Brain-like adaptive optimal control method and system based on Lyapunov stability and information geometric constraint
By employing multi-timescale adaptive state updates and Lyapunov stability and information geometry constraint mechanisms, the slow convergence speed and oscillation problems of adaptive control methods under random disturbances are solved, achieving global stability and near-optimal control performance of the system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-24
- Publication Date
- 2026-03-27
AI Technical Summary
Existing adaptive control methods are prone to slow convergence, oscillation, or even divergence when the system has random disturbances, parameter uncertainties, or partial observability. Furthermore, existing methods lack a joint constraint mechanism for global stability and parameter identifiability.
An adaptive optimal control method is constructed by employing a multi-timescale adaptive state update mechanism, Lyapunov stability constraints, and information geometry constraints. The stability and parameter updates of the system are constrained by the Lyapunov energy function and Fisher information matrix, thereby achieving global convergence and near-optimal control of the system under random disturbances.
It ensures the global stability of the system under random disturbance conditions, improves the identifiability and robustness of online updates of control parameters, achieves near-optimal feedback control performance, and has a simple and easy-to-implement structure.
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Abstract
Description
TECHNICAL FIELD
[0002] The present application relates to the technical field of adaptive control, intelligent control and computer control,
[0003] In particular, it relates to a brain-like adaptive optimal control method and system that integrates multi-time scale adaptive mechanism, stability constraint and information geometry constraint. BACKGROUND
[0004] Existing adaptive control methods mostly rely on fixed parameter models or single time scale update mechanism, and under the conditions of random disturbance, parameter uncertainty or partial observability, the convergence speed is slow, oscillation or even divergence.
[0005] Although the multi-time scale adaptive model can improve the convergence performance to some extent, most methods are designed from the experience or statistical point of view, and lack of joint constraint mechanism for global stability and parameter identifiability.
[0006] On the other hand, existing methods based on optimal control or Bayesian inference often focus on performance optimization or parameter estimation accuracy, and fail to introduce explicit stability criteria in the online update process of control parameters, making it difficult to guarantee the boundedness of system state under noise environment.
[0007] Therefore, there is an urgent need for an adaptive control method that can guarantee the global stability of the system, the controllability of the parameter update and the approximate optimal control performance under random disturbance conditions.
[0008] PURPOSE OF THE INVENTION
[0009] The purpose of the present application is to provide a brain-like adaptive optimal control method and system based on Lyapunov stability and information geometry constraint,
[0010] By introducing multi-time scale adaptive state update mechanism, stability constraint mechanism and information geometry constraint mechanism,
[0011] Global convergence of system state is achieved under random disturbance conditions, and the control performance is approximated to the preset optimal feedback control solution.
[0012] TECHNICAL SCHEME
[0013] I. Overall flow of the method
[0014] The adaptive optimal control method provided by the present application comprises the following steps:
[0015] · Obtain the system state and the reference input signal;
[0016] · Construct a multi-time scale adaptive state update model based on error signal;
[0017] • Construct Lyapunov energy function based on the adaptive state to constrain the system stability;
[0018] • Construct Fisher information matrix using the partial derivative of the system output with respect to the control parameters, and constrain the parameter update in information geometry under the stability constraint condition;
[0019] • Update the control parameters online under the above joint constraint condition, and apply the control input signal to make the system state gradually converge under random vibration conditions.
[0020] II. Multi-time scale adaptive model
[0021] In a preferred embodiment, the adaptive process is composed of at least one fast adaptive state variable and one slow adaptive state variable, and their update relationship is:
[0022] And through different state holding coefficients and learning gains, the fast and slow processes are updated cooperatively.
[0023] III. Stability constraint mechanism (Lyapunov)
[0024] Construct Lyapunov function with system state vector as the independent variable, constrain the energy function to be monotonically decreasing at discrete time,
[0025] And further constrain the spectral radius of the system state transition matrix to be within the unit circle, so as to ensure the global asymptotic stability of the system under random disturbance.
[0026] IV. Information geometric constraint mechanism (Fisher)
[0027] By calculating the partial derivative of the system output with respect to the control parameters, construct the Jacobian matrix, and obtain the Fisher information matrix from it.
[0028] Use the eigenvalues or eigenvalues of the Fisher information matrix to constrain the update direction and update amplitude of the control parameters,
[0029] So as to improve the identifiability and noise immunity of parameter estimation.
[0030] V. Optimal control approximation (LQR alignment)
[0031] In the steady state phase, align or approximate the adaptive control parameters with the feedback gain corresponding to the linear quadratic regulator,
[0032] So that the control performance approximates the preset optimal control index under the premise of meeting the stability constraint.
[0033] Advantages
[0034] The present application has at least the following beneficial effects:
[0035] Guarantee the global stability of the system under random disturbance conditions;
[0036] Improve the identifiability and robustness of the control parameters in the online updating process;
[0037] Achieve approximate optimal feedback control performance without explicitly solving the optimal control problem;
[0038] Simple structure, easy to implement in electronic devices or embedded control systems. BRIEF DESCRIPTION OF DRAWINGS Figure 1 The dynamic stability and uncertainty structure of the adaptive optimal control method of the present application under different feedback gain conditions are shown, including Lyapunov index distribution, convergence time constant statistical distribution, and error variance stability landscape; Figure 2 The structural complexity and optimal control performance of different control architectures are shown; Figure 3 The control parameter identifiability and noise resistance performance analysis results based on Fisher information are shown; Figure 4 The time domain and frequency domain coordination characteristics of the multi-time scale adaptive process are shown; Figure 5 The parameter posterior distribution based on hierarchical Bayesian inference and model generalization performance verification results are shown. DETAILED EMBODIMENTS
[0039] Embodiment one: stability and robustness verification of adaptive control system (corresponding to Figure 1 )
[0040] In an embodiment, the method of the present application is used to analyze the dynamic stability and disturbance resistance performance of the control system under different feedback gain conditions.
[0041] Figure 1 A shows the Lyapunov index distribution of the system under different control gain conditions, and the Lyapunov index analysis of this embodiment corresponds to step S3 of claim 1. It can be seen that all Lyapunov indices are negative in the stable state, indicating that the system remains asymptotically stable under random disturbance conditions.
[0042] Figure 1 B shows the distribution of the system convergence time constant τ under ±5% control parameter disturbance conditions, corresponding to step S5 of claim 1, and the results show that the convergence time varies within a small range, verifying the robustness of the system to parameter disturbance.
[0043] Figure 1C presents a three-dimensional error variance stability landscape, with the error minimum forming a smooth basin, corresponding to steps S3 and S5, indicating that the system has a stable attractor under the nominal gain configuration, ensuring global convergence of the control process.
[0044] This embodiment verifies that the method of the present application realizes global stability and robust performance of the system through Lyapunov stability constraints and multi-time scale adaptive state update.
[0045] Embodiment Two: Multi-state adaptive control structure and optimal control approximation (corresponding to Figure 2 )
[0046] In another embodiment, a multi-time scale adaptive controller based on two-state, three-state and nonlinear extension is constructed to analyze its control performance and complexity.
[0047] Figure 2 A shows simulation results of three control architectures, corresponding to steps S2 and S3 of claim 1, wherein the Triple model can capture the nonlinear saturation characteristics, the error is significantly reduced and no additional instability is introduced.
[0048] Figure 2 B shows the comparison results of control input signals and linear quadratic regulator (LQR) feedback gains, corresponding to steps S5 and S6, the biological PID approximation signal is highly consistent with the LQR output, indicating that the approximate optimal control is realized by online updating of the control parameters.
[0049] Figure 2 C is a complexity analysis, corresponding to steps S2 and S5, showing that the fitting accuracy of the Beyond Triple model is limited, verifying the characteristics of the system structure being simple and close to optimal control.
[0050] Figure 2 D presents the bias-variance decomposition results, further illustrating that the Triple structure minimizes the error while maintaining low variance, embodying the high efficiency of the controller, corresponding to steps S2 and S4.
[0051] This embodiment proves that the method of the present application can realize the balance between stability and optimal control performance through an extensible multi-state control structure.
[0052] Embodiment Three: Control parameter identifiability and noise resistance performance analysis (corresponding to Figure 3 )
[0053] In an embodiment, a Jacobian matrix is constructed by calculating the partial derivative of the controller output with respect to the control parameters, and a Fisher information matrix is further calculated to evaluate the parameter identifiability.
[0054] Figure 3A shows Fisher information spectrum exhibits significant eigenvalues in mid-frequency band, indicating that the key control gain is highly sensitive to system output, which corresponds to step S4 of claim 1, and reliable identification can be achieved.
[0055] Figure 3 B presents A_f-B_f parameter interaction surface, which corresponds to step S4 and reflects the nonlinear coupling relationship between learning gain and state retention coefficient, indicating the constraint region of stability and error minimization.
[0056] Figure 3 C shows that under the condition of introducing random noise, by estimating the control parameters multiple times, the parameter recovery error is maintained within ±2%, which corresponds to steps S4 and S5, verifying the robustness of control parameter estimation.
[0057] This embodiment shows that the present application combines Lyapunov constraint and information geometric constraint to achieve the identifiability and robustness of control parameters under random disturbance.
[0058] Example Four: Multi-time scale adaptive characteristics and frequency domain coordination (corresponding to Figure 4 )
[0059] In an embodiment, by performing principal component analysis and frequency domain analysis on multi-time scale adaptive state variables, the synergistic characteristics of fast and slow adaptive processes are evaluated.
[0060] Figure 4 A shows the PCA projection result, which corresponds to steps S2 and S6, and most of the variance of the adaptive state variable is explained by the first two principal components, indicating that the system behavior evolves in a low-dimensional feature subspace.
[0061] Figure 4 B shows the power distribution changes in different frequency bands, which corresponds to step S2, and there is energy transfer between fast and slow processes, reflecting the synergistic relationship of multi-time scale feedback.
[0062] Figure 4 C is the circular histogram of the instantaneous phase difference of the adaptive state, which corresponds to steps S2 and S6, and indicates that the fast and slow processes maintain consistent phase relationship, supporting the multi-time scale cooperation mechanism.
[0063] This embodiment is an optional implementation for analyzing the low-dimensional features and frequency domain coordination of the internal state of the system.
[0064] Example Five: Bayesian parameter modeling and generalization verification (corresponding to Figure 5 )
[0065] In an embodiment, hierarchical Bayesian inference is used to probabilistically model the control parameters to evaluate the parameter uncertainty and system generalization ability.
[0066] Figure 5 A display and The posterior distribution and high density interval of the parameters, corresponding to steps S4, S5, S6, verify the high confidence of the parameter estimation results.
[0067] Figure 5 B. Perform model space comparison, PID and LQR model WAIC weight is higher, corresponding to steps S4, S5, show that its prediction ability is better than the traditional two-state model.
[0068] Figure 5 C. Through Leave-One-Subject-Out cross-validation, it is confirmed that the prediction error of the controller under unseen samples is low, which reflects good generalization ability, corresponding to steps S5, S6.
[0069] This embodiment is a preferred embodiment, which is used to further enhance the reliability of the control parameter estimation and the adaptability of the system.
Claims
1. An adaptive optimal control method based on Lyapunov stability and information geometric constraints, characterized in that, Includes the following steps: S1. Obtain the system state information and reference input signal of the controlled object at discrete time t, and generate an error signal based on the difference between the reference input signal and the system output signal; S2. Based on the error signal, update the multi-timescale adaptive state variables inside the controller. The multi-timescale adaptive state variables include at least one fast adaptive state variable and one slow adaptive state variable, and the two have different state preservation coefficients and learning gains. S3. Construct a system state vector containing the multi-timescale adaptive state variables, and construct a Lyapunov function based on the system state vector to determine the system stability, and constrain the system state transition matrix to satisfy the stability condition that the spectral radius is less than a preset threshold. S4. Construct a Jacobian matrix based on the partial derivatives of the system output with respect to the control parameters, and construct a Fisher information matrix from the Jacobian matrix. Under the premise of satisfying the Lyapunov stability constraint, use the information geometric constraint as one of the parameter update conditions to constrain the update direction and update magnitude of the control parameters. S5. Under the combined effect of the stability constraint and the information geometry constraint, the control parameters are updated online adaptively, and a control input signal is generated based on the updated control parameters. S6. Apply the control input signal to the controlled object so that the system state gradually converges under the condition of random disturbance, and make the control input signal approach the optimal feedback control solution under the preset performance index in the steady state stage.
2. The adaptive optimal control method according to claim 1, characterized in that, The fast adaptive state variables and slow adaptive state variables are updated according to the following discrete state update methods: in, , These are the state preservation coefficients, and they satisfy 0 < 1. < <1, , Here, e(t) represents the learning gain parameter, and e(t) represents the error signal. The values of the state preservation coefficient and the learning gain are chosen such that the spectral radius of the system state transition matrix is less than 1, thereby ensuring system stability.
3. The adaptive optimal control method according to claim 1 or 2, characterized in that, The multi-timescale adaptive state variables also include at least one additional adaptive state variable, which is used to describe medium- to long-term integral effects or nonlinear dynamic characteristics, and is updated as part of the state update rule through a nonlinear function, a threshold function, or a saturation function to limit the amplitude of the state variables and suppress divergence or oscillation in the adaptive process.
4. The adaptive optimal control method according to claim 1, characterized in that, The Lyapunov function is a quadratic energy function of the system state vector. By constraining the energy function to decrease monotonically at discrete update times, the asymptotic stability of the system under random disturbance conditions is guaranteed.
5. The adaptive optimal control method according to claim 1, characterized in that, The Fisher information matrix is calculated from the Jacobian matrix formed by the partial derivatives of the system output with respect to the control parameters. By weighting the eigenvalues or eigenspectrum of the Fisher information matrix, the update step size of the control parameters is adaptively adjusted to improve the identifiability and noise resistance of the control parameter estimation.
6. The adaptive optimal control method according to claim 1, characterized in that, A hierarchical Bayesian inference method is used to probabilistically model the control parameters, and the update range of the control parameters is constrained according to the confidence interval of the posterior distribution to improve the robustness and repeatability of the parameter estimation results.
7. The adaptive optimal control method according to claim 1, characterized in that, The control input signal is aligned or approximated by the feedback gain corresponding to the linear quadratic regulator so that the adaptive control process satisfies the near-optimal control characteristics under the preset performance index in the steady state stage.
8. A brain-like adaptive optimal control system based on Lyapunov stability and information geometric constraints, characterized in that, The control system is used to execute the adaptive optimal control method as described in any one of claims 1 to 7. It also includes: - a state acquisition module, used to acquire the system state information and reference input signal of the controlled object at the current discrete moment; - Error signal generation module, used to generate an error signal based on the difference between the reference input signal and the system output signal; - A multi-time-scale adaptive state update module is used to update at least one fast adaptive state variable and one slow adaptive state variable based on the error signal, so as to form a multi-time-scale adaptive control structure. - Stability constraint module, used to construct Lyapunov function and determine the stability of system state vector containing the fast adaptive state variable and slow adaptive state variable, so as to constrain the system state transition matrix to meet the preset stability condition. - Information geometric constraint module, used to calculate the Jacobian matrix based on the partial derivatives of the system output with respect to the control parameters, and to construct the Fisher information matrix based on the Jacobian matrix to constrain the update direction and update magnitude of the control parameters; - A parameter adaptive update module is used to update the control parameters online under the combined action of the stability constraint module and the information geometry constraint module; - A control output module is used to generate a control input signal based on the updated control parameters and apply the control input signal to the controlled object so that the system state remains stable and gradually converges under random disturbance conditions.
9. The control system according to claim 8, characterized in that, Preferably, the multi-timescale adaptive state update module further includes at least one additional adaptive state variable for describing medium- to long-term integral characteristics or nonlinear saturation characteristics.
10. The control system according to claim 8, characterized in that, The stability constraint module constructs a quadratic energy function of the system state vector, constrains the spectral radius of the system state transition matrix to be within the unit circle, and constrains the energy function to decrease monotonically at continuous update times, so as to ensure the asymptotic stability of the system.
11. The control system according to claim 8, characterized in that, The information geometric constraint module adjusts the step size and direction of the control parameter update by weighting the eigenvalues of the Fisher information matrix, thereby improving the identifiability and noise resistance of the parameter estimation.
12. An electronic device, characterized in that, include: - At least one processor; - A memory that is communicatively connected to the processor; The memory stores a computer program, which, when executed by the processor, causes the processor to perform the adaptive optimal control method as described in any one of claims 1 to 7.