing instructions, such as program code and / or data, stored in one or more computer-readable media to carry out the various applications, data, and steps described herein. For example, such instructions may be stored in one or more computer-readable media, such as memory or data storage devices, located inside and / or outside the various components of the system 700 and / or accessible over the network 760.

[0080]

[0096] The user device 710 can be implemented as a communication device that can utilize appropriate hardware and software configured for wired and / or wireless communication with the server 720. For example, in one embodiment, the user device 710 can be implemented as an autonomous vehicle, a personal computer (PC), a smartphone, a laptop / tablet computer, a wristwatch with appropriate computer hardware resources, eyeglasses with appropriate computer hardware (e.g., GOOGLE GLASS®), other types of wearable computing devices, embedded communication devices, and / or other types of computing devices capable of transmitting and / or receiving data (such as Apple's iPad®). Although only one communication device is shown, multiple communication devices can also be made to function similarly.

[0081]

[0097] The user device 710 in Figure 7 includes an alert application 712 that may correspond to executable processes, procedures, and / or applications with associated hardware. For example, the user device 710 may receive a message from the server 720 indicating the status of the time-varying system 105 (i.e., whether it is operating normally or on the verge of failure) and display that message via the alert application 712. In some embodiments, estimated parameters may be received by the user device 710 and displayed to the user via the alert application 712. In some cases, the alert application 712 may be activated when it receives system parameter estimates or when the system parameter estimates are abnormal. In other embodiments, the user device 710 may include additional or different modules with dedicated hardware and / or software as needed.

[0082]

[0098] In some embodiments, the user device 710 may include an adaptive state and parameter estimator 730. The adaptive state and parameter estimator 730 can perform the processes and methods described with respect to the adaptive state and parameter estimator 130. The user device 710 may further include a database stored in the temporary and / or non-temporary memory of the user device 710 or an external component communicably connected to the network 760, which may store data generated by the time-varying system 105, the control system 110, and / or the adaptive state and parameter estimator 130.

[0083]

[0099] Server 720 may also include an adaptive state and parameter estimator 730. Similarly, Server 720 may include a database stored in the server 720's temporary and / or non-temporary memory, which can store data generated by the time-varying system 105, the control system 110, and / or the adaptive state and parameter estimator 130.

[0084]

[0100] In some embodiments, the user device 710 and the server 720 may store parts of the adaptive state and parameter estimator 730. For example, the server 720 may store parts of the adaptive state and parameter estimator 730 that estimate parameters and states, and the user device 710 may include not only parts that determine the errors of filtered parameters and states, but also parts that display the parameters and states.

[0085]

[0101] Figure 8 is an exemplary logic flow diagram illustrating a method for estimating the state and parameters of a time-varying system according to several embodiments. One or more processes of Method 800 can be at least partially implemented in the form of executable code stored in a non-temporary, tangible, machine-readable medium, and the executable code, when executed by one or more processors, can cause one or more processors to execute one or more processes. In some embodiments, Method 800 corresponds to all or part of the operation of an adaptive state and parameter estimator 730 that performs prediction and estimation of the internal state and parameters of a time-varying system 105, as shown in Figure 7. Method 800 includes many enumerated steps, but embodiments of Method 800 may include additional steps before, after, and between the enumerated steps. In some embodiments, one or more of the enumerated steps can be omitted, executed concurrently, or executed in a different order. Furthermore, Method 800 can be started to operate as a loop while the time-varying system 105 is operating.

[0086]

[0102] In step 802, samples of the input signal (e.g., 155 in Figures 1-4) and output signal (e.g., 160 in Figures 1-4) of a time-varying system (e.g., 105 in Figures 1-3) are received by the adaptive state and parameter estimator 130 via the interface. Signal transmission can be performed in real time. Alternatively, transmission can be performed at predefined time increments to conserve network bandwidth. Transmission may also include only system inputs, only system outputs, or a combination of both. Transmissions received at predefined time increments are sometimes referred to as samples.

[0087]

[0103] In step 804, a multidimensional hypersurface corresponding to the sample (e.g., object {v(.)}260 in Figures 2 and 3) is generated. As discussed above, the multidimensional hypersurface is generated based on the system output y 160 and system input u 150, as well as the previous filtered estimated system state 270 and previous filtered estimated system parameters 245 generated during the previous iteration of the adaptive state and parameter estimator 130. Also, as discussed above, aggregate sequence data of the multidimensional hypersurface can be generated using HFIL 220, which includes filters 205A-C. Filters 205A-C operate concurrently, with each filter adapting one estimated system parameter. For example, the i-th filter is:

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[0088]

[0104] In step 806, filtered system parameter estimates and filtered system state estimates (e.g., 265 and 275 in Figure 2) for a time-varying system are generated based on aggregated sequence data of a multidimensional hypersurface. As discussed above, LFOL 225 can generate filtered system parameter estimates and filtered system state estimates for a time-varying system based on aggregated sequence data of a multidimensional hypersurface.

[0089]

[0105] In step 808, filtered system parameter estimates and filtered system state estimates for the time-varying system are transmitted to the control system (e.g., 110 in Figure 1). For example, the adaptive state and parameter estimator 130 can transmit filtered system parameter estimates and filtered system state estimates for the time-varying system (e.g., 265 and 275 in Figure 2) to the control system 110.

[0090]

[0106] In step 810, the updated HFIL 220 is updated using the filtered system parameter estimates and filtered system state estimates of the time-varying system. For example, the state and parameter updater 215 can update the preceding filtered estimated system state 270 and preceding filtered estimated system parameters 245 using the filtered system parameter estimates and filtered system state estimates (e.g., 265 and 275 in Figure 2). The state and parameter updater 215 then supplies the updated filtered estimated system state 270 and updated filtered estimated system parameters 245 to the HFIL 220, which can then determine the aggregate sequence data of the multidimensional hypersurface (e.g., object {v(.)}260 (not shown) in step 804).

[0091]

[0107] Figure 9 is an exemplary logic flow diagram illustrating a filtering process according to several embodiments. One or more processes of Method 900 can be at least partially implemented in the form of executable code stored in a non-temporary, tangible, machine-readable medium, and the executable code, when executed by one or more processors, can cause one or more processors to execute one or more processes. In some embodiments, Method 900 corresponds to all or part of the operation of adaptive state and parameter estimators 130, 730 that perform prediction and estimation of the internal state and parameters of a time-varying system 105, as shown in Figures 1 and 7. Method 900 includes many enumerated steps, but embodiments of Method 900 may include additional steps before, during, and after the enumerated steps. In some embodiments, one or more of the enumerated steps can be omitted, executed concurrently, or executed in a different order. Figure 9 shows object {v(.)}260 of object {v i This shows how to generate (.)}.

[0092]

[0108] In step 902, the first neural network (e.g., 410A in Figure 4) of a filter (e.g., one of 205A-C in Figure 3) within a set of filters (e.g., 205A-C in Figure 3) generates a predicted system state (e.g., 442 in Figure 4) from the input signal in the sample (e.g., 155 in Figure 4), the estimated prior system parameters of the time-varying system, and the estimated prior system state (270 and 265 from previous iterations of LFPL 225). If the first neural network is configured as shown in Figure 5B, then 442 and 265 are the estimated predicted system output and the estimated prior system output, respectively.

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[0093]

[0109] In step 904, the second neural network of the filter generates the predicted system output from the predicted system state. As described above, the neural network output estimator (h NN )415 is the prediction system state

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[0094]

[0110] In step 906, the error is determined based on the difference between the predicted system output and the output signal in the sample. For example, as described above, the filter 405 determines the predicted system output

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[0095]

[0111] In step 908, updated filtered estimated system parameters are generated from the error. For example, as described above, function module 420 can generate smoothed estimated system parameters 445F based on the output prediction error e(.)255. The smoothed estimated system parameters 445F are the updated filtered estimated system parameters

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[0096]

[0112] In step 910, the third neural network generates a subsequent filtered estimated system state or a subsequent predicted system output. As described above, the third neural network 410B generates a subsequent filtered estimated system state 440 based on the updated filtered estimated system parameters 445, the input signal 155 in the sample, and the previous filtered estimated system state from the previous time step (e.g., 440). Also, if the third neural network 410B is configured as shown in Figure 5B, the third neural network 410B may also generate a subsequent predicted system output.

[0097]

[0113] In step 912, the first neural network (e.g., 410A) of the filter (one of 205A-C in Figure 3) processes the input signal in the sample (e.g., 155 in Figure 4), the subsequent filtered estimated system state 440, or the subsequent predicted system output (e.g., 435 if the third neural network 410B is configured as shown in Figure 5B).

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[0098]

[0114] In step 914, the second neural network of the filter generates a predicted system output from the second predicted system state. For example, for a subsequent time step, the second neural network 415 of the filter 405 generates the second predicted system state

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[0099]

[0115] In step 916, the error is determined based on the difference between the second prediction system output and the output signal in the sample. For example, for a subsequent time step, as described above, the second prediction system output is determined by the filter 405.

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[0100]

[0116] In step 918, a second updated filtered estimated system parameter is generated based on the error. For example, for a subsequent time step, as described above, function module 420 generates the second updated filtered estimated system parameter from the error e(.)255.

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[0101]

[0117] Figure 10 is an exemplary logic flow diagram illustrating the LFOL process according to several embodiments. One or more processes of Method 1000 can be at least partially implemented in the form of executable code stored in a non-temporary, tangible, machine-readable medium, and the executable code, when executed by one or more processors, can cause one or more processors to execute one or more processes. In some embodiments, Method 1000 corresponds to all or part of the operation of adaptive state and parameter estimators 130, 730 that perform prediction and estimation of the internal state and parameters of a time-varying system 105, as shown in Figures 1 and 7. Method 1000 includes many enumerated steps, but embodiments of Method 1000 may include additional steps before, during, and after the enumerated steps. In some embodiments, one or more of the enumerated steps can be omitted, executed concurrently, or executed in a different order.

[0102]

[0118] In step 1002, a multidimensional hypersurface containing a time-series object is received from HFIL 220 to the parameter estimator 610 of the state and parameter estimator 210. For example, a multidimensional hypersurface containing the time-series object {v(.)}260 can be received by the state and parameter estimator 210 included in LFOL 225.

[0103]

[0119] In step 1004, a subset of the time-series object {v(.)}260 of the multidimensional hypersurface 260 is extracted by the sampling function in the state and parameter estimator 210. For example, as described above with respect to Figure 2, the Sample() function can be used to extract a subset of the time-series object {v(.)}260 of the state and parameter estimator 210.

[0104]

[0120] In step 1006, the parameter estimator generates filtered system parameter estimates for a time-varying system from a subset of time-series objects. For example, the neural network of parameter estimator 610 generates filtered system parameter estimates from a subset of time-series objects {v(.)}260 and previous time steps.

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[0105]

[0121] In step 1008, the state filter of the state and parameter estimators generates filtered system state estimates or predicted system outputs (for example, as shown in Figure 5B). For example, the neural network of state filter 620 generates filtered system parameter estimates.

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[0106]

[0122] Figure 11 is a block diagram of a computer system 1100 suitable for implementing the various methods and devices described herein. In various implementations, the devices on which the steps can be performed may include network communication devices (e.g., mobile phones, laptops, personal computers, tablets, etc.), network computing devices (e.g., network servers, computer processors, electronic communication interfaces, etc.), or other suitable devices. Accordingly, it should be understood that the adaptive state and parameter estimator 130, as well as the devices on which the various method steps of methods 800-1000 discussed above can be implemented as a computer system 1100.

[0107]

[0123] According to various aspects of this disclosure, a computer system 1100, such as a network server or mobile communication device, includes a bus component 1102 or other communication mechanism for transmitting information, the bus component 1102 interconnects subsystems and components such as a computer processing component 1104 (e.g., a processor, microcontroller, digital signal processor (DSP), etc.), a system memory component 1106 (e.g., RAM), a static storage component 1108 (e.g., ROM), a disk drive component 1110 (e.g., magnetic or optical), a network interface component 1112 (e.g., a modem or Ethernet card), a display component 1114 (e.g., a cathode ray tube (CRT) or liquid crystal display (LCD)), an input component 1116 (e.g., a keyboard), a cursor control component 1118 (e.g., a mouse or trackball), and an image capture component 1120 (e.g., an analog or digital camera). In one implementation, the disk drive component 1110 may include a database having one or more disk drive components.

[0108]

[0124] In some aspects of this disclosure, the computer system 1100 performs a specific operation by having a processing component 1104 execute one or more sequences of one or more instructions contained in a system memory component 1106. Such instructions may be read into the system memory component 1106 from another computer-readable medium, such as a static storage component 1108 or a disk drive component 1110. In other aspects, the disclosure can be implemented using hardwired circuitry instead of (or in combination with) software instructions. In some aspects, various components of the adaptive state and parameter estimator 130 may be in the form of software instructions, executable by the processing component 1104, and capable of automatically performing contextual tasks on behalf of the user.

[0109]

[0125] Logic can be encoded in a computer-readable medium, which can refer to any medium that provides instructions for execution to the processing component 1104. Such a medium can take many forms, including but not limited to non-volatile and volatile media. In one embodiment, the computer-readable medium is non-transient. In various implementations, the non-volatile medium includes optical or magnetic disks, such as the disk drive component 1110, and the volatile medium includes dynamic memory, such as the system memory component 1106. In one embodiment, data and information related to execution instructions can be transmitted to the computer system 1100 via a transmission medium, such as acoustic or optical waves, including those generated during radio and infrared data communications. In various implementations, the transmission medium can include coaxial cables, copper wires, and optical fibers, including wires including the bus 1102.

[0110]

[0126] Some common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, any other optical media, punch cards, paper tapes, any other physical media having any pattern of holes, RAM, PROMs, EPROMs, FLASH-EPROMs, any other memory chips or cartridges, carriers, or any other media adapted for computer reading. These computer-readable media may also be used to store the programming code for the adaptive state and parameter estimator 130 discussed above.

[0111]

[0127] In various aspects of this disclosure, the execution of instruction sequences for implementing this disclosure may be performed by a computer system 1100. In other aspects of this disclosure, multiple computer systems 1100 connected by a communication link 1130 (e.g., a communication network such as a LAN, WLAN, PTSN, and / or various other wired or wireless networks including telecommunications, mobile and cell phone networks) may cooperate with each other to execute instruction sequences for implementing this disclosure.

[0112]

[0128] The computer system 1100 can send and receive messages, data, information, and instructions, including one or more programs (i.e., application code), through the communication link 1130 and the network interface component 1112. The received program code can be executed by the processing component 1104 upon receipt and / or stored in the disk drive component 1110 or some other non-volatile storage component for execution. The communication link 1130 and / or the network interface component 1112 can be used to communicate electronically between the adaptive state and parameter estimator 130 and an external device (e.g., a user device 710), depending on the exact location where the adaptive state and parameter estimator 130 is implemented.

[0113]

[0129] Figures 12 and 13 are block diagrams showing examples of non-limiting implementations of aspects of the present disclosure. Figures 12 and 13 illustrate exemplary implementations that support autonomous navigation and artificial intelligence control.

[0114]

[0130] Figure 12 is a block diagram of an autonomous navigation system for a time-varying system of systems according to various aspects of the present disclosure. Figure 12 shows an environment 1200 characterized as a system of systems, which can guide the interaction of multiple systems, which may be uncoupled or loosely coupled, toward optimized coordination by a control system. The environment 1200 may include a time-varying system 1205, a time-varying environment 1220 of a specific range of the subject, a control system 1210, and an adaptive state and parameter estimator 1230, all of which can be implemented in hardware, software, or a combination thereof.

[0115]

[0131] The adaptive state and parameter estimator 1230 includes sufficient mechanical and electronic functions to receive, transmit, and convert information in order to support interaction with other parts of the environment 1200. The adaptive state and parameter estimator 1230 can receive system input / control messages 1255, system outputs 1260, and environment outputs 1262. In some embodiments, the total system output y = [y sys ,y envA ] can be defined, i.e., the outputs of the system and the environment can be coupled. As described herein, the adaptive state and parameter estimator 1230 estimates specific parameters 1270 and states 1265 of the time-varying system 1205 and informs the control system 1210 of the parameters and states to form the basis for a control response to achieve its purpose. In non-limiting embodiments, the time-varying system 1205 and the time-varying environment 1220 within a particular range of subjects may include space propulsion systems, space environments (e.g., including stars, planets, spacecraft, and gravitational fields), external collision threats, artificial intelligence, quantum computers, autonomous vehicles, stochastic nonlinear dynamical systems such as densely populated urban environments, or other systems and environments. In non-limiting embodiments, the control system 1210 may be a control system, a detection system, or a decision system. The adaptive state and parameter estimator 1230 may have a similar structure to components of similar names described herein (e.g., adaptive state and parameter estimator 130). In some embodiments, the system outputs 1260, 1262 of the time-varying system 1205 and the time-varying environment 1220 may also be provided to the control system 1210.

[0116]

[0132] Figure 13 is a block diagram of an artificial intelligence superalignment system for time-varying artificial intelligence according to an aspect of the present disclosure. Figure 13 shows an environment 1300 in which control of a time-varying strong artificial intelligence 1305 can be performed via a weak artificial intelligence 1310. The environment 1300 includes a time-varying artificial intelligence 1305, an artificial intelligence 1310 that asserts control, a specific region of the time-varying environment 1320 that is affected by the artificial intelligence 1305 (e.g., through the output 1360 of the artificial intelligence) and provides feedback 1325 to the artificial intelligence 1305, and an adaptive state and parameter estimator 1330, all of which can be implemented in hardware, software, or a combination thereof. In some embodiments, the system input u = [u c ,z] can be defined, that is, the control response / message 1355 and the output / feedback 1325 from the time-varying environment 1320 can be linked.

[0117]

[0133] The adaptive state and parameter estimator 1330 includes sufficient mechanical and electronic functions to receive, transmit, and transform information in order to support interaction with other parts of the environment 1300. The adaptive state and parameter estimator 1330 can receive system inputs / control responses 1355, system outputs 1360, and environment outputs / feedback 1325. The adaptive state and parameter estimator 1330 estimates specific parameters 1370 and states 1365 of specific regions of the time-varying artificial intelligence 1305 and the time-varying environment 1320, and informs a weaker artificial intelligence 1310 (which performs the functions of the control system) of the parameters and states to update implicit or explicit reference models concerning the interacting systems (e.g., the artificial intelligence 1305 and the time-varying environment 1320), and to form the basis for control responses 1355 to achieve that purpose. In non-limiting embodiments, the time-varying artificial superintelligence 1305 and the time-varying environment 1320 of a particular domain of interest may have stochastic nonlinear dynamical system behavior, and the time-varying environment of a particular domain of interest may be the general public, a swarm of robots, a space propulsion system, a space environment, an external collision threat, artificial intelligence, a quantum computer, an autonomous vehicle, a natural system, a biological system, a densely populated urban environment, or other systems. In non-limiting embodiments, the artificial intelligence system 1310 may be a control system, a detection system, or a decision system. The adaptive state and parameter estimator 1330 may have a similar structure to components of similar names described herein (e.g., adaptive state and parameter estimator 130). In some embodiments, the output 1360 of the time-varying system 1305 and the feedback 1325 of the time-varying environment 1320 may also be provided to the control system 1310.

[0118]

[0134] Figures 14–17 are block diagrams providing examples of non-limiting implementations of this disclosure for distributed systems. Due to the scale and complexity of many time-varying systems, distributed support as shown in Figures 14–17 can optimize practical deployment, cost, sustainability, maintainability, and other metrics.

[0119]

[0135] Figure 14 is a block diagram of a time-varying distributed system comprising multiple time-varying subsystems, each having subsystem-specific adaptive state and parameter estimators, according to various aspects of this disclosure. Figure 14 shows an environment 1400, which includes multiple time-varying interrelated subsystems 1405, multiple control systems 1410, and distributed adaptive state and parameter estimators 1430, all of which can be implemented in hardware, software, or a combination thereof. Any number of control systems, time-varying subsystems, and subsystem-specific adaptive state and parameter estimators exist, and any number of inputs and outputs associated with them. Three examples of subsystems are shown in Figures 15A, B, and 16, as will be discussed below.

[0120]

[0136] The subsystem-specific adaptive state and parameter estimator 1430 includes sufficient mechanical and electronic functions to receive, transmit, and convert information in order to support interaction with other parts of the environment 1400. Each subsystem-specific adaptive state and parameter estimator 1430 can receive a system input / control response 1455 and an associated subsystem-specific output 1460. The subsystem-specific adaptive state and parameter estimator 1430 estimates specific parameters and states of the time-varying subsystem 1405 and notifies the appropriate control system 1410 of the correct parameters 1470 and states 1465 to form the basis of the control response 1455 for achieving its purpose. In non-limiting embodiments, the time-varying subsystem 1405 may be a stochastic nonlinear dynamical system such as a turbine, pipeline, motor, microprocessor, tank, heart, lung, microorganism, natural environment, or sensor. In non-limiting embodiments, the control system may be a control system, detection system, or decision system. Each subsystem-specific adaptive state and parameter estimator 1430 may have a structure similar to that of similarly named components described herein (e.g., adaptive state and parameter estimator 130). In some embodiments, the output 1460 of one or more time-varying subsystems 1405 may be provided to one or more control systems 1410.

[0121]

[0137] Figures 15A and 15B show a distributed embodiment relating to a simplified diagram of a liquid propulsion rocket engine 1500A (LPRE) according to aspects of the present disclosure. Figure 15A is a simplified schematic block diagram of the liquid propulsion rocket engine 1500A. Figure 15A shows that the LPRE diagram includes three time-varying subsystems of interest (liquid oxygen (LOX) turbopump 1405A, liquid hydrogen (LH2) turbopump 1405B, and combustion chamber 1405C), three system outputs (LOX flow rate via flowmeter 1460A, LH2 flow rate via flowmeter 1460B, and combustion chamber pressure via pressure transducer 1460C), and two control inputs (LOX valve position 1455A and LH2 valve position 1455B). In addition, a liquid hydrogen tank 1502, a liquid oxygen tank 1504, and a rocket nozzle 1506 are shown.

[0122]

[0138] Figure 15B is a block diagram of an exemplary time-varying liquid propulsion rocket engine 1500B, including several interrelated time-varying subsystems, according to various aspects of the present disclosure. In Figure 15B, the controller block 1410 provides control inputs 1455A, 1455B to subsystem / filter blocks representing the LOX turbopump 1405A and LOX turbopump filter 1430A, and the LH2 turbopump 1405B and LH2 turbopump filter 1430B. The LOX turbopump block receives the main LOX valve position input 1455A from the controller 1410 and outputs the detected LOX flow rate 1460A (from the LOX flow meter) and the estimated parameters 1470A and status 1465A of the LOX turbopump 1405A. The LH2 turbopump block receives the main LH2 valve position input 1455B from the controller 1410 and outputs the detected LH2 flow rate 1460B (from the LH2 flow meter) and the estimated parameters 1470B and status 1465B of the LH2 turbopump 1405B. The combustion chamber block receives the flow rate output (i.e., LOX flow rate 1460A and LH2 flow rate 1460B) as input and outputs the detected combustion chamber pressure 1460C (from the pressure transducer) and the estimated parameters 1470C and status 1465C of the combustion chamber 1405C. For all subsystems / filter blocks, the estimated parameters 1470A-C and status 1465A-C are fed back to the control system 1410.

[0123]

[0139] Figure 16 is a block diagram of an exemplary time-varying liquid propulsion rocket engine of Figure 15B, including adaptive state and parameter estimators 1430A-C for interrelated time-varying subsystems 1405A-C of the liquid propulsion rocket engine 1500 according to various aspects of the present disclosure. Figure 16 is an enlargement of Figure 15B, enlarging the subsystem / filter blocks and revealing the distributed subsystem-specific adaptive state and parameter estimators 1430A-C. In each subsystem / filter block, subsystem inputs 1455A-C and outputs 1460A-C are supplied to its subsystem-specific adaptive state and parameter estimators 1430A-C, generating state estimates 1465A-C and parameter estimates 1470A-C (for example, 1455A and 1460A are supplied to 1430A, generating 1465A and 1470A), which are then supplied to the control system 1410. In some embodiments, the control system 1410 itself may be distributed among two or more control systems that are isolated but connectable and / or interactable.

[0124]

[0140] Figure 17 is a 1700 example of a pseudocode implementation of adaptive control for a liquid propulsion rocket engine according to various aspects of the present disclosure. This pseudocode implements the block diagram flow shown in Figures 15B and 16. The pseudocode includes an instruction loop in which the code is repeated as long as the variable run is set to True. This pseudocode demonstrates that the disclosed method can be used in a computer code implementation for monitoring and controlling a complex time-varying system consisting of many interrelated time-varying subsystems (e.g., 1405A-C). In the pseudocode, subsystems / filter blocks 1405A-C / 1430A-C are shown as functions that receive inputs (e.g., inputs 1455A and 1455B) and return outputs (e.g., outputs 1460A and 1460B). Similarly, an implementation of a control system (e.g., 1410) is shown as a function that receives inputs (e.g., inputs 1465A-C) and returns outputs (e.g., 1470A-C). The inputs and outputs of these functions are reflected in Figures 15A, B, and 16. A function may consist of other functions that perform a specific task. As can be expected from Figure 16, each function representing a specific subsystem / filter block in Figure 17 may include functions that provide input information (function arguments) to that particular subsystem and collect the subsystem's output. Each subsystem / filter block function may also include functions that represent the adaptive state and parameter estimators (e.g., 1430A-C) for a specific subsystem (e.g., 1405A-C).

[0125]

[0141] Adaptive state and parameter estimators can be implemented in software, hardware, or a combination of both. In some embodiments, subsystem-specific adaptive state and parameter estimators can be easily developed. The controllability and maintainability of the software for subsystem-specific adaptive state and parameter estimators are very high because the development and testing costs for a given subsystem are far lower than those for a fully integrated, complex system. Furthermore, when a hardware subsystem is replaced or updated, only the relevant subsystem-specific estimator needs to be replaced (or updated), thereby saving development and testing costs and providing a traceable system for fault management of evolving, complex, nonlinear systems. Such fault management solutions can offer significant advantages in developing reliable and secure systems in application areas such as aerospace, defense, nuclear power, and oil exploration.

[0126]

[0142] In this specification, terms such as “first,” “second,” etc., may be used to describe various elements, but it should be understood that these elements are not limited by these terms. These terms are used solely for the purpose of distinguishing each element. For example, to the extent that it does not deviate from the scope of this disclosure, the first element may be referred to as the second element, and similarly, the second element may be referred to as the first element. As used herein, the term “and / or” includes any combination of one or more of the enumerated items relating to the information.

[0127]

[0143] The terms used herein are intended solely to describe specific aspects and are not intended to limit the disclosure. Where used herein, singular forms such as “a,” “an,” and “the” are intended to include plural forms unless explicitly indicated in the context. Furthermore, where used herein, the terms “comprises,” “comprising,” “includes,” and / or “including” specify the presence of the described features, integers, steps, actions, elements, and / or components, but are not intended to exclude the presence or addition of one or more other features, integers, steps, actions, elements, components, and / or groups thereof.

[0128]

[0144] Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as those generally understood by those skilled in the art to which this disclosure belongs. Furthermore, terms used herein should be interpreted as having meanings consistent with their meanings in the context of this specification and the related art, and should not be interpreted in an idealized or overly formal sense unless expressly defined herein. In addition, similar reference numerals indicate similar characteristics throughout the specification and drawings.

[0129]

[0145] It should be understood that each block in a diagram or flowchart, and combinations of diagrams or flowcharts, can be executed by computer program instructions. Since computer program instructions are present in the processors of general-purpose computers, dedicated computers, or other programmable data processing devices, instructions executed through the processor of a computer or other programmable data processing device generate means for performing the functions described in relation to each block in a signal flowchart or flowchart. Since computer program instructions can be stored in computer-available or computer-readable memory, which can be directed to enable a computer or other programmable data processing device to perform functions in a specified manner, instructions stored in computer-available or computer-readable memory can generate a product containing instructions for performing the functions described in relation to each block in a signal flowchart or flowchart. Since computer program instructions are present in a computer or other programmable data processing device, instructions that generate a process executed by a computer as a series of operational steps can be executed by a computer or other programmable data processing device, causing the computer or other programmable data processing device to operate and provide steps for performing the functions described in relation to each block in a signal flowchart or flowchart.

[0130]

[0146] Each block may represent a module, segment, or portion of code containing one or more executable instructions for performing a specified logical function. Furthermore, it should be noted that in some alternative execution examples, the functions mentioned within a block may occur in a different order. For example, two consecutively presented blocks may be executed substantially simultaneously or in reverse order, depending on their corresponding functions.

[0131]

[0147] Where applicable, the various embodiments provided herein can be implemented using hardware, software, or a combination of hardware and software. Where applicable, the various hardware and / or software components described herein can be combined into composite components comprising software, hardware, and / or both, without departing from the spirit of this disclosure. Where applicable, the various hardware and / or software components described herein can be separated into subcomponents comprising software, hardware, or both, without departing from the scope of this disclosure. In addition, where applicable, it is intended that software components can be implemented as hardware components, and vice versa.

[0132]

[0148] According to this disclosure, software such as computer program code and / or data may be stored in one or more computer-readable media. It is also intended that the software identified herein may be implemented using one or more general-purpose or dedicated computers and / or computer systems (networked and / or other forms). Where applicable, the order of the various steps described herein may be modified, combined into compound steps, and / or divided into substeps in order to provide the features described herein. It is understood that at least a portion of the adaptive state and parameter estimator 130 may be implemented as such software code.

[0133]

[0149] Based on the above considerations, the systems and methods described herein offer several important advantages over conventional methods and systems. However, it is understood that not all advantages are necessarily discussed in detail herein, different embodiments may offer different advantages, and certain advantages are not essential to all embodiments. One advantage is improved computer functionality. For example, conventional computer systems used as control systems, even with the advantages of machine learning, are limited by the number of independent equations, which is determined by the number of associated detection outputs, and have not been able to implement control systems that exceed the number of potential degradation and failure events under consideration. This is because conventional systems could not process sufficient data in real time using sufficient equations with the available computing resources and memory of a time-varying system. The management systems, as well as the adaptive state and parameter estimators described herein, enable this by generating information-rich hypersurfaces based on pre-trained neural networks.

[0134]

[0150] The original ideas described herein have also been incorporated into practical applications, such as the adaptive state and parameter estimator 130 discussed above. Such practical applications can generate outputs (estimated parameters of the time-varying system 105) in a format that is easily understandable to human users or receivable by control systems, and are useful in many situations.

[0135]

[0151] Similar reference numbers are used to identify similar elements shown in one or more figures, and it should be understood that these labeled figures are intended to illustrate aspects of the disclosure and not to limit those aspects.

[0136]

[0152] The foregoing disclosure is not intended to limit the disclosure to any specific form of use or particular field of use. Therefore, it is intended that various alternative forms and / or modifications to the disclosure are possible, whether expressly described or implied herein. Having described the forms of the disclosure, those skilled in the art will recognize that modifications are possible in form and detail, without departing from the scope of the disclosure. Therefore, the disclosure is limited solely by the claims.

Claims

1. A method for estimating the state and parameters of a time-varying system, To receive samples of the input and output signals of the aforementioned time-varying system, A multidimensional hypersurface corresponding to the sample is generated using a high-frequency processing loop including multiple filters, the samples of the input and output signals, prior system parameter estimates of the time-varying system, and prior system state estimates of the time-varying system. Using a low-frequency processing loop including state and parameter estimators, and the multidimensional hypersurface corresponding to the sample, the filtered system parameter estimates and filtered system state estimates of the time-varying system are generated. The filtered system parameter estimates and filtered system state estimates of the time-varying system are transmitted to the control system. Methods that include...

2. For subsequent iterations of the high-frequency processing loop, the high-frequency processing loop is updated using the filtered system parameter estimates and filtered system state estimates of the time-varying system. The method according to claim 1, further comprising: The filtered system parameter estimates and filtered system state estimates of the time-varying system are the preceding system parameter estimates and preceding system state estimates of the time-varying system for the subsequent iterative processing. A method wherein the subsequent iterations of the high-frequency processing loop generate updated multidimensional hypersurfaces corresponding to new samples of the input and output signals.

3. The method according to claim 1, wherein the high-frequency processing loop operates at a frequency higher than or equal to that of the low-frequency processing loop.

4. The method according to claim 1, wherein each of the plurality of filters in the high-frequency processing loop adapts a subset of the estimated system parameters from the prior estimated system parameters, each subset of the estimated system parameters differs for each filter, and when each filter determines a time-series object for the multidimensional hypersurface, other prior estimated system parameters from the prior estimated system parameters that are not included in the subset of the estimated system parameters for each filter are kept constant for each filter, and the size of each subset of the estimated system parameters must be less than or equal to the size of the predicted system output generated by each filter.

5. The method according to claim 1, wherein the multidimensional hypersurface includes a time series object aggregated from the plurality of filters, and each time series object in the time series object includes one or more of the following: a sequence of prediction errors, a sequence of filtered estimated system parameters, a sequence of filtered estimated system states, a gradient of the output prediction error cost function, a formulation of the signal-to-noise ratio of the gradient, and a sequence of system outputs.

6. The prediction system output is generated using at least one neural network of filters within the plurality of filters, the input signal in the sample, the estimated prior system parameters, and at least one of the estimated prior system state of the time-varying system, the predicted prior system output, or the predicted prior system output. The error is determined based on the difference between the output of the prediction system and the output signal in the sample. Based on the aforementioned error, updated filtered estimated system parameters are generated, Using the at least one neural network, the updated filtered estimated system parameters, the input signals in the samples, and the preceding filtered estimated system state or preceding system output, a subsequent filtered estimated system state or subsequent predicted system output is generated. The method according to claim 1, further comprising:

7. Using the at least one neural network of the filter, the input signal in the sample, the subsequent filtered estimated system state or the subsequent predicted system output, and the updated filtered system parameters, a second predicted system output is generated. The second error is determined based on the difference between the output of the second prediction system and the output signal in the sample. The filter generates a second updated filtered estimated system parameter based on the error. The method according to claim 6, further comprising:

8. Training the at least one neural network using a training dataset that includes system inputs, system parameters, and at least one of system outputs and system states. The method according to claim 6, further comprising:

9. In the state and parameter estimator of the parameter estimator, the multidimensional hypersurface corresponding to the sample is received, In the parameter estimator, the filtered system parameter estimates of the time-varying system are generated using the hypersurface, the previous filtered system parameter estimates, and at least one of the previous filtered system state estimates or the previous system output. In the state filter of the state and parameter estimator, the filtered system state estimate or predicted system output of the time-varying system is generated using the input signal in the sample, the filtered system parameter estimate, or the preceding filtered system state estimate, and at least one of the preceding system output. The method according to claim 1, further comprising:

10. To sample a subset of time-series objects within the aforementioned multidimensional hyperplane. The method according to claim 9, further comprising: A method for generating the filtered system parameter estimates based on the subset of time-series objects.

11. The method according to claim 9, wherein the state and parameter estimator includes a neural network, Training the neural network using a training time-series object and a dataset that includes at least one of known training system parameters, known training system states, known training system outputs, and known training system inputs. Methods that further include the above.

12. Non-volatile memory and One or more hardware processors coupled to the non-volatile memory and configured to read instructions from the non-volatile memory and cause the system to execute operations. A system including the above operation, Receiving samples of input and output signals from a time-varying system, A multidimensional hypersurface corresponding to the sample is generated using a high-frequency processing loop including multiple filters, the samples of the input and output signals, prior system parameter estimates of the time-varying system, and prior system state estimates of the time-varying system. Using a low-frequency processing loop including state and parameter estimators, and the multidimensional hypersurface corresponding to the sample, the filtered system parameter estimates and filtered system state estimates of the time-varying system are generated. The filtered system parameter estimates and filtered system state estimates of the time-varying system are transmitted to the control system. A system that includes this.

13. The aforementioned one or more hardware processors For subsequent iterations of the high-frequency processing loop, the high-frequency processing loop is updated using the filtered system parameter estimates and filtered system state estimates of the time-varying system. Further configured to perform actions including, The filtered system parameter estimates and filtered system state estimates of the time-varying system are the preceding system parameter estimates and preceding system state estimates of the time-varying system for the subsequent iterative processing. The system according to claim 12, wherein the subsequent iterations of the high-frequency processing loop generate updated multidimensional hypersurfaces corresponding to new samples of the input and output signals.

14. The system according to claim 12, wherein each of the plurality of filters in the high-frequency processing loop adapts a subset of the estimated system parameters from the prior estimated system parameters, each subset of the estimated system parameters differs for each filter, and when each filter determines a time-series object for the multidimensional hypersurface, other prior estimated system parameters from the prior estimated system parameters that are not included in the subset of the estimated system parameters for each filter are kept constant for each filter, and the size of each subset of the estimated system parameters must be less than or equal to the size of the predicted system output generated by each filter.

15. The aforementioned one or more hardware processors The multidimensional hypersurface includes a time-series object aggregated from the plurality of filters, where each time-series object includes one or more sequences of prediction errors, filtered estimated system parameters, filtered estimated system states, the gradient of the output prediction error cost function, the formulation of the signal-to-noise ratio of the gradient, and the system output. The system according to claim 12, further configured to perform operations including the operation.

16. The aforementioned one or more hardware processors The prediction system output is generated using at least one neural network of filters within the plurality of filters, the input signal in the sample, the estimated prior system parameters, and at least one of the estimated prior system state of the time-varying system, the predicted prior system output, or the predicted prior system output. The error is determined based on the difference between the output of the prediction system and the output signal in the sample. Based on the aforementioned error, updated filtered estimated system parameters are generated, Using the at least one neural network, the updated filtered estimated system parameters, the input signals in the samples, and the preceding filtered estimated system state or preceding system output, a subsequent filtered estimated system state or subsequent predicted system output is generated. The system according to claim 12, further configured to perform operations including the operation.

17. The aforementioned one or more hardware processors Using the at least one neural network of the filter, the input signal in the sample, the subsequent filtered estimated system state or the subsequent predicted system output, and the updated filtered system parameters, a second predicted system output is generated. The second error is determined based on the difference between the output of the second prediction system and the output signal in the sample. The filter generates a second updated filtered estimated system parameter based on the error. The system according to claim 16, further configured to perform operations including the operation.

18. The aforementioned one or more hardware processors In the state and parameter estimator of the parameter estimator, the multidimensional hypersurface corresponding to the sample is received, In the parameter estimator, the filtered system parameter estimates of the time-varying system are generated using the hypersurface, the previous filtered system parameter estimates, and at least one of the previous filtered system state estimates or the previous system output. In the state filter of the state and parameter estimator, the filtered system state estimate or predicted system output of the time-varying system is generated using the input signal in the sample, the filtered system parameter estimate, or the preceding filtered system state estimate, and at least one of the preceding system output. The system according to claim 12, further configured to perform operations including the operation.

19. The aforementioned one or more hardware processors To sample a subset of time-series objects within the aforementioned multidimensional hyperplane. Further configured to perform actions including, The system according to claim 18, wherein generating the filtered system parameter estimates is based on the subset of time-series objects.

20. A non-temporary machine-readable medium storing machine-readable instructions that can be executed to cause a machine to perform an action, wherein the action is Receiving samples of input and output signals from a time-varying system, A multidimensional hypersurface corresponding to the sample is generated using a high-frequency processing loop including multiple filters, the samples of the input and output signals, prior system parameter estimates of the time-varying system, and prior system state estimates of the time-varying system. Using a low-frequency processing loop including state and parameter estimators, and the multidimensional hypersurface corresponding to the sample, the filtered system parameter estimates and filtered system state estimates of the time-varying system are generated. The filtered system parameter estimates and filtered system state estimates of the time-varying system are transmitted to the control system. Non-temporary, machine-readable media, including [specific examples of such media].

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