Data-driven state estimation and system control under uncertainty

Abstract

A control method for controlling an electromechanical system based on a task uses an adaptive surrogate model of the system to estimate the state of the system, thereby generating an estimate of the system's state. The adaptive surrogate model includes a neural network that employs a weighted combination of neural operating functions (ODEs) of the system's dynamics in a latent space, such that the weights of the weighted combination of the neural ODEs represent uncertainty. The method controls the system according to the task based on the estimate of the system's state and fine-tunes the weights of the weighted combination of the neural ODEs based on the control.

Description

Technical Field

[0001] This disclosure generally relates to system modeling, prediction, and control, and more specifically, to systems and methods for adaptive reduction modeling and control of high-dimensional physical systems under model and environmental uncertainties using neural network models. Background Technology

[0002] Control theory in control systems engineering is a subfield of mathematics that deals with the control of continuously operating dynamic systems in engineering processes and machines. The goal is to develop a control strategy for controlling and regulating the behavior of such systems. The control strategy specifies appropriate control actions for the system at each time step to achieve the desired outcome defined by the control objective function. Examples of desired outcomes specified by the control objective function include stabilizing the system or tracking a desired state trajectory while minimizing certain costs.

[0003] The control strategy can be open-loop, in which the control action at a given time is not a function of the system's current state. The control strategy can also be closed-loop, in which the control action at a given time is a function of the system's current state, reconstructed in real-time from physical sensor data using an estimation algorithm.

[0004] Developing control strategies includes: model-based techniques, in which the physical model of the system is used directly when designing the control strategy; or data-driven techniques, which utilize computational data generated by the system to construct control strategies that achieve the desired results.

[0005] The physical model of a system's dynamics, or physical model of a system, uses ordinary differential equations (ODEs) or partial differential equations (PDEs) to describe the system's dynamics. These ODEs or PDEs are constructed based on physical conservation laws and principles, and they can be linear or nonlinear. Given an initial state and an arbitrary sequence of control actions, the physical model of the system can be used to predict the future state of the system at any desired time.

[0006] Physical models are typically high-dimensional, meaning the system's state is described by a large number of variables or by functions in a continuous space, and due to incomplete knowledge, multiple sources of uncertainty exist in the governing equations. Examples of such systems include power grids, buildings, room airflow, and smart grids. Solving physical models for such systems can be computationally very expensive. Furthermore, the physical parameters of the model, such as load requirements, the conductivity of insulation materials, air viscosity, and wind speed, are uncertain and can be modeled as random variables that capture prior knowledge about the system and its operating conditions, as well as fields falling within the bounded uncertainty range.

[0007] To reduce the computational cost of high-dimensional physical models, surrogate models, typically constructed through repeated simulations, are employed. One class of surrogate models includes reduced-order models, usually derived using a projection framework; that is, the governing equations of the physical model are projected onto a reduced-dimensional subspace. This reduced subspace is defined by a set of basis vectors, which, for general nonlinear problems, can be computed using appropriate orthogonal decomposition (POD) or reduced-basis methods. The constructed reduced-order model is used as a surrogate for the high-dimensional physical model, and then model-based techniques with manageable computational costs are used to design control strategies. For both approaches, the reduced basis is pre-constructed using full forward problem simulations. However, care must be taken to ensure the efficient construction and solution of the reduced-order model, as high-dimensional systems may not be suitable for sufficient forward simulations.

[0008] On the other hand, data-driven techniques utilizing operational data generated by the system have been used to construct control strategies that achieve desired results. The drawback of this approach is that it may require large amounts of data and lacks performance guarantees when the system's state during operation differs from the state present in the data used to construct the control strategy.

[0009] To address the aforementioned challenges of model-based and data-driven techniques, operator learning models for physical systems have been proposed. Such models generate agents for physical systems that describe their dynamics using neural network models with lower computational costs. To meet the data-intensive requirements of neural network models, the physical model represented by a PDE can be incorporated into the training process. An advantage is that the resulting operator learning model may require less training data because it learns to satisfy the physical conservation laws of the control system dynamics. However, traditional optimization frameworks used to train operator learning models cannot accurately quantify the parameter uncertainties associated with incomplete system knowledge. Therefore, operator learning models constructed using these methods may not exhibit sufficient accuracy and robustness to ensure good performance of model-based control strategies under all operating conditions.

[0010] Therefore, there is a need for methods and systems for incorporating uncertainty into operator learning models to generate adaptive and robust surrogate models, such that control strategies based on these models can: (i) effectively control high-dimensional systems, and (ii) robustly capture state trajectories under significant system disturbances and / or under all operating conditions. Summary of the Invention

[0011] The aim of various implementations is to provide a computer-implemented method and system for training, deploying, and / or adapting operator-learning surrogate models for high-dimensional dynamic systems under parametric uncertainties. Another aim of some implementations is to provide adaptive surrogate models for high-dimensional dynamic systems trained using physical information under parametric uncertainties. Some implementations address these uncertainties by adaptively formulating operator learning into a weighted representation (e.g., a polyhedral representation) of such a surrogate model.

[0012] Specifically, some implementations are based on the understanding that different surrogate models can be learned for different parameter values, and that the final surrogate model (i.e., the model used to complete the task) is a weighted combination of these models. Furthermore, some implementations are based on the understanding that these weights can be fine-tuned online, for example, using an online estimator such as a Kalman filter during task execution, either as part of a feedback loop or as dedicated tuning. This allows for the separation of computationally demanding offline training from lightweight online tuning during task execution by a system with uncertain parameters.

[0013] System parameters with uncertainties should not be confused with optimization variables for optimizing system dynamics during control. To illustrate the problem addressed by some implementations, an example of such a task is a robotic arm moving between two points according to a reference trajectory. While the optimization variables may be the position and / or velocity of the robotic arm, uncertainties in the dynamics affecting the robotic arm's motion may include uncertainties in the mass of the arm carrying the object. For example, the mass of the arm can have one of several values. To address this uncertainty, implementations determine surrogate models of the different possible values ​​of the robotic arm's mass and use weighted combinations of these surrogate models during robot control, where the weights are updated based on feedback from control.

[0014] Another example of a system with uncertainty is controlling a train with dynamics that include uncertainties such as friction between the wheels and the rails. Yet another example is controlling an air conditioning system under uncertainties related to the current heat load or ambient air temperature.

[0015] However, some implementations are based on the understanding that using the conventional architecture of neural networks as the structure for building surrogate models of dynamic systems would require a large number of neural network layers. To address this issue, some implementations use neural ODEs trained for different parameters within the parameter uncertainty boundary, such that the model used to perform tasks on the system comprises a weighted (e.g., polyhedral) combination of neural ODEs. While neural networks are defined by a fixed architecture with a certain number of layers, neural ODEs make the network depth a dynamic function of the input data, which is beneficial for representing the dynamics of the system.

[0016] Furthermore, to reduce the computational cost of high-dimensional physical systems of neural ODEs, some implementations use reduced-order models obtained by projecting onto a low-dimensional latent space. Some implementations are based on projection using an autoencoder architecture comprising an encoder neural network, a nonlinear propagator including the neural ODE, and a decoder neural network. The encoder is configured to encode a digital representation of the high-dimensional state at initial time into a low-dimensional latent vector belonging to the latent space. The neural ODE propagator is configured to propagate the latent vector in the latent space using a nonlinear transformation. Finally, the decoder is configured to decode the propagated latent vector back into a digital representation of the high-dimensional state.

[0017] Therefore, one embodiment discloses a control method for controlling an electromechanical system according to a task, wherein at least one of the system parameters includes uncertainty, wherein the method uses a processor coupled to stored instructions implementing the method, wherein the instructions, when executed by the processor, perform the steps of the method, the method comprising the steps of: estimating the state of the system using an adaptive surrogate model of the system to generate an estimate of the state of the system, wherein the adaptive surrogate model includes a neural network that employs a weighted combination of neural ODEs of the system's dynamics in a latent space, such that the weights of the weighted combination of the neural ODEs represent uncertainty; controlling the system according to the task based on the estimate of the system's state; and fine-tuning the weights of the weighted combination of the neural ODEs based on the control.

[0018] In some implementations, the weighted combination is a polyhedral weighted combination of the neural ODEs of the system's dynamics in the latent space.

[0019] Another embodiment discloses a controller for controlling an electromechanical system according to a task, wherein at least one of the system parameters includes uncertainty, wherein the controller includes: a processor; and a memory storing instructions that, when executed by the processor, cause the controller to perform the following operations: estimating the state of the system using an adaptive surrogate model of the system to generate an estimate of the state of the system, wherein the adaptive surrogate model includes a neural network that employs a weighted combination of neural ODEs of the system's dynamics in a latent space, such that the weights of the weighted combination of the neural ODEs represent uncertainty; controlling the system according to the task based on the estimate of the system's state; and fine-tuning the weights of the weighted combination of the neural ODEs based on the control.

[0020] Another embodiment discloses a non-transitory computer-readable storage medium on which a processor-executable program is implemented. The program is used to execute a control method for controlling an electromechanical system according to a task, wherein at least one of the parameters of the system includes uncertainty. The method includes the steps of: estimating the state of the system using an adaptive surrogate model of the system to generate an estimate of the state of the system, wherein the adaptive surrogate model includes a neural network that employs a weighted combination of neural ODEs of the system's dynamics in a latent space, such that the weights of the weighted combination of the neural ODEs represent uncertainty; controlling the system according to the task based on the estimate of the system's state; and fine-tuning the weights of the weighted combination of the neural ODEs based on the control. Attached Figure Description

[0021] [ Figure 1A ]

[0022] Figure 1A This is a flowchart of a method for offline construction of an operator learning model of a dynamic system and online fine-tuning of a control system using a polyhedral operator learning model, according to embodiments of the present disclosure.

[0023] [ Figure 1B ]

[0024] Figure 1B Is it about Figure 1A The described implementation method is a block diagram of a control method for controlling an electromechanical system based on the principle of the task.

[0025] [ Figure 2A ]

[0026] Figure 2A This is a schematic diagram of the architecture of a polyhedral operator learning model with a robust autoencoder and a polyhedral neural ODE propagator according to some embodiments of the present disclosure.

[0027] [ Figure 2B ]

[0028] Figure 2B This is a schematic diagram of the architecture of a polyhedral operator learning model with a polyhedral autoencoder and a neural ODE propagator according to some embodiments of the present disclosure.

[0029] [ Figure 3A ]

[0030] Figure 3A This is a schematic diagram illustrating the first training phase of an operator learning model according to an embodiment of the present disclosure.

[0031] [ Figure 3B ]

[0032] Figure 3B This is a schematic diagram illustrating the second training phase of an operator learning model according to an embodiment of the present disclosure.

[0033] [ Figure 3C ]

[0034] Figure 3C This is a schematic diagram illustrating the construction of a polyhedral operator learning model according to an embodiment of the present disclosure.

[0035] [ Figure 4A ]

[0036] Figure 4A This is a block diagram illustrating real-time online fine-tuning of parameters of an operator learning model according to embodiments of this disclosure.

[0037] [ Figure 4B ]

[0038] Figure 4B It is a block diagram of a method for controlling the operation of a system based on a reference trajectory of an operational task, according to some implementation methods.

[0039] [ Figure 5A ]

[0040] Figure 5A This is a block diagram illustrating online open-loop control of the operation of a dynamic system using a polyhedral operator learning model according to some embodiments of the present disclosure.

[0041] [ Figure 5B ]

[0042] Figure 5B This is a block diagram illustrating online closed-loop control of the operation of a dynamic system using a polyhedral operator learning model according to some embodiments of the present disclosure.

[0043] [ Figure 6 ]

[0044] Figure 6 This is a block diagram illustrating online closed-loop control of the operation of a dynamical system using a polyhedral operator to learn a model and model adaptation, according to some embodiments of this disclosure.

[0045] [ Figure 7 ]

[0046] Figure 7 This is a schematic diagram illustrating steps performed by a probabilistic filter to estimate the state of a controlled system according to some embodiments of the present disclosure.

[0047] [ Figure 8A ]

[0048] Figure 8AThis is a schematic diagram of a control method for controlling a controller configured to control a vapor compression system according to some embodiments of the present disclosure.

[0049] [ Figure 8B ]

[0050] Figure 8B This is a schematic diagram of a method for controlling a vapor compression system according to some embodiments of the present disclosure.

[0051] [ Figure 9 ]

[0052] Figure 9 This is a schematic diagram of a method for controlling a robot manipulator according to some embodiments of the present disclosure.

[0053] [ Figure 10 ]

[0054] Figure 10 This is a schematic diagram of a computing device that can be used to implement the control method of this disclosure. Detailed Implementation

[0055] In describing embodiments of this disclosure, the following definitions apply throughout the disclosure. "Control system" or "controller" can refer to a device or set of devices used to manage, command, direct, or regulate the behavior of other devices or systems. A control system can be implemented in software or hardware and may include one or more modules. A control system including feedback loops can be implemented using a microprocessor. A control system can be an embedded system.

[0056] "Central Processing Unit (CPU)" or "processor" can refer to a computer or computer component that reads and executes software instructions. Furthermore, a processor can be "at least one processor" or "one or more processors".

[0057] Various implementations provide a computer-implemented method and system for training, deploying, and adapting operator-learning surrogate models for high-dimensional dynamic systems under parameter uncertainty. Some implementations achieve these goals by constructing a polyhedral representation of such a surrogate model and designing an online adaptive law to select the optimal portion of the polyhedral model that most accurately represents the high-dimensional system at any given time. The operator-learning surrogate model can be used to estimate the future state of the system at any desired time given an initial state and arbitrary control sequence. During inference, the state and parameters of the model are estimated using measurement data, and the dynamics are adapted based on the polyhedral model construction by fine-tuning the weights of the polyhedral representation.

[0058] The operator learning agent model employs an autoencoder architecture comprising an encoder neural network, a nonlinear propagator composed of neural ODEs, and a decoder neural network. The encoder is configured to encode a digital representation of the high-dimensional state at initial time into a low-dimensional latent vector belonging to the latent space. The neural ODE propagator is configured to propagate the latent vector in the latent space using a nonlinear transformation. Finally, the decoder is configured to decode the propagated latent vector back into a digital representation of the high-dimensional state.

[0059] In some implementations, the computer-implemented method involves collecting digital representations of high-dimensional state sequences at different time instances during the system's operation, along with all possible parameter combinations within a bounded range of uncertainty corresponding to various operating conditions. Furthermore, digital representations of the time series of control action values ​​given during system operation may be available. This collection begins with different initial state conditions, different parameter vector implementations, and is performed multiple times using the time series of control action values. For a given initial condition of the state and parameter vector implementations, the state sequences at different time instances and the time series of control action values ​​are referred to as solution trajectories. The collection of solution trajectories is called the training set. In some implementations, the training set is divided into several sets corresponding to each parameter vector implementation; these sets are called parameter training sets. In other implementations, the training set includes all trajectories and is referred to as the robust training set.

[0060] For example, the training of a computer-implemented operator learning model can be performed in two phases. In the first training phase, the encoder and decoder are trained to compress high-dimensional states into low-dimensional latent vectors and vice versa. To achieve this, in each training iteration, a sequence of high-dimensional states belonging to randomly sampled solution trajectories in the training set is applied as input to the encoder, which outputs a corresponding sequence of low-dimensional latent vectors. These latent vectors are then applied as input to the decoder, which outputs a corresponding sequence of high-dimensional states. The loss penalty is then calculated by the mean squared error between the state sequence returned as output by the decoder and the baseline ground truth state sequence applied as input to the encoder.

[0061] In some implementations, the set of solution trajectories used to train the encoder and decoder comprises the set of all trajectories obtained for all possible initial conditions and parameter implementations; i.e., a robust training set. In this robust training, the encoder-decoder network constructs a low-dimensional latent vector representation corresponding to any parameter implementation without explicitly depending on the parameters. In other implementations, the encoder-decoder network has an explicit dependency on the parameters. Then, an encoder-decoder network library is constructed for each individual parameter vector implementation using the corresponding parameter training set, and the latent vector representation is then constructed as an adaptive polyhedral representation of these individual networks.

[0062] In the second training phase, a library of neural ODE propagators is trained to learn the dynamics of the system in the latent space. To achieve this, each solution trajectory in the parameter training set is first mapped to the latent space by passing a high-dimensional state sequence of each solution trajectory to the encoder, thus obtaining a corresponding ground truth latent vector sequence. Then, in each training iteration, the initial ground truth latent vector and the time series of control action values ​​corresponding to the randomly sampled trajectories are applied to the parametric neural ODE propagator, which returns the corresponding latent vector sequence. Then, in the corresponding parameter vector implementation, the loss penalty is the mean squared error between the latent vector sequence predicted by the neural ODE propagator and the ground truth latent vector sequence. In this adaptive approach, the neural agent model has an explicit dependence on the parameters, and during inference, an adaptive polyhedral representation of individual ODE propagators is used, where parameter-related weights determine the contribution of each propagator.

[0063] During inference, this parameter-dependent polyhedral representation of the encoder-decoder network and / or neural ODE propagators allows for the development of adaptive online estimators for systems controlled by high-dimensional PDEs with parameter uncertainties. In particular, embodiments of the invention enable parameter state estimation using surrogate models with online adaptive laws, which allow interpolation between learned dynamics captured by the neural ODE propagator library.

[0064] In some implementations, parameter state estimation is accomplished using a modular dual algorithm that combines an adaptive polyhedral operator learning model with two nonlinear data assimilation filters (e.g., particle filters, a family of Kalman filters including unscented Kalman filters (KFs), extended KFs, ensemble KFs, etc.) to estimate the state and unknown parameters, respectively. In other implementations, a single nonlinear filter in which the state is augmented by uncertain parameters is used to jointly estimate both the state and parameters.

[0065] In some implementations, the uncertain parameters considered are coefficients of the PDE terms describing the dynamic model. These parameters may be low-dimensional and can be directly used to construct a polyhedral representation, while in other implementations, these parameters are high-dimensional, or they may themselves be random spaces and / or time-varying fields that are first simplified to low-dimensional latent representations using an encoder-decoder network. In other implementations, these parameters also include boundary conditions controlling the PDE. In other implementations, these parameters also include the geometry of the physical domain of the high-dimensional system.

[0066] In some implementations, the training set of the solution trajectory is obtained by a numerical solver that solves the PDE defined by the physical model of the system. For example, if the system of interest is airflow in a room with air conditioning control, computational fluid dynamics (CFD) simulation can be used to compute the solution trajectory. The CFD simulation solves the physical Navier-Stokes equations governing the fluid flow to obtain a sequence of states corresponding to the initial state and any sequence of control actions.

[0067] In some implementations, the method further includes incorporating the physical model represented by the PDE into a second training phase for the neural ODE propagator. In this case, the loss includes an additional physical information term penalizing the mean square error between the time derivative of the latent vectors predicted by the neural ODE and the benchmark truth time derivative of the PDE defined by the physical model. The second part can be evaluated on latent vectors corresponding to states in the training set trajectory, or on latent vectors corresponding to arbitrary states satisfying boundary conditions or other constraints associated with the system. This incorporation of the physical model into the training method yields a physical information manipulator learning model.

[0068] In some embodiments, the method further includes generating control commands to control the system using a model-based control strategy, wherein the model used to design the control strategy is a trained operator-learning agent model.

[0069] In some implementations, the method further includes generating control commands to control the system based on a hybrid model-based and reinforcement learning control policy, wherein the model used to design the control policy is a trained operator-learning agent model. Starting with a model-based control policy as a warm start, the hybrid model-based and reinforcement learning approach iteratively refines the policy parameters to achieve better control performance by alternating between collecting data using the current control policy and updating the policy parameters to improve the cost objective of interest.

[0070] Figure 1A and Figure 1B This is a flowchart illustrating methods for constructing a surrogate polyhedral operator learning model 103 of a high-dimensional dynamical system 100 in an offline phase 101 and for fine-tuning and / or controlling the system using the polyhedral operator learning model in an online phase 102, according to some embodiments of this disclosure. The physical model of the system can be described by a PDE. In some embodiments, the system may have control inputs.

[0071] The offline phase 101 includes the polyhedral operator learning model 103. Figure 2A and Figure 2B The polyhedral operator learning model 103 described herein includes an encoder neural network 108, a neural ODE 109, and a decoder neural network 110. The offline phase 101 may further include an experimental module 104, a physical model 105 describing the dynamics of system 100 using an ODE or PDE, a high-fidelity numerical solver module 106, and a training dataset 107 consisting of a set of solution trajectories of the system. Each solution trajectory includes initial conditions of the states, a time series of control action values, and a sequence of states generated at different time instances corresponding to the realization of the uncertain parameter vector during the operation of system 100. For example, the solution trajectory of airflow in a room might describe the velocity and temperature fields evolving from initial conditions at different times due to the forced action of the HVAC unit. The online phase 102 may include a fine-tuning module 120, a prediction module 121, an estimation module 122, an open-loop control module 123, and a closed-loop control module 124 to control system 100 during online operation of system 100.

[0072] The encoder neural network 108, the neural ODE 109, and the decoder neural network 110 may include fully connected neural networks (FNNs) or convolutional neural networks (CNNs) whose parameters are trained offline and tuned online based on a computer-implemented method of this disclosure. In the offline phase 101, the method trains a polyhedral operator learning model 103 using solution trajectories contained in a training dataset 107, which is generated by using... The trajectory set is obtained by implementing the parameters. The training determines the parameter values ​​of the polyhedral operator learning model 103 so that it can predict the state evolution of the system 100 given the initial conditions of the state and the time series of control action values.

[0073] The method disclosed herein improves predictive performance compared to state-of-the-art techniques by constructing a polyhedral representation of such a model and designing an online adaptive law to select the optimal portion of the high-dimensional system at any given time that most accurately represents the polyhedral model, even in the presence of parameter uncertainties. Furthermore, in some embodiments, the polyhedral operator learning model 103 can be additionally trained using a physical model 105 such that the system dynamics predicted by the polyhedral operator learning model 103 obey the PDE describing the physical model 105. In the online phase 102, according to some embodiments, the method can fine-tune the polyhedral operator learning model 103 using sensor measurements obtained from the online operation of the real system by enabling joint state parameter estimation and adaptive model switching and interpolation.

[0074] In some applications, it may be advantageous to use a surrogate operator to learn model 103 instead of the physical model 105 of system 100. For example, on platforms with limited computing power, such as embedded devices and autonomous devices, solving the physical model 105, considering parameter uncertainties, may be computationally difficult. For instance, in an HVAC system, solving the physical model means solving the Navier-Stokes equations in real time on a fine mesh, and considering model uncertainties such as viscosity coefficients and the number of people in the room requires multiple model simulations, which may exceed the computing power of the HVAC system's CPU. On the other hand, solving the model 103 using a surrogate polyhedral operator may be computationally cheaper. Finally, even if the physical model 105 can be solved (e.g., by utilizing a remote cluster), implementing control over the resulting model, which is the ultimate goal of the HVAC system, may be difficult. In fact, implementing control may require multiple iterative evaluations of the physical model 105 at each time step.

[0075] The computer-implemented method of this disclosure may include collecting solution trajectories contained in training dataset 107. The solution trajectories contained in training dataset 107 may be implemented for all possible I parameters, generated by performing experiments using experimental module 104 or by computing numerical solutions of physical model 105 using high-fidelity numerical solver module 106.

[0076] In some implementations, the numerical solver module 106 may consist of a computational fluid dynamics (CFD) solver that utilizes numerical analysis and data structures to solve the Navier-Stokes equations governing fluid flow dynamics. For example, a computer may be used to perform the calculations required to simulate the flow of a fluid interacting with a surface defined by boundary conditions. Furthermore, some implementations employ multiple software solutions to provide good accuracy in complex simulation scenarios associated with transonic or turbulent flows that may occur in an application, such as describing airflow in an HVAC room. Initial validation of such software is typically performed using experimental data. Additionally, prior analyses or empirical studies of specific airflow-related issues associated with the system can be used for comparison in CFD simulations.

[0077] According to some embodiments of this disclosure, in the online phase 102, the polyhedral operator learning model 103 can be used in conjunction with one or a combination of the open-loop control module 123 or the closed-loop control module 124 to control the system 100. Since the polyhedral operator learning model 103 learns the dynamics of the system 100 for various parameter implementations, this operator learning model can be used to predict the evolution of states or control the system's operation outside the time range of solution trajectories present in the training dataset 107. Furthermore, when the parameter implementations are not included in the training dataset 107, the polyhedral operator learning model 103 allows for accurate and efficient model switching and interpolation.

[0078] The open-loop control module 123 includes an open-loop control strategy that generates commands to control the operation of the system 100 in order to achieve the desired result defined by the control objective function. The prediction module 121 can be used to generate a trajectory of the state of the system 100, and the open-loop control module 123 can then use these trajectories to generate optimal control actions.

[0079] Alternatively, the closed-loop control module 124 includes a closed-loop control strategy that generates commands to control the operation of the system in order to achieve the desired result defined by the control objective function, wherein each control command is calculated based on the current estimated state of the system 100. The estimation module 122 can be used to perform parameter state estimation, thereby allowing the adjustment of the polyhedral model based on historical data of noisy sensor measurements up to the current time. The closed-loop control module 124 can then use this adjusted polyhedral model to generate optimal control actions.

[0080] For example, in a room controlled by an HVAC system, sensors can record data such as temperature, velocity, and humidity at specific locations. An estimation module can then be used to reconstruct the spatial distribution of temperature and velocity within the room in real time based on the sensor measurements. The control module 124 can then utilize the reconstructed temperature and velocity model to generate HVAC control actions to achieve the desired distribution of velocity and temperature within the room.

[0081] Figure 1B It shows the use of about Figure 1A The described implementation uses a block diagram of a control method for controlling an electromechanical system based on a task. The method uses a processor coupled to stored instructions implementing the method, wherein the instructions, when executed by the processor, perform the steps of the method.

[0082] The method includes using an adaptive surrogate model of the system to estimate the state of system 150, the adaptive surrogate model comprising a weighted combination 190 of the neural ODEs of the system's dynamics in the latent space to produce an estimate of the system state. In some implementations, the weighted combination 190 is a polyhedral weighted combination of the neural ODEs of the system's dynamics in the latent space.

[0083] In various implementations, at least one of the system parameters includes uncertainty represented by weights 180, which are weighted combinations of neural ODEs. Therefore, to reduce uncertainty, the method includes controlling the system 160 based on an estimate of the system state according to the task, and fine-tuning 170 the weights 180 of the weighted combination based on feedback from the control.

[0084] Figure 2A This is a schematic diagram of the architecture of a polyhedral operator learning model 103 having robust autoencoders (200 and 202) and a polyhedral neural ODE propagator 201, according to some embodiments of this disclosure. The robust encoder neural network 200 is composed of... This indicates that the neural network defining the polyhedral neural network ODE 201 is composed of... It is stated that the robust decoder neural network 202 is composed of It means, and This refers to the trainable parameters of all three neural networks. In some implementations, the system state is represented as... It is described by a continuous space function, where, It is a physical quantity. These are spatial coordinates, and For example, regarding airflow in a room, It can represent time Spatial distribution of velocity and temperature in a room. From the initial time... Initial conditions of the state Start, and give the time series of control action values. , The polyhedral operator learning model 103 can be used to predict the system at any time. future state As described below. First, In a limited number of spatial locations The digital representation of the initial conditions of the sampled sample is applied as input to the robust encoder 200, which outputs a low-dimensional latent vector at the initial time.

[0085]

[0086] The latent vector is then passed to the polyhedral neural network ODE 201, which uses a neural network... The polyhedral construction of the defined neural ODE is used to represent the dynamics of the latent vector, as shown below:

[0087] in, It depends on the model parameters that are assumed to be known or estimated later as part of the estimation algorithm. The weight function, and It controls the action value.

[0088] By transferring the polyhedral neural ODE 201 from Points to To obtain the latent vector The robust decoder 202 is based on... and any spatial location The input is a neural network, and the output is:

[0089] This is the actual situation. An approximation of . By... As input, the robust decoder 202 generates continuous states. continuous representation This type of parameterization of continuous functions using neural networks is called implicit neural representation.

[0090] The computer implementation method disclosed herein Figure 3A and Figure 3C The polyhedral operator learning model 103 is trained in a two-stage process described in the paper. This two-step training process determines the robust encoder neural network 200. ), Polyhedral Neural ODE 201 ( ) and robust decoder neural network 202 ( ) parameter value So that From arbitrary initial conditions Start and any time series with a given control action value and model parameters In the case of time estimation The true state of being An accurate approximation.

[0091] We use Let represent the solution trajectory in training dataset 107, where This refers to the implementation of parameters in the training dataset. Corresponding One of the different solution trajectories, and In a limited number of spatial locations This is a time instance for sampling the state. Along with each solution trajectory, it also stores the time instance for... and Time series of control action values .

[0092] Figure 2B This is a schematic diagram of the architecture of a polyhedral operator learning model 103 having a polyhedral autoencoder (203 and 204) and a polyhedral neural ODE propagator 201, according to some embodiments of this disclosure. In addition to the polyhedral neural ODE propagator discussed in the previous figure, other embodiments of the invention may also include a polyhedral representation for the autoencoder. In this case, a low-dimensional latent vector is obtained from the digital representation of the initial conditions using the polyhedral encoder 203, as follows:

[0093] in, This corresponds to a parameter-dependent encoder neural network.

[0094] Similarly, the polyhedral decoder 204 is a polyhedral construct of a neural network, which will and any spatial location As input, and output:

[0095] about Figure 3A and Figure 3B The process for training the polyhedral encoder 203 and decoder 204 is further described.

[0096] Figure 3A The first stage of training a polyhedral operator learning model 103 for a robust autodecoder (200 and 202) and a polyhedral neural network ODE 201, according to some embodiments of this disclosure, is shown. The first stage determines the robust encoder neural network 200 ( ) and robust decoder neural network 202 ( ) parameter value The goal is for the trained encoder to process continuous states. Compressed into low-dimensional latent vectors Furthermore, the trained decoder is able to process low-dimensional latent vectors. Decompress back to the same continuous state For training, all trajectories are achieved by considering all parameter vectors (i.e., , To construct a robust training dataset 300. Each training iteration includes a forward pass 301, where a given plot is drawn based on the training dataset 300. The entire solution trajectory This is then applied as input to encoder 200. The robust encoder 200 then outputs the corresponding trajectory of the low-dimensional latent vector as:

[0097] Then, the trajectory of the low-dimensional latent vector is applied as input to the robust decoder 202, and the decoder 202 outputs the trajectory of the reconstructed system state:

[0098] All trajectories All iterations combined, robust training loss 302 means:

[0099] This ensures the robust encoder 200 ( ) and robust decoder 202 ( ) are inverse mappings of each other.

[0100] In other implementations, another term can be added to training loss 302:

[0101] The second term ensures low-dimensional latent vectors. It evolves smoothly from one time step to the next.

[0102] During each training iteration, the loss 302 is used to update the parameters of robust encoder 200 and robust decoder 202 using gradient descent algorithms such as stochastic gradient descent or Adam optimizer. .

[0103] In some implementations, each trajectory, compared to other trajectories, Can be in different spatial locations and time instances The trajectory is captured. In this case, the loss function should be modified accordingly. To simplify the symbolic representation without sacrificing its generality, it is assumed that all trajectories are located at the same spatial location and recorded at the same time instance.

[0104] Figure 3BThe first stage of training the polyhedral operator learning model 103 for a polyhedral automatic decoder (203 and 204) and a polyhedral neural ODE 201, according to some embodiments of this disclosure, is illustrated. In this case, the training dataset is split into a parameter training set 303, where only the trajectories obtained for each parameter vector implementation are considered. The training process then follows the procedure explained in the previous figure to construct the parameter encoder network 305 using the parameter encoder-decoder training loss 307. and parameter decoder network 306 ,

[0105] It can be modified to additionally include the Jerk loss term, as shown below:

[0106] Figure 3C The second stage of training a polyhedral operator learning model 103 according to some embodiments of this disclosure is shown. The second stage determines the parameters of the neural ODE propagator 309 ( ) parameter value The goal is to train. The neural ODE propagator can be reproduced for each parameter. latent vectors in the latent space The dynamics. Each training iteration includes a forward pass 308, where a plot is drawn for a given training dataset 303 based on the parameters. The entire solution trajectory And apply it as input to the robust encoder 200 or the polyhedral encoder 203.

[0107] Then, the encoder outputs the trajectory corresponding to the low-dimensional latent vector of the baseline ground truth as:

[0108] Then the first potential vector in the trajectory Time series of control action values ​​for the same trajectory ( Together, they are applied as input to the parameter neural ODE propagator 309. Then the neural ODE... from Points to The predicted potential vector trajectory is obtained. , .

[0109] Then, each training iteration includes building the loss. 310, which includes a prediction loss term that ensures the trajectory of the predicted latent vector is similar to the trajectory of the ground truth latent vector. It is calculated based on the mean squared error as follows:

[0110] Finally, during each training iteration, the loss... The parameters of the neural ODE propagator 309 are used to update the parameters using gradient descent algorithms (such as stochastic gradient descent or Adam optimizer). .

[0111] In some implementations, the method for training the parameter neural ODE propagator 309 further includes incorporating the PDE of the physical model 105 into the training loss. In this case, the method may include generating at a finite number of spatial locations. Any state sampled Each state satisfies the system's boundary conditions and other constraints. Furthermore, the states... This should be physically achievable by the system. Then the item... Add to In these states The consistency between the dynamics caused by the parametric neural ODE propagator 309 and the dynamics given by the PDE in the physical model 105 is enhanced.

[0112] Figure 4A This is a block diagram of a weighted combination of parameters for real-time online fine-tuning of a polyhedral operator learning model 103, according to some embodiments of this disclosure. During online operation, at different locations... Measurement status Sensors 401 with different components can be placed in the actual system 100. Once... Figure 3A , Figure 3B and Figure 3C The polyhedral operator learning model 103 was trained offline, and this model can be used to calculate the sensor output prediction 402 in real time. Furthermore, the sensor 401 in the real system 100 can be used to obtain the sensor output measurement value 403 in real time. Then, the polyhedral operator learning model 103 can be adapted in real time in the fine-tuning module 120 based on the difference between the sensor output prediction 403 and the sensor output measurement value 402.

[0113] Various embodiments of the present invention update uncertainty parameters during control itself by weighting a weighted combination of neural ODEs fine-tuned based on feedback from control. For example, the weights of the weighted combination are updated based on the difference between an estimate of the system's state and a measured value of the system's state. Furthermore, it is recognized that, in some cases, the similarity of control over repeatedly performing operational tasks can be used to update the uncertainty of subsequent task completion. The uncertainty of subsequent task execution can be updated based on the performance of the system in completing the current task. In some embodiments, the uncertainty is iteratively updated over multiple completions of the task to mimic the true value of the uncertainty parameters.

[0114] Figure 4B A block diagram is shown of a method for controlling the operation of a system based on a reference trajectory of an operational task, according to some embodiments. This method can be implemented using a suitably programmed processor. In some embodiments, the method is used for open-loop control of a task that is repeated multiple times, and according to some embodiments, the repetition of the task is used to update the weights of the polyhedral combination of the neural ODE.

[0115] The method controls system 410 to perform multiple control steps, such as three or more, based on a reference trajectory 405 of the operational task, to generate the actual trajectory 415 of the system completing the operational task. For each control step, the control input of the system is determined using the solution of a model-based controller that employs an adaptive surrogate model of the system, which includes a weighted combination of neural ODEs of the system's dynamics in the latent space. The uncertainty of the controlled system is represented by the weights of the weighted combination, and fine-tuning 120 updates the weights during control.

[0116] Next, the method determines a value 425 of the learning cost function that represents the distance between the reference trajectory and / or estimated state of the system and the actual trajectory and / or measured state of the system. The method used to determine the value 425 can vary between implementations. For example, one implementation uses the Euclidean distance between corresponding samples of the trajectory to determine this value. The sum of the Euclidean distances can be normalized to determine the value 425. Other methods for determining the tracking error can also be used.

[0117] After obtaining value 425, the method uses model-free optimization 450 to determine the weights of the weighted combination 430, thereby reducing the value of the learning cost function to produce updated weights 435. Next, the method uses a model that includes a weighted combination of neural ODEs with the system dynamics of the updated weights 435 to determine the set of control inputs 445 for completing the task based on reference trajectory 405.

[0118] Some implementations update the weights of the weighted combination to reduce the value of the learning cost function. Since uncertainty implicitly affects the value of the learning cost function, these implementations do not use standard optimization methods. Instead, some implementations use various model-free optimization methods to update the weights. For example, one implementation uses an extremum search method, such as multivariate extreme value search (MES). Another implementation uses reinforcement learning optimization. These model-free optimization methods are typically used to optimize control by analyzing real-time changes in the system output.

[0119] Figure 5A This is a block diagram illustrating the online open-loop control of the operation of a dynamic system 100 using a polyhedral operator learning model 103 according to some embodiments of this disclosure. Once as Figure 3A , Figure 3B and Figure 3C The polyhedral operator learning model 103, trained offline, can be used in the prediction module 121 to calculate the system trajectory under various initial conditions, time series of control action values, and various parameter implementations. Based on these trajectories and the polyhedral operator learning model 103, the open-loop control strategy in the control module 123 can be used to calculate the time series of the optimal control action value 501 in real time. These time series can be used for the online operation of the control system 100 to achieve the desired result defined by the control objective function.

[0120] Figure 5B This is a block diagram illustrating online closed-loop control of the operation of a dynamic system 100 using a polyhedral operator learning model 103 according to some embodiments of the present disclosure. Sensors 502 can be placed in the actual system 100 at various locations during online operation of the system. In collection state The measured values ​​of different components are 503. Once such Figure 3A , Figure 3B and Figure 3C The polyhedral operator learning model 103, trained offline, can be used in the estimation module 122 to perform two-parameter or joint-parameter state estimation of the system 100 based on the history of sensor output measurement values ​​503. Based on the estimated state and the polyhedral operator learning model 103, the closed-loop control strategy in the control module 124 can be used to calculate the time series of optimal control action values ​​501 in real time. These time series can be used for online operation of the control system 100 to achieve the desired result defined by the control objective function.

[0121] Figure 6This is a block diagram illustrating online closed-loop control of the operation of a dynamic system 100 using a polyhedral operator learning model 103 and a model adaptation 500 according to some embodiments of the present disclosure. As part of an estimation module 122 for performing two-parameter or joint-parameter state estimation, a polyhedral model adaptation module 600 can be used to adapt the polyhedral operator learning model 103 based on the estimated parameters.

[0122] For example, in some implementations, the polyhedral model adaptive module 600 uses a probabilistic filter to update the weights of a weighted combination. This probabilistic filter uses one or a combination of a measurement model and a prediction model employing a neural network to track the state of the system. The probabilistic filter can be used directly to track the weights of the weighted combination, and / or the state variables of the system state can be augmented using the weights of the weighted combination, and the probabilistic filter can be used to track the augmented state of the system. Examples of probabilistic filters used in different implementations include one or a combination of a Kalman filter (e.g., an extended Kalman filter) and a particle filter.

[0123] Figure 7 A schematic diagram 700 illustrates steps exemplified by a probabilistic filter for estimating the state of a controlled system according to some embodiments of the present disclosure. The probabilistic filter (e.g., a Kalman filter) uses a predictive model affected by process noise and a measurement model affected by measurement noise. At least one of the predictive and measurement models includes a neural network that estimates the state using a weighted combination of neural ODEs of the system's dynamics in the latent space. The Kalman filter iteratively tracks the weights of the weighted combination to improve the accuracy of the estimation.

[0124] The steps performed by the probability filter 700 include a prediction step 770, a measurement step 780, and / or a correction step 790. In the prediction step 770, the probability filter uses a prediction model that includes a neural network with the current weight values ​​to estimate the predicted state value PDF 720 from the probability distribution function (PDF) 710 of the state value. For example, PDF 720 may correspond to a Gaussian distribution. A Gaussian distribution may be defined by a mean and a variance, where the mean defines the central location of the distribution 720, and the variance defines the spread (or width) of the distribution 720.

[0125] Return to reference Figure 7 The measurement model uses measurements indicating the output of the mechanical system in the current control step to generate an estimate 740 of the mechanical system state. A correction step 790 updates the probability distribution of the system 750's state to initialize the next iteration 760 of the probability filter and / or the weights of the weighted combination. Values ​​of the internal states used to perform the task are sampled on distribution 750.

[0126] Exemplary Implementation

[0127] "Air conditioning system" or heating, ventilation, and air conditioning (HVAC) system can refer to a system that uses a vapor compression cycle to move refrigerant between the system's components based on thermodynamic, fluid dynamics, and / or heat transfer principles. Air conditioning systems encompass a wide range of systems, from those that supply only outdoor air to the occupants of a building, to those that control only the building's temperature, and even those that control both temperature and humidity.

[0128] Figure 8A A schematic diagram of a control method using a controller 800 configured to control a vapor compression system 810, according to some embodiments of the present disclosure, is shown. The controller 800 uses a digital twin 820 of the vapor compression system 810 to control the vapor compression system 810. The vapor compression system 810 and the digital twin 820 are communicatively connected to the controller 800. The vapor compression system is configured to perform the task of maintaining the environment in a target state. The target state may include a target temperature.

[0129] The vapor compression system 810 includes an evaporative heat exchanger 807, a compressor 801, a condensing heat exchanger 803, and an expansion valve 805 located in space 809. Heat transfer from the condensing heat exchanger 803 is facilitated by using a fan 811, while heat transfer from the evaporative heat exchanger 807 is facilitated by using a fan 813. The vapor compression system 810 may include variable actuators, such as variable compressor speed, variable expansion valve position, and variable fan speed. This disclosure relates to many other alternative device architectures, including multiple heat exchangers, compressors, valves, and other components such as accumulators or reservoirs, piping, etc., and the illustration of the vapor compression system 810 is not intended to limit the scope or application of this disclosure to any system.

[0130] In the vapor compression system 810, the compressor 801 compresses the low-pressure, low-temperature gaseous fluid (refrigerant) into a high-pressure, high-temperature vapor state, which then enters the condensing heat exchanger 803. As the refrigerant passes through the condensing heat exchanger 803, heat transfer facilitated by the fan 811 allows the high-temperature, high-pressure refrigerant to transfer its heat to the cooler ambient air. As the refrigerant transfers heat to the ambient air, it gradually condenses until it reaches a high-pressure, low-temperature liquid state. Furthermore, the refrigerant leaves the condensing heat exchanger 803 and expands to a low-pressure boiling state through the expansion valve 805, from which it enters the evaporating heat exchanger 807. When the air passing through the evaporating heat exchanger 807 is hotter than the refrigerant itself, the refrigerant gradually evaporates as it passes through the evaporating heat exchanger 807. The refrigerant leaving the evaporating heat exchanger 807 is in a low-pressure, low-temperature state. The low-pressure, low-temperature refrigerant re-enters the compressor 801, and the same VCS is repeated.

[0131] The controller 800 uses a digital twin 820 employing a weighted polyhedral combination of ODEs to simulate and control the operation of the vapor compression system 810.

[0132] Figure 8B A block diagram of a method 815 for controlling a vapor compression system 810 according to some embodiments of the present disclosure is shown. In block 817, method 815 submits a sequence of control inputs to the vapor compression system 810. The sequence of control inputs includes one or a combination of the speed of compressor 801, the speed of fan 813, and the position of expansion valve 805 of the vapor compression system 810.

[0133] In block 819, method 815 receives an output sequence of vapor compression system 810 caused by a corresponding control input sequence. The output sequence of vapor compression system 810 may correspond to a measurement sequence. Each measurement indicates the output of vapor compression system 810 caused by a corresponding control input. For example, the measurement includes the temperature, humidity, and / or velocity of the air output by vapor compression system 810.

[0134] In box 821, method 815 uses a neural network to estimate the current internal state of the digital twin 820. In box 823, method 815 determines the current control input for controlling the vapor compression system 810 based on the current internal state of the digital twin 820. The current control input is submitted to the vapor compression system 810. The current control input changes the current state to a target state. For example, the current control input changes the current temperature to a target temperature to perform the task of maintaining the target temperature.

[0135] Figure 9 A method for controlling a robot manipulator 901 according to some embodiments of the present disclosure is illustrated. The robot manipulator 901 is configured to perform a manipulation task of moving an object 903 to a target state 905 (e.g., a target position). The robot manipulator 901 is communicatively coupled to a controller 900 and a digital twin 907 of the robot manipulator 901. The digital twin 907 employs a polyhedral combination of neural ODEs.

[0136] The controller 900 submits a control input sequence to the robot manipulator 901. The control input sequence includes voltages and / or currents to the actuators of the robot manipulator 901. Furthermore, the controller 900 collects the output sequence of the robot manipulator 901 caused by the corresponding control input sequence.

[0137] Furthermore, the controller 900 uses a neural network comprising a weighted combination of neural ODEs (Optical Derivatives) including the dynamics of the robot manipulator in the potential space to estimate the current internal state of the digital twin 907. Additionally, based on the current internal state of the digital twin 907, the controller 900 determines the current control input for controlling the robot manipulator 901, and controls the actuators of the robot manipulator 901 according to the current control input, causing the end effector 909 to push the object 903 from the current state to the target state 905.

[0138] Figure 10 A schematic diagram of a computing device 1000 that can be used to implement the control method of this disclosure is shown. The computing device 1000 includes a power supply 1001, a processor 1003, a memory 1005, and a storage device 1007, all of which are connected to a bus 1009. Furthermore, a high-speed interface 1011, a low-speed interface 1013, a high-speed expansion port 1015, and a low-speed connection port 1017 can be connected to the bus 1009. Additionally, a low-speed expansion port 1019 is connected to the bus 1009. Furthermore, an input interface 1021 can be connected via the bus 1009 to an external receiver 1023 and an output interface 1025. A receiver 1027 can be connected via the bus 1009 to external transmitters 1029 and 1031. External memory 1033, external sensors 1035, a machine 1037, and an environment 1039 can also be connected to the bus 1009. Furthermore, one or more external input / output devices 1041 can be connected to the bus 1009. The network interface controller (NIC) 1043 may be adapted to be connected to the network 1045 via the bus 1009, wherein data or other data may be presented on a third-party display device, a third-party imaging device and / or a third-party printing device outside the computer device 1000.

[0139] Memory 1005 may store instructions executable by computer device 1000 and any data usable by the methods and systems of this disclosure. Memory 1005 may include random access memory (RAM), read-only memory (ROM), flash memory, or any other suitable memory system. Memory 1005 may be one or more volatile memory cells and / or one or more non-volatile memory cells. Memory 1005 may also be another form of computer-readable medium, such as a magnetic disk or optical disk.

[0140] Storage device 1007 may be adapted to store supplementary data and / or software modules used by computer device 1000. Storage device 1007 may include hard disk drives, optical disk drives, thumb drives, drive arrays, or any combination thereof. Furthermore, storage device 1007 may contain computer-readable media, such as floppy disk devices, hard disk devices, optical disk devices, or magnetic tape devices, flash memory or other similar solid-state storage devices, or include devices in a storage area network or other configured arrays of devices. Instructions may be stored in an information carrier. When executed by one or more processing devices (e.g., processor 1003), the instructions perform one or more methods such as those described above.

[0141] The computing device 1000 may optionally be linked via a bus 1009 to a display interface or user interface (HMI) 1047, which is adapted to connect the computing device 1000 to a display device 1049 and a keyboard 1051. The display device 1049 may include a computer monitor, camera, television, projector, or mobile device, etc. In some implementations, the computing device 1000 may include a printer interface connected to a printing device, which may include a liquid inkjet printer, solid ink printer, large format printer, thermal printer, UV printer, or dye-sublimation printer, etc.

[0142] High-speed interface 1011 manages bandwidth-intensive operations of computing device 1000, while low-speed interface 1013 manages lower bandwidth-intensive operations. This functional allocation is just one example. In some implementations, high-speed interface 1011 may be connected to memory 1005, user interface (HMI) 1047, keyboard 1051, and display 1049 (e.g., via graphics processor or accelerator), as well as high-speed expansion port 106 that can accept various expansion cards via bus 1009.

[0143] In this implementation, the low-speed interface 1013 is connected to the storage device 1007 and the low-speed expansion port 1017 via a bus 1009. The low-speed expansion port 1017 may include various communication ports (e.g., USB, Bluetooth, Ethernet, Wireless Ethernet) and may connect to one or more input / output devices 1041. The computing device 1000 may be connected to the server 1053 and the rack server 1055. The computing device 1000 may be implemented in many different forms. For example, the computing device 1000 may be implemented as part of the rack server 1055.

[0144] The description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of this disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with a description of the feasibility of implementing one or more exemplary embodiments. Various changes may be made to the function and arrangement of the elements without departing from the spirit and scope of the subject matter set forth in the appended claims.

[0145] Specific details are set forth in the following description to provide a full understanding of the embodiments. However, those skilled in the art will understand that embodiments may be practiced without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form so as not to obscure the embodiments with unnecessary details. In other instances, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. Furthermore, the same reference numerals and names in the various figures denote the same elements.

[0146] Furthermore, the various implementations can be described as processes depicted as flowcharts, flow diagrams, data flow diagrams, structural diagrams, or block diagrams. Although flowcharts may describe operations as sequential processes, many operations can be performed in parallel or simultaneously. Additionally, the order of operations can be rearranged. A process may terminate upon completion of its operations, but may include additional steps not discussed or included in the diagrams. Furthermore, not all operations within any specifically described process will occur in all implementations. A process can correspond to a method, function, procedure, subroutine, subroutine, etc. When a process corresponds to a function, the termination of the function can correspond to the function returning to the calling function or the main function.

[0147] Furthermore, implementations of the disclosed subject matter can be carried out, at least partially, manually or automatically. Manual or automatic implementation can be performed, or at least assisted in, using machines, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, program code or code segments for performing the necessary tasks can be stored in a machine-readable medium. The processor can then perform the necessary tasks.

[0148] The various methods or processes outlined in this article can be encoded as software that can be executed on one or more processors employing any of a variety of operating systems or platforms. Furthermore, such software can be written using a variety of suitable programming languages ​​and / or programming or scripting tools, and can also be compiled into executable machine language code or intermediate code that executes on a framework or virtual machine. Typically, the functionality of program modules can be combined or distributed according to the needs of various implementation methods.

[0149] The embodiments of this disclosure can be implemented as a method, examples of which have been provided. The actions performed as part of the method can be ordered in any suitable manner. Therefore, embodiments can be constructed in which the order of action execution differs from the order shown, and even actions shown as sequential in the illustrative embodiments may include the simultaneous execution of certain actions.

[0150] Furthermore, the embodiments of this disclosure and the functional operations described in this specification can be implemented in digital electronic circuits, tangibly implemented computer software or firmware, computer hardware (including the structures disclosed in this specification and their structural equivalents), or one or more combinations thereof. Additionally, some embodiments of this disclosure can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transient program carrier, for execution by a data processing device or to control the operation of a data processing device. Furthermore, program instructions can be encoded on artificially generated propagation signals (e.g., machine-generated electrical signals, optical signals, or electromagnetic signals), which are generated to encode information for transmission to a suitable receiving device for execution by the data processing device. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or one or more combinations thereof.

[0151] According to embodiments of this disclosure, the term "data processing apparatus" can encompass all types of devices, apparatuses, and machines for processing data, including, for example, programmable processors, computers, or multiple processors or computers. The apparatus may include dedicated logic circuitry, such as FPGAs (Field-Programmable Gate Arrays) or ASICs (Application-Specific Integrated Circuits). In addition to hardware, the apparatus may also include code that creates an execution environment for the computer program involved, such as code constituting processor firmware, protocol stacks, database management systems, operating systems, or combinations thereof.

[0152] Computer programs (also referred to or described as programs, software, software applications, modules, software modules, scripts, or code) can be written in any form of programming language, including compiled, interpreted, declarative, or procedural languages, and can be deployed in any form, including as standalone programs, modules, components, subroutines, or other units suitable for a computing environment. A computer program may (but does not necessarily) correspond to a file in a file system. A program may be stored as part of a file containing other programs or data (e.g., in one or more scripts within a markup language document), in a single file dedicated to the program in question, or in multiple coordinating files (e.g., in a file storing one or more modules, subroutines, or portions of code).

[0153] Computer programs can be deployed to execute on a single computer, or on multiple computers located at a single site or distributed across multiple sites and interconnected via a communication network. Computers suitable for executing computer programs can be based on, for example, general-purpose or special-purpose microprocessors, or both, or any other type of central processing unit (CPU). Typically, the CPU receives instructions and data from read-only memory (ROM) or random access memory (RAM), or both. The basic components of a computer are the CPU for executing instructions and one or more storage devices for storing instructions and data.

[0154] Typically, a computer also includes one or more mass storage devices for storing data, such as disks, magneto-optical disks, or optical disks, or is operatively connected to these devices to receive or transfer data, or both. However, computers are not required to have these devices. Furthermore, computers can be embedded in other devices, such as mobile phones, personal digital assistants (PDAs), mobile audio or video players, game consoles, GPS receivers, or portable storage devices (such as Universal Serial Bus (USB) flash drives), and so on.

[0155] To provide interaction with the user, embodiments of the subject matter described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor), and a keyboard and pointing device (e.g., a mouse or trackball), through which the user provides input to the computer. Other types of devices may also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback, such as visual, auditory, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. Furthermore, the computer can interact with the user by sending documents to and receiving documents from the device used by the user; for example, in response to a request received from a web browser, sending a webpage to a web browser on the user's client device.

[0156] The embodiments of the subject matter described in this specification can be implemented in a computing system that includes back-end components (e.g., a data server), middleware components (e.g., an application server), front-end components (e.g., a client computer with a graphical user interface or a web browser through which a user can interact with the implementation of the subject matter described in this specification), or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected via digital data communication (e.g., a communication network) of any form or medium. Examples of communication networks include local area networks (“LANs”) and wide area networks (“WANs”), such as the Internet.

[0157] Computing systems can include clients and servers. Clients and servers are typically geographically separated and usually interact through communication networks. The client-server relationship originates from computer programs running on their respective computers, and a client-server relationship exists between them.

[0158] While this disclosure has been described with reference to certain preferred embodiments, it should be understood that various other adaptations and modifications can be made within the spirit and scope of this disclosure. Therefore, the appended claims cover all such variations and modifications within the true spirit and scope of this disclosure.

Claims

1. A control method for controlling an electromechanical system according to a task, wherein, At least one of the parameters of the system includes uncertainty, wherein the method uses a processor coupled to stored instructions implementing the method, wherein the instructions, when executed by the processor, perform steps of the method, the method comprising the following steps: An adaptive surrogate model of the system is used to estimate the state of the system to produce an estimate of the state of the system, wherein the adaptive surrogate model includes a neural network that employs a weighted combination of neural ODEs of the dynamics of the system in the latent space, such that the weights of the weighted combination of the neural ODEs represent the uncertainty. Based on the estimation of the system's state, the system is controlled according to the task; and The weights of the weighted combination of the neural ODEs are fine-tuned based on the control.

2. The control method according to claim 1, wherein, The weighted combination is a polyhedral weighted combination of the neural ODEs of the system's dynamics in the potential space.

3. The control method according to claim 1, wherein, The weights of the weighted combination are updated based on the difference between the estimated state of the system and the measured state of the system.

4. The control method according to claim 1, wherein the control method further comprises: The neural network is trained for different parameter values ​​of the system, such that each of the neural ODEs is trained for a specific combination of parameter values ​​of the system.

5. The control method according to claim 1, wherein, The adaptive proxy model includes an autoencoder architecture having: an encoder trained to encode the previous states of the system into the latent space; a weighted combination of neural ODEs trained to propagate the encodings of the previous states in a timely manner; and a decoder trained to decode the estimated state of the system from the propagated encodings of the previous states.

6. The control method according to claim 5, wherein, The encoder includes a weighted combination of encoders, and the decoder includes a weighted combination of decoders.

7. The control method according to claim 6, wherein, The weights in the weighted combination of the encoder and the weights in the weighted combination of the decoder are equal to the weights in the weighted combination of the neural ODE, such that updating the weights in the weighted combination of the neural ODE automatically updates the weights in the weighted combination of the encoder and the weighted combination of the decoder.

8. The control method according to claim 5, wherein, The weighted combination of the neural ODE propagates the encoding of the previous state according to the input control command.

9. The control method according to claim 1, wherein, The state variables of the system are augmented with the weights of the weighted combination.

10. The control method according to claim 9, wherein, The weights of the weighted combination are updated using a probabilistic filter that tracks the augmented state of the system.

11. The control method according to claim 10, wherein, The probability filter includes one or a combination of a Kalman filter and a particle filter.

12. The control method according to claim 1, wherein, The weights of the weighted combination are updated using a probabilistic filter that uses one or a combination of a measurement model and a prediction model employing the neural network to track the state of the system.

13. The control method according to claim 12, wherein the control method further comprises: The probabilistic filter is executed iteratively to generate a state sequence of the system using a prediction model affected by process noise and a measurement model affected by measurement noise, wherein at least one of the prediction model and the measurement model includes the neural network.

14. The control method according to claim 13, wherein, The probabilistic filter is an extended Kalman filter that linearizes the model by differentiating the neural network.

15. The control method according to claim 1, wherein, The system is a robot, and the parameter with uncertainty is the mass value of the robot arm.

16. The control method according to claim 1, wherein, The system is a train, and the parameter with uncertainty is the friction value between the train's track and wheels.

17. The control method according to claim 1, wherein, The system is an air conditioning system, and the parameters with uncertainties are heat load value or ambient air temperature.

18. A controller for controlling an electromechanical system according to a task, wherein, At least one of the parameters of the system includes uncertainty, wherein the controller includes: a processor; and a memory storing instructions that, when executed by the processor, cause the controller to perform the following operations: An adaptive surrogate model of the system is used to estimate the state of the system to produce an estimate of the state of the system, wherein the adaptive surrogate model includes a neural network that employs a weighted combination of neural ODEs of the dynamics of the system in the latent space, such that the weights of the weighted combination of the neural ODEs represent the uncertainty. Based on the estimation of the system's state, the system is controlled according to the task; and The weights of the weighted combination of the neural ODEs are fine-tuned based on the control.

19. The controller according to claim 18, wherein, The weighted combination is a polyhedral weighted combination of the neural ODEs of the system's dynamics in the potential space.

20. A non-transitory computer-readable storage medium having a program executable by a processor embodied thereon, the program being configured to execute a control method for controlling an electromechanical system according to a task, wherein... At least one of the parameters of the system includes uncertainty, and the method includes the following steps: An adaptive surrogate model of the system is used to estimate the state of the system to produce an estimate of the state of the system, wherein the adaptive surrogate model includes a neural network that employs a weighted combination of neural ODEs of the dynamics of the system in the latent space, such that the weights of the weighted combination of the neural ODEs represent uncertainty. Based on the estimation of the system's state, the system is controlled according to the task; and The weights of the weighted combination of the neural ODEs are fine-tuned based on the control.

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