Method for evaluating uncertain time effects when controlling a system

Abstract

A method for evaluating uncertain time effects in control systems. One aspect of this disclosure relates to a computer-implemented method for evaluating uncertain time effects in one or more state variables of a system (particularly a vehicle system) when controlling the system. The method aims to classify uncertain time effects as critical or non-critical to the control of the system in the presence of stochastic uncertainties in the control loop.

Description

Technical Field

[0001] This invention relates to techniques for evaluating uncertain time effects when one or more state variables of a system are used to control the system. Related aspects include a computer program, a computer system, and a computer-readable medium or signal. Background Technology

[0002] Highly automated or autonomous systems are gaining increasing attention in industries such as robotics and automotive. Control systems, in particular, are becoming increasingly important in the operation of autonomous or highly automated systems. While many methods for controlling driving functions have been proposed, most are based on nominal models, which fail to adequately account for uncertain time effects (in other words, time uncertainty) combined with external disturbances (such as constantly changing environmental influences like slippery lanes and crosswinds), vehicle-specific variations (such as heavy loads or continuous tire wear), and time delays / fluctuations in evaluating sensor signals (such as cameras, lidar, or radar), as well as the associated delays / fluctuations throughout the action chain (such as lateral control delays).

[0003] For example, in distributed systems, time delays and, additionally, sampling time fluctuations may occur due to varying physical conditions affecting signal transmission or due to different channel loads in, for example, vehicle-to-vehicle (V2X) communication. These time delays and sampling time fluctuations are nondeterministic (i.e., stochastic) and therefore uncertain. For example, situations with unusually high channel loads compared to others might include networked adaptive cruise control, swarm start, or cooperative lane changing. Nondeterministic delays and / or jitter may arise, for example, in feedback loops, in bus communication, in distributed electrical / electronic (E / E) architectures involved in vehicle control functions, and / or in signal processing and transmission within sensor systems. In control systems, such as longitudinal or lateral guidance of the vehicle, these nondeterministic time delays can adversely affect the success of control. In addition, other uncertain time effects (combined with internal or external disturbances), such as external wind force that varies over time during vehicle operation, or other (deterministic) time effects, such as the skew stiffness of the vehicle's front and / or rear axles, may adversely affect the success of control if these time effects are not adequately assessed.

[0004] Furthermore, the time effects discussed above are unknown or difficult to quantify during the controller development and parameterization phases. Therefore, the controller must undergo intensive testing and tuning for these uncertainties during the application phase. This is time-consuming and expensive. Especially with increasingly shorter development cycles, and even more so due to the rising proportion of software, longer product delivery times can lead to market-specific disadvantages. Another challenge is that obtaining reliable information about the discrete nature of the target variable requires significant computational or implementation work. This might include, for example, sampling-based simulation methods (such as Monte Carlo simulations or non-intrusive Uncertainty Quantification (UQ) methods), which require numerous function calls.

[0005] For these reasons, new and improved techniques are needed to assess uncertain time effects in control systems. Summary of the Invention

[0006] A first general aspect of this disclosure relates to a computer-implemented method for evaluating uncertain time effects when one or more state variables of a system are used to control the system. The method includes: receiving a continuous-time dynamic model describing the controlled system, wherein the continuous-time dynamic model is represented by a specified function. The specified function of the first aspect includes time-varying independent variables: The method comprises: a state vector including one or more state variables; an input vector including one or more input variables and related to the state vector by a feedback matrix of a state controller describing the system; and an uncertainty vector having at least one component including a time-varying uncertainty parameter representing a stochastic process associated with uncertain time effects. The method further comprises: forming a discrete-time representation of the continuous-time dynamics model by time discretizing the continuous-time dynamics model; and determining a surrogate model of the discrete-time representation of the state-space model. The method further comprises: solving the surrogate model to determine the mean and deviation, particularly the variance, of the state vector at multiple discrete time points; and, using the determined mean and deviation, particularly the variance, of the state vector, searching from the multiple discrete time points for one or more discrete time points that do not meet a specified coarse requirement criterion for the state vector. Finally, the first aspect of this disclosure includes: if one or more discrete time points that do not meet the coarse requirements of the state vector have been identified, then classifying uncertain time effects as critical to the control of the system is important; and otherwise, classifying uncertain time effects as not critical to the control of the system is not important.

[0007] The second general aspect of this disclosure relates to a computer program designed to: perform a computer implementation of the method described in the first general aspect for evaluating uncertain time effects when controlling a system with one or more state variables in relation to the system.

[0008] The third general aspect of this disclosure relates to a computer system designed to: perform a computer-implemented method as described in the first aspect for evaluating uncertain time effects when controlling the system in relation to one or more state variables; and / or perform a computer program as described in the second aspect.

[0009] The fourth general aspect of this disclosure relates to a computer-readable medium or signal that stores and / or contains a computer program as described in the second general aspect.

[0010] The technologies of the first to fifth overall aspects can have one or more of the following advantages.

[0011] First, the technology disclosed herein provides a method for evaluating uncertain time effects in a controlled system. Specifically, the proposed method enables a small number of simulation steps (in some cases even just one simulation) to characterize / quantify the impact of time-related uncertainties on the control system, particularly to determine which uncertain time effects are likely critical to the control of the system and which are likely not. The small number of simulation steps used here significantly improves efficiency (in terms of computing time and hardware resources) compared to the inefficient uncertainty quantification (UQ) methods of the prior art, which require numerous simulations. This saves both runtime and the computing resources required for the simulation.

[0012] Secondly, this technology can achieve a better mapping of reality by using the discrete-time representation of the dynamic model, taking into account time-varying uncertainty parameters based on stochastic processes, especially in distributed control systems, and thereby improve the evaluation of uncertain time effects when controlling the system.

[0013] Another advantage is the reduced time-to-market for highly automated control functions, as the associated time uncertainties can be considered during the development phase. This reduces the workload required during the verification / validation phase. In particular, this technology allows for compelling conclusions during development regarding whether the system's functionality (e.g., lateral guidance of a vehicle) still meets specified requirements (e.g., customer-specific requirements) and / or complies with legal regulations (e.g., automotive industry standards / safety standards), despite the impact of time uncertainties in the controlled system.

[0014] In this disclosure, some terms are used as follows: A "state controller" can contain an algorithm, i.e., a computational rule, that feeds back all or part of the state variables (i.e., the internal state of the controlled system) to the input variables. The state controller can contain parameters that can weight the state variables. In the examples, the state controller can execute on a computer system. In the examples, the state controller can execute in a vehicle's control device, in the cloud, or at the edge. The state controller can, for example, contain a hardware module with inputs and outputs, or be part of such a hardware module. In these examples, the state controller can be a controller, part of a controller, or the controller itself.

[0015] The "controlled system" in this disclosure can be designed to be arranged in a vehicle and / or for controlling vehicle functions (especially driving functions). For example, vehicle functions can be autonomous driving and / or driver assistance functions. In some examples, the state controller can be designed to execute on a computer system of the vehicle (e.g., an autonomous, highly automated, or driver-assisted vehicle). For example, the computer system can be implemented locally in the vehicle or (at least partially) in a backend that is communicatively connected to the vehicle. For example, the computer system can include a control device on which the state controller can execute. In some examples, the vehicle can include a computer system with a communication interface capable of communicating with the backend. For example, the state controller can execute in the backend. In these examples, time uncertainties may arise due to data transmission between the controlled system and the computer system executing the state controller. In one example, the "controlled system" can be a system for lateral and / or longitudinal guidance of the vehicle. In these examples, the "state vector" can be based on speed or distance information. In these examples, the state vector can include relative speeds and / or distances between a first vehicle, a second vehicle, a human, and / or a stationary object. In one example, the "state vector" may contain state variables based on at least one of the following: steering angle, heading angle, yaw rate, slip angle, and / or lateral error. In another example, the state vector may contain information from the network, such as the motion and / or orientation information of other vehicles. This information may be provided via vehicle-to-vehicle communication (V2V communication) or via a backend (V2X communication). In yet another example, the "state vector" may contain state variables based on one or more sensor signals. These sensor signals may be generated by appropriate sensors, such as lidar sensors, radar sensors, cameras, ultrasonic sensors, GPS, accelerometers, temperature sensors, etc. In one example, the "input vector" may contain: steering angle; steering speed; or target specifications for acceleration and / or braking. In yet another example, the "controlled system" may be designed to be arranged in a drive control system or drive unit, and / or to control motor-related functions (especially for motor control). In yet another example, the "controlled system" may be configured to be arranged in a motor drive control system. For example, the "state vector" may contain components based on at least one of the motor's control signals, operating mode, or power settings.

[0016] Within the scope of this disclosure, it is also conceivable that a "controlled system" may be arranged within a robot and / or designed to control robot functions (especially driving functions and / or movement functions of the robot, such as a robotic arm). For example, the "controlled system" may be a system for lateral and / or longitudinal guidance of the robot. In some examples, the state controller may execute on the robot's computer system. For example, the computer system may be implemented locally on the robot or (at least partially) in a backend that is communicatively connected to the robot. In some examples, the state controller may execute in the backend. In examples, the "state vector" may be based on velocity information or distance information. In examples, the "state vector" may contain relative velocities and / or distances between a first robot, a human, another mobile device, and / or a stationary object. In one example, the state vector may contain state variables based at least on one of a steering angle, heading angle, yaw rate, slip angle, and / or lateral error. In examples, the state vector may contain information from the network, such as motion and / or orientation information of other robots, mobile devices, and / or humans. In examples, this information may be provided by means of direct communication or by means of a backend. In the example, the "state vector" can contain state variables based on one or more sensor signals. These sensor signals can be generated by appropriate sensors, such as lidar sensors, radar sensors, cameras, ultrasonic sensors, GPS, accelerometers, temperature sensors, etc. In one example, the "input vector" can contain: steering angle; steering speed; or target specifications for acceleration and / or braking.

[0017] Furthermore, the "controlled system" can be used for the control of distributed systems, such as the longitudinal guidance of multiple vehicles ("platooning" is one example). Besides longitudinal vehicle guidance, the "controlled system" can provide control of distributed systems, such as automated guided vehicles (AGVs). This control can be designed, for example, to drive and / or coordinate driverless transport vehicles within a defined area, particularly in logistics centers and / or production facilities, using a local network (e.g., local edge, 5G network, 6G network, etc.). As another example, a distributed system can include robotic arms within a local network, such as in a manufacturing system. Here, at least the regulation and / or control algorithms of these robotic arms can be at least partially outsourced (i.e., at least partially decentralized).

[0018] For the purposes of this disclosure, a "time-varying uncertainty parameter" can be associated with an "uncertain time effect" that is nondeterministic (e.g., stochastic). This uncertain time effect (sometimes also called "time uncertainty") may occur in the feedback of the control loop of a state controller and thus affect the performance of that state controller. In other words, a "time-varying uncertainty parameter" can be understood as any time-varying uncertainty parameter that fluctuates over continuous time and should therefore be considered a time-dependent scalar in the "controlled system". A "time-varying uncertainty parameter" can represent a stochastic process associated with uncertain time effects (e.g., in the feedback of the control loop of a state controller). Here, in some cases, a "time-varying uncertainty parameter" can be described (in other words, modeled) by a specified (in other words: a known) stochastic process.

[0019] An example of the “uncertain time effect” is time delay (also known as dead time), which represents the delay in which a change at the input (e.g., given by the input vector) becomes noticeable in the response of the controlled system at the output of the control loop (e.g., thus, the state vector may change significantly compared to the case where there is no time delay). Such time delays can occur, for example, during data transmission in distributed systems where the control algorithm and the controlled system are executed physically separately (e.g., by means of cloud computing or edge computing). This time delay can also be related to sensor signal acquisition.

[0020] Another example of the “uncertain time effect” is jitter, which is the fluctuation in the accuracy of the transmission clock in the computing units of a distributed system (such as the state controller and actuators of a vehicle, the vehicle’s sensors and the state controller (or any combination thereof)). Such jitter can, for example, cause time-varying discrepancies in the sampling time of one or more computing units in a distributed system (e.g., a distributed control system), or it can be such time-varying discrepancies in the sampling time within those computing units. In the case of specific vehicle longitudinal guidance (e.g., platooning), jitter could, for example, be the time-varying discrepancy in the sampling time of the computing units of the distributed control system that manage the dynamics of one or more vehicles.

[0021] Another example of an "uncertain time effect" is a time disturbance in a "controlled system" that affects the system (e.g., a vehicle) and thus contributes to the feedback of the control loop of the system's state controller. Time-varying physical effects outside the system are an example of external disturbances. Time-varying physical effects inside the system are an example of internal disturbances. Time-varying external wind forces during vehicle operation and the skew stiffness of the vehicle's front and / or rear axles are non-exhaustive examples of such time-uncertain physical effects.

[0022] A "dynamic model" used to describe a "controlled system" can be a model that quantitatively describes one or more functions of the system (e.g., one or more vehicle functions of a vehicle or one or more robot functions of a robot). This quantitative description may, for example, include the time and / or space dependencies of one or more "state variables" and / or one or more "input variables," representing the behavior of that function or these functions of the system. Furthermore, the "dynamic model" may include parameters (e.g., uncertainty parameters as defined above) on which the state variables and / or input variables may depend. Alternatively or additionally, the "dynamic model" may include parameters that may affect the dynamic changes of these state variables and / or input variables. The "dynamic model" can be a comprehensive and computationally complex simulation model (in terms of equations, such as a system of coupled equations, e.g., differential equations, describing the behavior of the device's functions). In this respect, within the scope of this disclosure, models can be derived by simplifying the dynamic model (in other words, models that will approximate the dynamic model) to be less computationally intensive than the (original) dynamic model. Hereinafter, in some cases, these simplified models are referred to as "surrogate models."

[0023] "Vehicle" can be any equipment used to transport passengers and / or goods. A vehicle can be a motor vehicle (e.g., a passenger vehicle (PKW) or a freight vehicle (LKW)), but can also be a rail vehicle. A vehicle can also be a two-wheeled or three-wheeled motorcycle. However, floating and flying devices can also be vehicles. A vehicle can operate at least partially autonomously or with assistance. Attached Figure Description

[0024] Figure 1a It is a flowchart that presents an example of an uncertain time effect used to evaluate one or more state variables of a system in relation to the system, as described in the first aspect. Figures 1b to 1d This is a flowchart illustrating other possible method steps according to the first aspect.

[0025] Figure 2 The schematic diagram illustrates an exemplary control loop according to one or more embodiments of this disclosure.

[0026] Figure 3a The exemplary illustration depicts the response produced by a specified state controller when using a proxy model according to the technology of this disclosure, the response being in the form of the mean and confidence interval of the lateral error when a vehicle returns to its lane while in motion. Figure 3b The distribution of the lateral error is shown, as well as its relationship with... Figure 3aThe two risk measures (Value-at-Risk and Conditional Value-at-Risk) are shown in the figure, corresponding to the maximum value of the lateral error within the time interval. Figure 3c An example of the statistical distribution of the skew stiffness of the front axle of a vehicle is shown. Detailed Implementation

[0027] First, based on Figures 1a to 1d and Figure 2 This describes a technique for evaluating uncertain time effects when one or more state variables of a system are used to control that system. Then, based on... Figures 3a to 3c This describes exemplary results of lateral error when a moving vehicle returns to its lane using this technique.

[0028] like Figures 1a to 1d As shown, the first general aspect relates to a computer-implemented method for evaluating uncertain time effects when one or more state variables of a system are used to control the system. Figures 1a to 1d In the text, the method steps of the corresponding independent claims are shown in boxes drawn with solid lines, while the method steps of some dependent claims are shown in boxes presented with dashed lines.

[0029] The first step of this method includes: receiving 100 continuous-time dynamic models (in the sense defined above) for describing the controlled system, wherein the continuous-time dynamic model is defined by a specified function. To represent. The specified function of the first aspect contains the following time-varying arguments: state vector The state vector includes one or more state variables; the input vector The input vector includes one or more input variables and is related to the state vector. By describing the feedback matrix of the state controller of the system This is related. In some cases, the input vector... It can include two or more, three or more, or four or more input variables. In one example, the control law can be implemented using a feedback matrix. To describe the state vector The effect is determined so that the result of this effect can be input into the controlled system as an input vector. In one example, the control law can be achieved using the equation To express this, and from it form the input vector. ( and Here, the components of the input vector or state vector are represented. In one example, it is possible to consider unmeasurable state variables ( These unmeasurable state variables accompany all The disappearing feedback matrix components Here, It can represent the row index of the feedback matrix, and This can represent the column index of the feedback matrix. This is a restricted definition set. Examples.

[0030] exist Figure 2 The controlled system 12 is illustrated exemplarily (e.g., a system for lateral and / or longitudinal guidance of a vehicle, or other systems as described above). In some cases, the state controller 14 can transmit the input vector... The output is given to one or more executors. In the example, the input vector... It can be output to one or more actuators via network 15. Figure 2 An example of such actuator 11 is shown in the figure. Furthermore, the state controller 14 can receive state vectors from one or more sensors and / or one or more state estimators (e.g., via network 15) of the controlled system 12. .exist Figure 2 An example of this sensor 13 is shown. In the example, network 15 can be a wired and / or wireless network. In the example, the network can include a LAN (Local Area Network), WLAN (Wireless Local Area Network), CAN (Controller Area Network), IoT (Internet of Things) network, 5G network, or Multi-Access-Edge-Computing network. In the example, state controller 14 can operate in the cloud or at the edge (other examples are as described above).

[0031] Furthermore, the specified function in the first aspect contains an uncertainty vector. As a time-varying independent variable, the uncertainty vector has at least one component, which includes a time-varying uncertainty parameter representing a stochastic process associated with uncertain time effects. In some cases, the uncertainty vector... It can include one or more, two or more, three or more, or four or more components. Time uncertainty can (at least in part) be mediated by random independent variables. To express. Random independent variable It can be a random vector, whose components are random numbers generated according to a specified statistical distribution. In some cases, this statistical distribution can be a meanless and normalized uniform distribution. For example, this distribution can be written in the following form: .

[0032] In the technology disclosed herein, uncertainty vector It can include delay parameters. This delay parameter represents the time delay in the controlled system (in the sense defined above) and is based on a specified statistical distribution. This specified statistical distribution can be a uniform distribution, a normal distribution, a Poisson distribution, a Wigner-Dyson distribution, or another distribution. In one example, the input vector... It can depend on this delay parameter This delay parameter can describe the input vector. The time delay is uncertain. In one example, the input vector It can be calculated at a location different from the controlled system, which may introduce time delays due to data transmission. In the example, this delay parameter... It can be evenly distributed. This can be applied in the example: ,in, and This indicates the minimum and maximum values ​​of the delay parameter. In special cases, this delay parameter can be represented by an equal probability transformation. For example, the following can be applied: ,in, It was defined in the previous paragraph.

[0033] Alternatively or additionally, the uncertainty vector of the first aspect It may include at least one perturbation parameter The disturbance parameter represents the time disturbance of the controlled system and is based on a specified statistical distribution (in other words, given by a specified statistical distribution). This specified statistical distribution can be a uniform distribution, a normal distribution, a Poisson distribution, a Wigner-Dyson distribution, or other distributions. The disturbance parameter can describe external or internal disturbances of the system, as defined above. Within the scope of this disclosure, it is also conceivable that the uncertainty vector can contain one or more, two or more, three or more, five or more disturbance parameters, where each disturbance parameter is based on a (corresponding) specified statistical distribution.

[0034] The continuous-time dynamics model of this technology can include a state matrix. and input matrix The state matrix and / or the input matrix depend on the at least one perturbation parameter. In one example, if the uncertainty vector Includes delay parameters and at least one disturbance parameter (As mentioned above), the continuous-time state-space model can be achieved through the equations ,in , To describe it. Here, It is assigned to the initial time point The initial state vector. As mentioned above, the input vector It can be derived from the feedback matrix and state vector This is determined (in other words, determined through the control law). For example, it can be applied to the following situations: In one example, the feedback matrix It can be time-varying, time-invariant, or constant. In one example, the feedback matrix... It can be deterministic. Therefore, continuous-time dynamical models can contain state vectors that depend on this statistical distribution (or these distributions). .

[0035] The next step of this method includes: forming a discrete-time representation of the continuous-time dynamics model by discretizing the continuous-time dynamics model in time.

[0036] The uncertainty vector is replaced by or added to the aforementioned delay and disturbance parameters. It can include sampling time. The sampling time is based on a specified distribution. This specified statistical distribution can be a uniform distribution, a normal distribution, a Poisson distribution, a Wigner-Dyson distribution, or another distribution. In this case, the time discretization of the continuous-time dynamics model in this disclosure can be performed using this sampling time (e.g., specifying a function). (Sampling is performed using its continuous independent variable). In one example, this sampling can be performed at multiple time steps. Execution. One of the multiple time steps can be determined by the sampling time. This multiple is formed by consecutive index parameters. To express this. For multiple time steps Applicable to: , …Time in continuous-time dynamics models Values ​​between the first and second sampling time points can be taken. In the example, the second sampling time point can be formed by adding the first sampling time point to the sampling time. In the example, for time in a continuous-time dynamics model... Applicable to: In the example, the sampling time... It can be evenly distributed. This can be applied in the example: ,in, and Indicates the minimum and maximum sampling times.

[0037] Forming a discrete-time representation of a continuous-time dynamics model can include transforming the general solution of the continuous-time state-space model to a time-discrete domain. In this example, in the discrete time domain, it can be assumed that at the initial time point... With time point There exists a piecewise constant vector of input variables. In one example, the initial time point... It can be set as the sampling time. any first (integer) multiple At this point in time... It can be set as the sampling time. Second (integer) multiple Here, the second multiple can be the next multiple of the first multiple or another multiple. In these examples, the following can be applied: , ,in, ,and yes One of them (in other words, the initial time point is unrestricted). In one example, the discrete-time representation of this continuous-time dynamics model (after time discretization) can be as follows: , , in, and These are the state matrix and input matrix in the discrete-time representation, and Is to make and Related matrices.

[0038] The technology disclosed herein also includes: a surrogate model for determining the discrete-time representation of a 200-state-space model. It should be noted that the advantage of the aforementioned discrete-time representation of this continuous-time dynamics model is that it addresses uncertain sampling times. The dependency is transferred to the state matrix. and input matrix This allows for the determination of the proxy model (200).

[0039] In this technique, the method step "determine 200 surrogate models" may include: specifying one or more polynomial basis functions, which are uncertainty vectors. The function. In the uncertainty vector. Includes the sampling time This delay parameter and the at least one disturbance parameter In the example, the uncertainty vector can be written in the following form: As mentioned above, the uncertainty vector may contain only one or two of the components: sampling time, delay parameter, and perturbation parameter.

[0040] Furthermore, the surrogate model for determining the discrete-time representation of the 200 state-space model may include: performing 210 to convert the state vector The series expansion is given by the basis functions of the one or more polynomials. The series expansion is a set of polynomials, wherein one or more corresponding expansion coefficients of the series expansion are independent of the uncertainty vector. In one example, the one or more polynomial basis functions can be at least one of Hermitian polynomials, Legendre polynomials, Jacobian polynomials, and / or generalized Laguerre polynomials. In a non-restrictive example, the series expansion of the state vector can be expressed as follows: .

[0041] Here, matrix The definition is as above. Here, These are polynomial basis functions (in this example, there are a total of...). (one), and Is the index as The corresponding expansion coefficients, this index numbers the time steps (e.g. (Superscript) This represents transpose. In one example, a variable can be specified. For example, larger ones A more accurate approximation can be obtained, but it requires a longer computation time, while a smaller one... It can yield a less accurate approximation, but it can achieve a shorter computation time.

[0042] In some cases, the determination of the surrogate model can be carried out by using polynomial chaotic expansion.

[0043] The method step "determine 200 surrogate models" may further include: projecting 215 of the discrete-time representation of the continuous-time dynamics model onto the one or more polynomial basis functions. In this disclosure, projecting 215 of the discrete-time representation of the continuous-time dynamics model can be performed by integrating the discrete-time representation of the continuous-time dynamics model by multiplying it by a corresponding function comprising the polynomial basis functions, wherein the integration is performed in the space of the uncertainty vector, and thereby forming multiple projective integrals. In some cases, after projecting the discrete-time representation of the continuous-time dynamics model, the surrogate model may include multiple matrices, each of which includes one or more projective integrals. In one example, the discrete-time representation formed after projecting the continuous-time dynamics model may include one or more products of one or more corresponding matrices among the multiple matrices with the corresponding expansion coefficients of the series expansion. For example, the discrete-time representation formed after projecting the continuous-time dynamics model may be equal to the product when there is only one product, or equal to the sum of the products when there are multiple one products.

[0044] Within the scope of this disclosure, it is also conceivable that the method step "determine the 200 agent model" further includes: based on the previous time step (e.g., One or more expansion coefficients of ) ), calculate the next time step (e.g. One or more expansion coefficients of ) In this case, one or more expansion coefficients for the next time step ( ) can be combined with one or more expansion coefficients from the previous time step ( The correlation is achieved through multiple matrices (as described above).

[0045] In one example, specifically, to determine the proxy model, the following can be applied: , ,in, , ; ; .

[0046] here, It is an uncertainty vector The range of the joint probability density function (PDF). Here, the differential can be expressed by the expression For more details on the proxy model, see, for example, the patent application “Method for Computer Implementation of Proxy Model for Determining State-Space Model”, DPMA application number: 102023206821.4.

[0047] The next step of this method involves solving the surrogate model 250 to determine the time points at multiple discrete time points. state vector mean and state vector deviation Especially variance. Here, the state vector The mean and bias (or variance) obtained within the framework of the surrogate model, as in this technique, without using sampling, can correspond to a large number of samples (e.g., more than 10) of the state vector that can be obtained by means of the uncertainty vector. 3 The mean and bias (or variance) of a sample (e.g., approximations thereof) are determined using UQ methods (such as Monte Carlo simulation or Latin-Hypercube-Sampling). In other words, with a surrogate model, it may be possible to determine the mean and bias (or variance) at multiple discrete time points without sampling. state vector The mean and deviation (or variance) of the values ​​compared to a large number of simulations using the UQ method (e.g., more than 10). 3 Compared to previous simulations, this can significantly improve efficiency.

[0048] In this technique, for multiple discrete time points state vector mean and state vector Deviation, especially variance The determination can be made by using one or more expansion coefficients of the surrogate model for these time points. This is performed under the following circumstances. In a non-restricted example, the state vectors at these multiple discrete time points... mean and variance It can be determined by the following expression: , , in, , and It is the corresponding matrix.

[0049] The next methodological step includes: using state vectors The determined mean and state vector Given the determined deviation, especially the variance, search from these discrete time points for one or more discrete time points that do not meet the specified coarse requirement criteria of the state vector. .

[0050] Then, this technique includes: if one or more discrete time points that do not meet the coarse requirement criteria of the state vector have been identified. If the uncertain time point is identified, then the uncertain time effect is classified as 400 as critical to the control of the system; otherwise (i.e., if such discrete time points are not identified), the uncertain time effect is classified as 600 as not critical to the control of the system. In the following text, these identified time points are also referred to as "critical time points".

[0051] Furthermore, the techniques disclosed herein may include: using state vectors at the plurality of discrete time points. The determined mean and state vector The confidence interval for the state vector is calculated based on the determined deviation, particularly the variance. In this case, the specified coarse requirement criterion may include: the state vector within the confidence interval is less than a specified maximum state value and / or greater than a specified minimum state value. In other words: if for discrete time points (from the plurality of discrete time points) If, at a given discrete time point, there exists at least one value of the state vector within the confidence interval, and this value reaches or exceeds the specified maximum state value and / or reaches or falls below the specified minimum state value, then the discrete time point can be considered... The time points classified as not meeting the specified coarse requirement criteria are defined as follows: (i.e., the confidence interval contains the specified maximum and / or minimum state values ​​at the discrete time points). Within the scope of this invention, it is conceivable that if the state vector includes more than one state variable (i.e., more than one component), a corresponding specified coarse requirement criterion can be formulated for each state variable (i.e., for each component of the state vector). (For simplicity, the state vector will sometimes be discussed only in the following text.)

[0052] exist Figure 3a In the example (see below for details), the time points within the time interval between time points 25 and 26 It is a "critical time point" (i.e., for which the specified coarse requirement criteria are not met) because, for that time interval, the state vector (considering its confidence interval) exceeds the specified maximum state value of 23. In one example, this confidence interval could be defined by the time interval... Lower limit within ;21 and the upper limit ;22 is used to define it. In a specific example, the lower limit and the upper limit can be given by the following formula: , .

[0053] Within the scope of this disclosure, it is conceivable that if one or more discrete time points that do not meet the coarse requirements of the state vector have been identified, the method may further include: reducing the uncertainty vector in the uncertain time effects. The degree of uncertainty associated with at least one component (i.e., the corresponding time-varying uncertainty parameter) is used to change the 410 uncertainty vector. In the example, the degree of uncertainty in the uncertain time effect can be reduced by accordingly modifying the specified statistical distribution describing the uncertainty parameters. Thus, for example, the width of the distribution can be reduced or its specified shape can be changed. Furthermore, the next methodological step may include resolving the 420 surrogate model using the modified uncertainty vector to determine the uncertainty at those discrete time points. state vector The changed mean and state vector The changed bias, especially the changed variance This method may also include: based on state vectors The determined modified mean and state vector The determined modified deviations, especially the modified variance, are examined at 430 at multiple discrete time points. Whether the specified coarse requirement criterion for the state vector is met. Here, changes to the uncertainty vector can be made until the specified coarse requirement criterion is met for the multiple discrete time points. This allows us to determine which ranges of the uncertainty parameters meet the specified coarse requirement criterion (and which do not). In this way, if the uncertainty vector... If there is more than one uncertainty parameter, then the method can be executed for more than one uncertainty parameter (e.g., for all uncertainty parameters).

[0054] Furthermore, if one or more discrete time points that do not meet the coarse requirements of the state vector have been identified, the technique of this disclosure may further include: calculating one or more statistical distributions of the state vector at the corresponding identified one or more discrete time points, using multiple samples of the uncertainty vector and the surrogate model. For example, natural numbers It can represent the number of samples. It can be equal to or greater than 10.2 , equal to or greater than 10 3 Or equal to or greater than 10 4 In the example, samples of the uncertainty vector can be grouped into a matrix. For example, It can contain Each component (i.e.) The first sample of the uncertainty vector (with several uncertainty parameters). Here, it can be... , , Or any other natural number. In the example, each sample of the uncertainty vector can be represented in the same way. In the example, the matrix of the sampled uncertainty vector can be written in the following form: .

[0055] In some cases, the uncertainty vector can be computed using one or more specified statistical distributions of one or more uncertainty parameters that appear as components in the uncertainty vector (see also the discussion above). The sampling (e.g., each sample). For the same purpose, in some cases, it can also be used for the random independent variable. Generate random numbers, as explained above.

[0056] In this technique, calculating one or more statistical distributions of the state vector at the corresponding identified one or more discrete time points may further include: calculating one or more polynomial basis functions for multiple samples of the uncertainty vector (in other words, for the sampled uncertainty vector) to determine the one or more polynomial basis functions. Multiple samples. The method step "Calculate 440" may also include: using one or more polynomial basis functions. The determined multiple samples and the corresponding one or more expansion coefficients of the series expansion. In this case, more than 450 empirical (in other words: sampled) state vectors are calculated. For example, the empirical state vector This can be computed as a sum of products, where each product can represent the product of the sampled polynomial basis functions and their corresponding expansion coefficients. In this way, in some cases, any empirical state vector can be determined. In one example, and according to the definition above, the empirical state vector can be computed as follows: : .

[0057] The advantage of the method disclosed here is that the process can replace the (original) dynamic model. This simulation, using a surrogate model in a single run, enables targeted targeting at key time points. random distribution of state vectors In particular, it is possible to use the expansion factor. Calculate the empirical state vector under the following conditions The determination of these expansion coefficients requires only one simulation of the alternative model (i.e., sampling is not used for these expansion coefficients, as exemplarily presented in the above formula).

[0058] In one scenario, a single statistical distribution of the state vector can be computed for each identified discrete time point. For this purpose, for example, the identified discrete time point can be selected, along with the upper limit of the confidence interval for that discrete time point. Take the maximum value or the lower limit of the confidence interval. Take the minimum value (within the considered time interval). This is in Figure 3a As exemplified in the figure, the identified discrete time point 27 is selected, and for this discrete time point, the upper limit of the confidence interval is... Take the maximum value (in this example, the lateral error) Represented as time (The function). For this discrete time point 27, at Figure 3b The calculated distribution is illustrated in the example below. (More precisely: probability distribution function, PDF) (more details below). In another example, the statistical distribution of this state vector can be calculated in relation to other (e.g., all) identified discrete time points.

[0059] If one or more discrete time points that do not meet the coarse requirement criterion of the state vector have been identified, the method may further include: determining one or more characteristics associated with the state vector at the identified one or more discrete time points, using the corresponding one or more statistical distributions of the state vector. The one or more characteristics may take different values ​​for different identified discrete time points (i.e., time points that do not meet the specified coarse requirement criterion according to the above discussion).

[0060] In this disclosure, the one or more characteristics may include a first characteristic that describes the probability of failure when the specified coarse requirement criterion of the state vector is not met. For example, the first characteristic may be a value-at-risk (VAT). The VAT may indicate the probability of exceeding or falling below a selected value (i.e., indicating the probability of failure). The VAT may be expressed, for example, as follows: , in, At the identified discrete time points state vector The inverse empirical distribution function (in other words: the quantile function) of (for example, a component of the state vector), and This represents the probability of error. Known methods in the existing technology can be used to determine this based on one or more corresponding statistical distributions of the state vector. This is used to calculate the inverse empirical distribution function. Returning to the example above, if the specified rough requirement criteria include: the state vector within the confidence interval is less than the specified maximum state value and / or greater than the specified minimum state value, then: in this case, one of the specified maximum or minimum state values ​​can be used as the value at risk. This is Figure 3b The example is further illustrated in this figure, from Figure 3a The specified maximum state value 23 has been selected as the value at risk. (and in Figure 3b The same reference numeral 23 is also given to it. The value of the describable state vector of the distribution (PDF) shown is higher than the value at risk. The shaded area 30 of the probability can correspond to the probability of error. Correspondingly, the unshaded area 31 of the displayed distribution (PDF) can describe the state vector taking values ​​below the value at risk. The probability of (i.e., no error occurring) .

[0061] Furthermore, the one or more characteristics may include a second characteristic that characterizes the extent to which the specified coarse requirement criterion has not been met. In some cases, the second characteristic may be related to the first characteristic. For example, the second characteristic may be Conditional Value-at-Risk (VAT). VAT can be used to calculate statistical distributions. The expected value of the portion of the risk value that exceeds or falls short of the risk value (in other words, a violation exists). Conditional risk value can be expressed, for example, as follows: , in, It is Value at Risk, as mentioned above. Figure 3b In the example, the conditional value of risk is represented by the vertical dashed line 32.

[0062] In some cases of this technique, the one or more characteristics may include a third characteristic that characterizes which uncertainty parameter contributes more to violating the specified coarse requirement criterion, and which uncertainty parameter contributes less to violating the specified coarse requirement criterion, when the uncertainty vector contains at least two uncertainty parameters. In other words, the third characteristic can describe the sensitivity of the state vector to different uncertainty parameters (e.g., two or more uncertainty parameters) (i.e., the third characteristic can provide information about which uncertainty parameters will produce more significant changes in the state vector and which uncertainty parameters will produce less significant changes in the state vector). In one example, the third characteristic may include one or more Sobol indices. In this case, these Sobol indices can be used to perform the above-described sensitivity analysis of the state vector in relation to two or more uncertainty parameters. Figure 3c In the example, a normal distribution is assumed as the specified statistical distribution 40 for the system’s internal time perturbation (the skew stiffness of the front shaft, see below). In this case, the resulting Sobol exponents (represented by multiple vertical lines 41) are relatively dispersed under the normal distribution, which may be attributed to the low sensitivity of the state vector to such internal time perturbations (the lateral error in this example).

[0063] Furthermore, after performing the method step "determine 460 or more characteristics", the method may further include: if the one or more characteristics associated with the state vector meet specified fine-grained requirements criteria, classifying the state controller 480 as suitable for the system; otherwise, adjusting 500 uncertainty vectors. Alternatively, adjust the 550 state controller. In some cases, the specified fine-grained requirement criteria may include: one or more characteristics associated with the state vector being less than one or more corresponding specified thresholds. For example, if the first characteristic is Value at Risk. Then the probability of error can be defined. Threshold: If the probability of error If the value is less than this threshold, it may mean that the specified fine-grained requirement criterion is met. In other cases, such as when the one or more characteristics are defined in other ways, the specified fine-grained requirement criterion may include that the one or more characteristics associated with the state vector are greater than the corresponding one or more specified thresholds.

[0064] In addition, adjust the 500 uncertainty vector. This can include: reducing the uncertainty vector in the uncertain time effect. The degree of uncertainty associated with at least one component is used to adjust the 510 uncertainty vector. As described above, the degree of uncertainty in uncertain time effects can be reduced by accordingly modifying the specified statistical distribution describing the uncertainty parameters. Thus, for example, the width of the distribution can be reduced or its specified shape can be changed. Furthermore, the next method step may include resolving the surrogate model 520 using the adjusted uncertainty vector. The method may also include, using multiple samples of the adjusted uncertainty vector and the surrogate model, calculating one or more adjusted statistical distributions of the state vector 530 at the corresponding identified one or more discrete time points. The next method step may include: determining one or more adjusted characteristics of the state vector associated with the state vector at one or more identified discrete time points, using the corresponding adjusted one or more statistical distributions of the state vector. Here, the adjustment of the uncertainty vector may continue until the specified fine-grained criterion is no longer met for the adjusted one or more characteristics.

[0065] In the technology disclosed herein, a 520-state controller is adjusted (which adjusts a 500-uncertainty vector). Alternatives could include: solving a 560 stochastic optimization problem using the surrogate model to determine the adjusted feedback matrix of the state controller. This involves performing stochastic optimization using an objective function based on the surrogate model. In the example, to solve this stochastic optimization problem, the objective function can be determined at multiple discrete time points within the framework of the surrogate model. state vector mean and variance Here, the stochastic optimization may include minimizing the objective function. For more details on this optimization problem, see, for example, patent application "Method for Designing a Computer-Aided State Controller with Stochastic Optimization," DPMA application number 102023203084.5. In some cases, for the adjusted feedback matrix... The modified state controller described herein can meet the specified fine-grained requirements of the state vector.

[0066] The advantages of the technology disclosed herein over the prior art have been established based on... Figures 3a to 3c This has been discussed. These accompanying figures show the result of a vehicle returning to its lane while performing a driving maneuver. In this non-limiting example, the state vector... It consists of three components, namely yaw rate lateral error and sideslip angle , and input vector Including steering angle As the only component (index) (This refers to a discrete time point as defined above). Here, the time delay in sensor signal acquisition... and the skew stiffness of the vehicle's front axle It is considered an uncertainty parameter. Therefore, in this example, the uncertainty vector... It consists of two components, namely, Regarding the skew stiffness of the front axle Assuming the normal distribution is used as the specified statistical distribution (through... Figure 3c (as shown by curve 40 in the figure), while for time delay A uniform distribution has been selected as an example (not shown in the attached figures).

[0067] Figure 3a An exemplary diagram illustrates the response produced by a specified state controller (i.e., whose feedback matrix K is known) using a proxy model according to the technology of this disclosure: the mean of the lateral error. The lateral error is represented by the solid line 20, and it lies within the lower limit. and upper limit The confidence intervals between these two values ​​are represented by two dashed curves 21 and 22. (This example is for...) To calculate, where The “critical time points” are located within the time interval between time points 25 and 26 (i.e., for these critical time points, the specified coarse requirement criterion is not met): for these critical time points, the confidence interval 24 for the lateral error overlaps with the maximum permissible lateral error 23 (“the specified maximum state value”). For the lateral error... Take the maximum value at "critical time point 27". Figure 3b The distribution is shown in the figure. (Probability distribution function, PDF). Through... Figure 3b The vertical solid line 23 in the figure represents the value of risk. Corresponding to Figure 3a The maximum permissible lateral error is 23. The value of the lateral error is greater than the value at risk. The shaded area 30 corresponds to the error probability. The unshaded area 31 of the distribution (PDF) shown describes the probability. .exist Figure 3b In the diagram, the conditional value of risk is represented by the vertical dashed line 32. Figure 3c In the example, the skew stiffness of the front axle Under a normal distribution 40, the obtained Sobol exponents (represented by multiple vertical lines 41) are relatively dispersed, indicating that the lateral error is relatively... The sensitivity is low. In contrast, in this example, the obtained Sobol exponent is located at a time delay. Near the limit of a uniform distribution, this means that the lateral error is... It has high sensitivity (not shown in the attached figure).

[0068] A computer program is also disclosed, designed to perform a computer-implemented method, as described in the first general aspect, for evaluating the uncertain time effects of controlling the system with respect to one or more state variables. The computer program may exist, for example, in an interpretable form or in a compiled form. The computer program may (and may also be partially) loaded into the computer's RAM, for example, as a sequence of bits or bytes, for execution.

[0069] A computer system is also disclosed, designed to: execute a computer-implemented method as described in the first aspect for evaluating uncertain time effects when controlling a system with respect to one or more state variables; and / or execute a computer program as described in the second aspect. The computer system may have at least one processor, at least one memory (which may contain programs that, when executed, implement the methods of this disclosure), and at least one interface for input and output. The computer system may be a "standalone" system or a distributed system that communicates via a network (e.g., the Internet).

[0070] A computer-readable medium (e.g., a machine-readable storage medium, such as an optical storage medium or a read-only memory, such as a flash memory) or signal is also disclosed, which stores and / or contains a computer program as described in the second general aspect.

Claims

1. A computer-implemented method for evaluating uncertain time effects when one or more state variables of a system are used to control the system, wherein, The method includes the following steps: - Receive (100) a continuous-time dynamic model describing the controlled system, wherein the continuous-time dynamic model is defined by a specified function ( The specified function contains the following time-varying arguments: State vector ( The state vector includes one or more state variables; the input vector ( The input vector includes one or more input variables and is related to the state vector. The feedback matrix of the state controller of the system is used to describe the system. ) to correlate; and uncertainty vector ( The uncertainty vector has at least one component, the component including a time-varying uncertainty parameter, the time-varying uncertainty parameter representing a stochastic process related to uncertain time effects; - By discretizing the continuous-time dynamics model in time, a discrete-time representation of the continuous-time dynamics model is formed (150); - Determine the surrogate model of the discrete-time representation of the (200) state-space model; - Solve the surrogate model described in (250) to determine at multiple discrete time points ( The state vector of ) The mean of ) ) and the state vector ( The deviation, especially the variance ( ); - When using the state vector ( The determined mean and the state vector () Given the determined deviation, especially the variance, from the plurality of discrete time points, search (300) for one or more discrete time points that do not meet the specified coarse requirement criteria of the state vector. ); - If one or more discrete time points that do not meet the rough requirement criteria of the state vector have been identified ( If the uncertain time effect is classified (400) as critical to the control of the system, then the uncertain time effect is classified (600) as not critical to the control of the system.

2. The method according to claim 1, further comprising: - Using the state vector at the plurality of discrete time points ( The determined mean and the state vector () The confidence interval of the state vector is calculated using the determined deviation, especially the variance. The specified rough requirement criteria include: the state vector within the confidence interval is less than the specified maximum state value and / or greater than the specified minimum state value.

3. The method according to claim 1 or 2, wherein, If one or more discrete time points that do not meet the coarse requirement criteria of the state vector have been identified, the method further includes: - By reducing the uncertainty vector in the uncertain time effect ( The degree of uncertainty associated with at least one component of ) to change the uncertainty vector (410) ); - Resolve the surrogate model (420) using the modified uncertainty vector to determine the results at the plurality of discrete time points ( The state vector of ) The changed mean () ) and the state vector ( The changed bias, especially the changed variance () ); - Based on the state vector ( The determined modified mean and the state vector () The determined modified deviation, especially the modified variance, is examined (430) at the plurality of discrete time points ( Whether the state vector meets the specified coarse requirement criterion. The uncertainty vector is continuously modified until the specified coarse requirement criterion is met for the plurality of discrete time points.

4. The method according to claim 1 or 2, wherein, If one or more discrete time points that do not meet the coarse requirement criteria of the state vector have been identified, the method further includes: - Using multiple samples of the uncertainty vector and the surrogate model, calculate (440) one or more statistical distributions of the state vector at the corresponding identified one or more discrete time points. ); - Using one or more statistical distributions of the state vector, determine (460) one or more characteristics associated with the state vector at one or more identified discrete time points; - If one or more characteristics associated with the state vector meet the specified fine-grained requirements criteria, then the state controller is classified (480) as suitable for control of the system; otherwise, the uncertainty vector is adjusted (500). Alternatively, adjust the state controller described in (550).

5. The method according to claim 4, wherein, The specified fine-grained requirements include: one or more characteristics associated with the state vector are less than one or more corresponding specified thresholds.

6. The method according to claim 4 or 5, wherein, The one or more characteristics include one or more of the following characteristics: - First characteristic, which describes the probability of error that the specified coarse requirement criterion of the state vector is not met; - Second characteristic, which characterizes the degree to which the specified coarse requirement standard has not been met; - The third characteristic represents: when the uncertainty vector contains at least two uncertainty parameters, which uncertainty parameter contributes more to violating the specified coarse requirement standard, and which uncertainty parameter contributes less to violating the specified coarse requirement standard.

7. The method according to any one of claims 4 to 6, wherein, Adjusting the uncertainty vector described in 500 ( )include: - By reducing the uncertainty vector in the uncertain time effect ( The degree of uncertainty associated with at least one component of ) is used to adjust (510) the uncertainty vector ( ); - Resolve the surrogate model (520) using the adjusted uncertainty vector; - Using multiple samples of the adjusted uncertainty vector and the surrogate model, calculate (530) one or more adjusted statistical distributions of the state vector at the corresponding identified one or more discrete time points. ); - Using one or more adjusted statistical distributions of the state vector, determine (540) one or more adjusted characteristics associated with the state vector at one or more identified discrete time points; The uncertainty vector is continuously adjusted until one or more of the adjusted characteristics no longer meet the specified fine-grained requirements.

8. The method according to any one of claims 4 to 6, wherein, Adjusting (550) the state controller includes: solving (560) a stochastic optimization problem using the surrogate model to determine the adjusted feedback matrix of the state controller. ( ), wherein stochastic optimization is performed using an objective function based on the surrogate model.

9. The method according to any one of claims 1 to 8, wherein, The uncertainty vector ( It contains one or more of the following uncertainty parameters: - Delay parameters ( The delay parameter represents the time delay in the controlled system and is based on a specified statistical distribution; - At least one perturbation parameter ( The disturbance parameter represents the time disturbance of the controlled system and is based on a specified statistical distribution; - Sampling time ( The sampling time is based on a specified distribution, and the time discretization of the continuous-time dynamics model is performed using the sampling time.

10. The method according to any one of claims 1 to 9, wherein, Determining the surrogate model for the discrete-time representation of the (200) state-space model involves the following steps: - Specify (205) one or more polynomial basis functions ( The one or more polynomial basis functions are the uncertainty vector ( The function of ). - Execute (210) to transfer the state vector ( The series expansion is a series of one or more polynomial basis functions, wherein the corresponding one or more expansion coefficients of the series expansion ( This is independent of the uncertainty vector; - Project (215) the discrete-time representation of the continuous-time dynamics model onto the one or more polynomial basis functions.

11. The method according to claim 4, wherein, Determining the surrogate model for the discrete-time representation of the (200) state-space model involves the following steps: - Specify (205) one or more polynomial basis functions ( The one or more polynomial basis functions are the uncertainty vector ( The function of ). - Execute (210) to transfer the state vector ( The series expansion is a series of one or more polynomial basis functions, wherein the corresponding one or more expansion coefficients of the series expansion ( This is independent of the uncertainty vector. - Project (215) the discrete-time representation of the continuous-time dynamics model onto the one or more polynomial basis functions. Furthermore, calculating one or more statistical distributions of the state vector at one or more of the corresponding identified discrete time points (440) further includes the following steps: - For the multiple samples of the uncertainty vector, compute (445) the one or more polynomial basis functions to determine the one or more polynomial basis functions ( Multiple samples; - When using one or more of the polynomial basis functions ( The determined multiple samples and the corresponding one or more expansion coefficients of the series expansion () In the case of ), calculate (450) multiple empirical state vectors ( ).

12. The method according to claim 10 or 11, wherein, The surrogate model for determining the discrete-time representation of the state-space model described in (200) further includes: - Based on one or more expansion coefficients from the previous time step ( ), calculate one or more expansion coefficients for the next time step ( ).

13. The method according to any one of claims 10 to 12, wherein, For the multiple discrete time points ( The state vector of ) The mean of ) ) and the state vector ( The deviation, especially the variance () The determination of ) is made using one or more expansion coefficients of the proxy model for the said time point. This is done under the following circumstances.

14. A computer program designed to: perform a computer-implemented method according to any one of claims 1 to 13 for evaluating uncertain time effects when controlling a system in relation to one or more state variables.

15. A computer system designed to: perform a computer-implemented method according to any one of claims 1 to 13 for evaluating uncertain time effects when controlling the system in relation to one or more state variables; and / or perform a computer program according to claim 14.

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