Distributed control method with unknown saturation hysteresis input

Abstract

The invention discloses a distributed control method with unknown saturation hysteresis input, and relates to the technical field of distributed control systems, and the method comprises the following steps: S1, training a meta-learning model through a meta-learning algorithm, learning parameters and structures of a dynamic adjustment robust controller, and forming an offline meta-training stage; s2, real-time system feedback data are received, controller parameters are adjusted through the meta learning model, nonlinear characteristics such as hysteresis and saturation are dynamically compensated, and an online adaptation stage is formed. The parameters of the controller are adjusted on line through the meta-learning model, the nonlinear influence caused by unknown saturation hysteresis can be dynamically compensated, and an accurate nonlinear model is not needed. And in combination with Lyapunov stability analysis and a parameter constraint mechanism, the stability of a closed-loop system in transient and steady-state processes is ensured, and system oscillation caused by parameter adjustment is avoided. And the online adaptation stage can quickly adapt to a new nonlinear scene, and the response speed is improved.

Description

Technical Field

[0001] This invention relates to the field of distributed control system technology, and in particular to a distributed control method for input with unknown saturation hysteresis. Background Technology

[0002] In distributed control systems, due to limitations in actuator physical characteristics or environmental disturbances, the system often exhibits nonlinear characteristics such as saturation (input signal exceeding the actuator's maximum output range) and hysteresis (a non-instantaneous, non-single-value mapping relationship between input and output). These unknown nonlinear characteristics can lead to decreased control accuracy, system response delays, and even instability, severely impacting the cooperative performance of the distributed system.

[0003] In existing technologies, traditional robust control methods (such as sliding mode control and H∞ control) can cope with some nonlinearities, but they rely on accurate system models and have limited adaptability to unknown saturation hysteresis. Adaptive control compensates for nonlinearities by adjusting parameters online, but it suffers from slow convergence speed and poor transient performance. Meta-learning technology has shown potential in rapidly adapting to new tasks, but research on combining it with robust control to handle unknown saturation hysteresis is still incomplete and lacks a systematic stability guarantee mechanism. Summary of the Invention

[0004] The embodiments of the present invention provide a distributed control method with unknown saturated hysteresis input, aiming to solve the problems of limited adaptability to unknown saturated hysteresis due to reliance on accurate system models; adaptive control compensates for nonlinearity through online parameter adjustment, but suffers from slow convergence speed and poor transient performance; meta-learning technology has shown potential in rapidly adapting to new tasks, but research on combining it with robust control to handle unknown saturated hysteresis is still incomplete, lacking systematic stability guarantee mechanisms.

[0005] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0006] A distributed control method for input with unknown saturation hysteresis includes the following steps:

[0007] S1: Train the meta-learning model through the meta-learning algorithm to learn and dynamically adjust the parameters and structure of the robust controller, forming the offline meta-training stage;

[0008] S2: Receive real-time system feedback data, adjust controller parameters through the meta-learning model, dynamically compensate for nonlinear characteristics such as hysteresis and saturation, and form an online adaptation phase;

[0009] S3: Constrain the parameter update range through Lyapunov stability analysis or projected gradient method to ensure the transient and steady-state performance of the closed-loop system, forming a robustness verification stage.

[0010] Furthermore, in S1, the meta-learning algorithms include Model Independent Meta-Learning (MAML), Reptile algorithm, and Online Bayesian Meta-Learning algorithm.

[0011] Furthermore, in S1, the training data of the meta-learning model includes: system state, tracking error, historical control input and corresponding robust controller parameter adjustment results, and the meta-learning model adopts a recurrent neural network (RNN), Transformer or LSTM network structure.

[0012] Furthermore, in S1, the robust controller includes a sliding mode controller and an H∞ controller.

[0013] Furthermore, when the robust controller is a sliding mode controller, the online adaptation phase includes:

[0014] The specific formula for slip surface design is as follows:

[0015] s i =e i +λ∫e i dt,e i =x i -x des .

[0016] Where: x i For the system state, x des This is the desired state;

[0017] The formula for generating online control laws is as follows:

[0018]

[0019] in: Generated by the meta-learning model, θ meta These are the meta-parameters of the meta-learning model, and sat(.) is the saturation function.

[0020] Furthermore, in the robustness verification stage, the sliding mode gain K ≥ Kmin output by the meta-learning model, where Kmin is derived from the system perturbation bound.

[0021] Furthermore, when the robust controller is an H∞ controller, the online adaptation phase includes:

[0022] The basic control law for designing the H∞ controller is as follows:

[0023] u = -Kx, minimize ||T zd || ∞ ,

[0024] Wherein: T zd The transfer function from the perturbation to the output;

[0025] Input: Real-time state x, disturbance estimate d; Output: Adjusted weight matrix Q, R or directly generated K; Initialization parameters are learned using the meta-learning model, fine-tuned online, and a hybrid control law is generated. The specific formula is as follows:

[0026]

[0027] Wherein: g θ (.) represents the meta-network, compensating for unmodeled dynamics.

[0028] Furthermore, it also includes memory-based meta-robust control steps:

[0029] Construct a memory bank: store historical data (xi, ui, H(ui)), where H(ui) is a hysteresis input-output pair;

[0030] Meta-learning query: A compensation signal is generated by retrieving the similarity between the current state x(t) and samples in the memory bank using KNN. The specific formula is as follows:

[0031]

[0032] Hybrid control: The specific formula is as follows:

[0033] u = u robust +u comp ,

[0034] Where u robust This is the robust control base signal.

[0035] Furthermore, in S1, the robustness verification phase includes:

[0036] Stability is ensured by embedding Lyapunov constraints into the loss function of the meta-learning model. The specific formula for the constraints is as follows:

[0037]

[0038] in: Let a be a Lyapunov function, where a > 0.

[0039] Beneficial effects: Online adjustment of controller parameters via a meta-learning model can dynamically compensate for the nonlinear effects of unknown saturation hysteresis without requiring a precise nonlinear model. Combining Lyapunov stability analysis and parameter constraint mechanisms ensures the stability of the closed-loop system during transient and steady-state processes, avoiding system oscillations caused by parameter adjustments. The online adaptation phase allows for rapid adaptation to new nonlinear scenarios, improving response speed. Attached Figure Description

[0040] Figure 1This is a schematic diagram of the process of the present invention; Detailed Implementation

[0041] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0042] In the description of this invention, it should be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0043] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0044] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0045] Combination Figure 1 As shown, this invention provides a distributed control method for inputs with unknown saturation hysteresis, comprising the following steps:

[0046] S1: Train the meta-learning model through the meta-learning algorithm to learn and dynamically adjust the parameters and structure of the robust controller, forming the offline meta-training stage;

[0047] S2: Receive real-time system feedback data, adjust controller parameters through the meta-learning model, dynamically compensate for nonlinear characteristics such as hysteresis and saturation, and form an online adaptation phase;

[0048] S3: Constrain the parameter update range through Lyapunov stability analysis or projected gradient method to ensure the transient and steady-state performance of the closed-loop system, forming a robustness verification stage.

[0049] This invention provides a distributed control method for inputs with unknown saturated hysteresis. By adjusting controller parameters online through a meta-learning model, it can dynamically compensate for the nonlinear effects of unknown saturated hysteresis without requiring a precise nonlinear model. Combining Lyapunov stability analysis and parameter constraint mechanisms, it ensures the stability of the closed-loop system in both transient and steady-state processes, avoiding system oscillations caused by parameter adjustments. The online adaptation phase can quickly adapt to new nonlinear scenarios, improving response speed.

[0050] In embodiments of the present invention, the meta-learning algorithm includes Model Independent Meta-Learning (MAML), Reptile algorithm, and Online Bayesian Meta-Learning algorithm.

[0051] In embodiments of the present invention, the training data of the meta-learning model includes: system state, tracking error, historical control input and corresponding robust controller parameter adjustment results, and the meta-learning model adopts a recurrent neural network (RNN), Transformer or LSTM network structure.

[0052] In embodiments of the present invention, the robust controller includes a sliding mode controller and an H∞ controller.

[0053] In an embodiment of the present invention, when the robust controller is a sliding mode controller, the online adaptation phase includes:

[0054] The specific formula for slip surface design is as follows:

[0055] s i =e i +λ∫e i dt,e i =x i -x des .

[0056] Where: x i For the system state, x des This is the desired state;

[0057] The formula for generating online control laws is as follows:

[0058]

[0059] in: Generated by the meta-learning model, θ meta These are the meta-parameters of the meta-learning model, and sat(.) is the saturation function.

[0060] In an embodiment of the present invention, during the robustness verification stage, the sliding mode gain K output by the meta-learning model is greater than or equal to Kmin, where Kmin is derived from the system perturbation bound.

[0061] In an embodiment of the present invention, when the robust controller is an H∞ controller, the online adaptation phase includes:

[0062] The basic control law for designing the H∞ controller is as follows:

[0063] u = -Kx, minimize ||T zd || ∞ ,

[0064] Wherein: T zd The transfer function from the perturbation to the output;

[0065] Input: Real-time state x, disturbance estimate d; Output: Adjusted weight matrix Q, R or directly generated K; Initialization parameters are learned using the meta-learning model, fine-tuned online, and a hybrid control law is generated. The specific formula is as follows:

[0066]

[0067] Wherein: g θ (.) represents the meta-network, compensating for unmodeled dynamics.

[0068] In embodiments of the present invention, a memory-based meta-robust control step is also included:

[0069] Construct a memory bank: store historical data ((xi,ui,(H)(ui)), where (H)(ui) are hysteresis input-output pairs;

[0070] Meta-learning query: A compensation signal is generated by using KNN to retrieve the similarity between the current state \(x(t)\) and the samples in the memory bank. The specific formula is as follows:

[0071]

[0072] Hybrid control: The specific formula is as follows:

[0073] u = u robust +u comp ,

[0074] Where u robust This is the robust control base signal.

[0075] In an embodiment of the present invention, the robustness verification stage includes:

[0076] Stability is ensured by embedding Lyapunov constraints into the loss function of the meta-learning model. The specific formula for the constraints is as follows:

[0077]

[0078] in: Let a be a Lyapunov function, where a > 0.

[0079] A distributed control method for input with unknown saturation hysteresis, comprising the following steps:

[0080] Example 1

[0081] S1: Offline meta-training phase:

[0082] The meta-learning algorithm is MAML, and the robust controller is sliding mode controller.

[0083] Training data acquisition: Simulating system states x under different hysteresis intensities (0.1–0.5) and saturation boundary conditions (±5V). i (Position, Velocity), Tracking Error e i Historical control input u i and the corresponding sliding mode gain adjustment results;

[0084] The meta-learning model uses an LSTM network, with input being (x i ,e i ,u i The output is the adjustment amount of the sliding mode gain K;

[0085] Training objective: To minimize control error while ensuring stability through Lyapunov constraints (V≤-0.2V).

[0086] S2: Online Adaptation Phase

[0087] Real-time acquisition of system status x i and desired state x des Calculate the tracking error e i =x i -x des ;

[0088] Sliding surface design: When λ = 0.5, s i =e i +0.5∫e i dt;

[0089] Meta-learning models are based on (x) i ,e i Output sliding mode gain K to generate control law:

[0090] (θ=0.3) is the saturation boundary.

[0091] S3: Robustness verification phase:

[0092] The system disturbance bound Δmax = 0.8 is calculated, and Kmin = 1.2 is derived. The output of the constraint meta-learning model is (K ≥ 1.2).

[0093] Verify using the Lyapunov function (V = 0.5s_i^2) that V ≤ -0.2V, ensuring s i It converges to 0.

[0094] Example 2

[0095] S1: Offline meta-training phase:

[0096] The Reptile meta-learning algorithm is selected, and the robust controller is the H∞ controller.

[0097] The training data includes grid frequency x, disturbance d (such as load fluctuation), historical control input u, and the adjustment results of H∞ weight matrices Q and R;

[0098] The meta-learning model adopts a Transformer structure, with input (x,d) and output corrections for Q and R.

[0099] S2: Online Adaptation Phase

[0100] Basic control law: K is solved by Q and R using the Riccati equation;

[0101] Meta-network output compensation signal u meta =g θ (x,d), mixed control law:

[0102] S3: Robustness verification phase:

[0103] By constraining Q>0 and R>0 using the projection gradient method, the performance index ||T of H∞ is ensured. zd || ∞ ≤γ, γ=1.5 are preset values;

[0104] The stability of the system is verified using the Lyapunov function V = x^TP x (where P is a positive definite matrix).

[0105] In the description of this specification, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0106] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A distributed control method with unknown saturation hysteresis input, characterized by, The method comprises the following steps: S1: training a meta-learning model by a meta-learning algorithm to learn to dynamically adjust parameters and structure of a robust controller, forming an offline meta-training stage; S2: receiving real-time system feedback data, adjusting controller parameters by the meta-learning model to dynamically compensate for nonlinear characteristics such as hysteresis and saturation, forming an online adaptation stage; S3: constraining the parameter update range by Lyapunov stability analysis or projection gradient method to ensure the transient and steady-state performance of the closed-loop system, forming a robustness verification stage.

2. The distributed control method with unknown saturation hysteresis input according to claim 1, wherein, In S1, the meta-learning algorithm comprises model-agnostic meta-learning (MAML), Reptile algorithm, and online Bayesian meta-learning algorithm.

3. The distributed control method with unknown saturation hysteresis input according to claim 1, wherein, In S1, the training data of the meta-learning model comprises system state, tracking error, historical control input, and corresponding robust controller parameter adjustment result, and the meta-learning model adopts a recurrent neural network (RNN), a Transformer, or an LSTM network structure.

4. The distributed control method with unknown saturation hysteresis input according to claim 1, wherein, In S1, the robust controller comprises a sliding mode controller and an H∞ controller.

5. The distributed control method with unknown saturation hysteresis input according to claim 4, wherein, When the robust controller is a sliding mode controller, the online adaptation stage comprises: sliding mode surface design, with the specific formula being: s i = e i + λ∫e i dt, e i = x i - x des . where: x i is the system state, x des is the desired state; generating an online control law, with the specific formula being: wherein: generated by the meta-learning model, θ meta is a meta-parameter of the meta-learning model, sat(.) is a saturation function.

6. The distributed control method with unknown saturation hysteresis input according to claim 5, wherein, In the robustness verification stage, the sliding mode gain K output by the meta-learning model is greater than or equal to Kmin, where Kmin is derived from the system disturbance bound.

7. The distributed control method with unknown saturation hysteresis input according to claim 4, wherein, When the robust controller is an H∞ controller, the online adaptation stage comprises: designing a basic control law of the H∞ controller, with the specific formula being: u = -Kx, minimize ||T zd || ∞ , where: T zd is the transfer function of the disturbance to the output; input: real-time state x, disturbance estimation d, output: adjustment weight matrix Q, R, or directly generating K, using the meta-learning model to learn the initialization parameters, online fine-tuning, generating a hybrid control law, with the specific formula being: where: g θ (.) is a meta-network that compensates for unmodeled dynamics.

8. The distributed control method with unknown saturation hysteresis input according to claim 1, wherein, It also comprises a memory-based meta-robust control step: constructing a memory bank: storing historical data ((xi, ui, H(ui)), where H(ui) is a hysteresis input-output pair; meta-learning query: retrieving the similarity between the current state x(t) and the memory bank samples by KNN to generate a compensation signal, with the specific formula being: hybrid control: with the specific formula being: u = u robust + u comp , where u robust is the robust control base signal.

9. The distributed control method with unknown saturation hysteresis input according to claim 1, wherein, In S1, the robustness verification stage comprises: embedding a Lyapunov constraint in the loss function of the meta-learning model to ensure stability, with the specific formula being: where: is a Lyapunov function, a > 0.

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