H-infinity control method of multi-drive servo system based on event triggering

Abstract

The invention relates to an H-infinity control method of a multi-drive servo system based on event triggering, which comprises the following steps of: establishing a multi-drive servo system model with interference, decoupling the interference, and establishing an optimal value function of the system under a time triggering mechanism; performing system identification on the system model by using the identification neural network to obtain an identification system model based on the neural network; based on an event triggering mechanism, judging whether an error triggered by an event violates a set threshold value, if not, not updating the controller, and if yes, updating the controller by using an optimal control strategy obtained by calculation to cope with the interference under the worst condition and complete the H-infinity control process; wherein the process of obtaining the optimal control strategy and the worst interference strategy obtained by calculation comprises the step of approaching an optimal value function by using a criticality neural network to obtain a final control strategy and a final interference strategy. Compared with the prior art, the method has the advantages that the accuracy of system state prediction is improved, and meanwhile waste of computing resources is reduced.

Description

Technical Field

[0001] The present invention relates to the field of control technology, and in particular to an H-type multi-drive servo system based on event triggering. ∞ Control method. Background Art

[0002] With the rapid development of artificial intelligence technology, multi-drive servo systems have also received more in-depth attention and research, and have been widely used in industrial automation, robotics, aerospace, energy production, medical equipment and other fields. Such systems are usually driven by multiple motors and require coordinated control to achieve complex motion and precise position control. However, the parameters and states of multi-drive servo systems are often difficult to accurately predict, and the dynamic characteristics of the system may be affected by various factors such as interference from the external environment. At the same time, when the system state does not change significantly, the time-triggered control strategy with a fixed update interval will lead to a waste of computing resources, especially in the face of external interference and system uncertainty.

[0003] Traditional servo control systems usually adopt a periodic sampling and control update strategy, which may lead to too frequent control input, increasing the energy consumption and computational burden of the system. In practical applications, such excessive control activity is not always necessary, especially when the system state changes slightly. Secondly, existing control methods often rely on complex mathematical models and precise parameter adjustments when dealing with the coupling characteristics and nonlinear dynamics of multi-drive systems. This not only increases the difficulty of system design, but also limits its adaptability to model uncertainties and external disturbances.

[0004] H ∞ The control method is a robust control method that designs the controller by minimizing the sensitivity of the system to external disturbances to ensure system performance. ∞ The application of control theory to servo control systems can effectively deal with system uncertainties and external disturbances and improve the robustness of the system.

[0005] In addition, many existing servo control systems have insufficient response speed and regulation capabilities when faced with rapidly changing working environments and load conditions. This can lead to system performance degradation or even loss of stability in extreme cases. In response to increasingly complex mission scenarios, a better control method is urgently needed to better meet actual needs. Summary of the invention

[0006] The purpose of the present invention is to provide a method for improving the prediction accuracy of system state and the stability control of the system based on event triggering of a multi-drive servo system. ∞ Control method.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A H-type multi-drive servo system based on event triggering ∞ The control method comprises the following steps:

[0009] A multi-drive servo system model with interference is established to decouple the interference and establish the optimal value function V of the system under the time trigger mechanism. i * (x);

[0010] The identification neural network is used to identify the multi-drive servo system model with interference, and the neural network-based identification system model is obtained;

[0011] Based on the event triggering mechanism, the error e(λ k ) Whether it violates the set threshold e T If not, the controller is not updated. If so, the controller is updated with the calculated optimal control strategy to cope with the worst-case disturbance. ∞ Control process;

[0012] The process of obtaining the calculated optimal control strategy and the worst interference strategy includes:

[0013] In combination with the neural network-based identification system model and event triggering mechanism, the optimal value function is approximated by the critical neural network to obtain the final control strategy and interference strategy.

[0014] Furthermore, the expression of the multi-drive servo system model with interference is:

[0015]

[0016] In the formula, is a multi-drive servo system model with disturbance, x is the system state vector, f(x), g j (x), k(x) are the drift system dynamics, input dynamics and disturbance dynamics respectively, u j represents the control input, d is the unknown, bounded input disturbance, satisfying d≤d m , where d m is a normal number, and N is a normal number.

[0017] Furthermore, the expression for decoupling interference is:

[0018] d(τ)=d1(τ)+…d i (τ)+…d N (τ)

[0019] Where d(τ) is the interference, d i(τ) is the i-th disturbance after decoupling.

[0020] Furthermore, the step of obtaining a neural network-based identification system model includes:

[0021] The drift system dynamics, input dynamics and disturbance dynamics in the multi-drive servo system model with disturbance decoupling are identified using an identification neural network. The system is expressed as:

[0022]

[0023] Using approximate weights Estimate the state variables x and the ideal weights W a ,W jb ,W c , the system is expressed as:

[0024]

[0025] According to the weight update rule, the approximate weights in the identification neural network are updated, and after repeated iterative optimization, the final neural network-based identification system model is obtained;

[0026] In the formula, is the multi-drive servo system model with disturbance, A is the constant matrix, W c T To identify the transpose of the ideal weight vector of a neural network, σ a (·),σ jb (·),σ c (·) is the activation function, ε a , ε jb , ε c is the residual of the neural network, u j is the jth control input, x is the system state vector, N is a positive integer, d is an unknown, bounded input disturbance, is the approximate multi-drive servo system model with disturbance, is the approximate system state vector, is the transpose of the approximate weights.

[0027] Furthermore, the weight update rule is:

[0028]

[0029] In the formula, is the transpose of the approximate weight, α a , α jb , α c is the learning rate, σ a (·),σ jb (·),σc (·) is the activation function, is the transpose of the state estimation error.

[0030] Furthermore, the optimal value function V of the system under the time trigger mechanism is established i * The step (x) comprises:

[0031] Based on the multi-drive servo system model after disturbance decoupling, the value function of the system is defined as follows:

[0032]

[0033] in:

[0034]

[0035] Based on the value function of the system, combined with the event trigger mechanism, a system H ∞ The optimal value function of the performance index reaching the overall optimal is expressed as:

[0036]

[0037] Where V i (x) is the value function, x is the system state vector, u i is the i-th control strategy, d is an unknown, bounded input disturbance, satisfying d≤d m , where d m is a normal number, u j represents the jth control input, Q i is a positive definite matrix, N is a positive integer, R ij is a symmetric positive definite matrix, w i (·) is the utility function, γ is a positive constant, indicating the degree of disturbance attenuation, V i * (x) is the optimal value function and T is the transpose of the matrix.

[0038] Furthermore, according to the value function of the system, the HJI equation of the system is defined and solved, and the expression is:

[0039]

[0040] According to the solved HJI equation, the theoretically nonlinear time-triggered control strategy and interference strategy of the system are obtained, and the expressions are:

[0041]

[0042] Where x is the system state vector, R ij is a symmetric positive definite matrix, w i(·) is the utility function, V i * (x) is the optimal value function, T is the transpose of the matrix, is the optimal control strategy, is the matrix R ii The inverse matrix of i * is the function V i * The gradient operator with respect to the variable x, is the interference strategy for the ith input, k(x) is the interference dynamics, is the ith disturbance after decoupling, g i (x) is the ith input dynamics, g j (x) is the jth input dynamics.

[0043] Furthermore, the error e(λ k )for:

[0044] e(λ k )=x k -x(t)

[0045] In the formula, e(λ k ) is the error triggered by the event, λ k is the kth sampling time, x k is the sampling state, and x(t) is the state variable.

[0046] Furthermore, the expressions of the control strategy and interference strategy obtained according to the optimal value function are:

[0047]

[0048] In the formula, R ij is a symmetric positive definite matrix, is the matrix R ii The inverse matrix of are the approximate weights of the identification neural network, T is the transpose of the matrix, σ a (·),σ ib (·),σ jb (·),σ c (·) is the activation function of the identification neural network, N is a positive integer, and γ is a positive constant, which indicates the degree of disturbance attenuation.

[0049] Furthermore, in the process of approximating the optimal value function, the optimal value function is approximated by a critical neural network. use Estimating ideal weights Get the approximate value function The specific steps to obtain the final event-triggered control law and interference strategy include:

[0050] The approximate Hamiltonian function is:

[0051]

[0052] The control law and interference law for:

[0053]

[0054] Select the residual square, the expression is:

[0055]

[0056] The gradient descent method is used to update the weights of the critical neural network to obtain an approximate optimal value function. The expression of the weight update is:

[0057]

[0058] Where η i is the learning rate, H i (·) is the Hamiltonian function, x is the system state vector,

[0059] λ k is the kth sampling time, yes The estimated value of yes The estimated value of yes The estimated value of To critique the ideal weights of a neural network, Criticizing the estimated weights of the neural network, b i is the reconstruction error, To criticize the activation function of the neural network, For function The derivative of x, w i (·) is the utility function, N is a positive integer, are the approximate weights of the identification neural network, σ a (·),σ jb (·),σ c (·) is the activation function of the identification neural network, E c is the objective function, For function Derivative of x, T is the transpose of the matrix, W a , W jb , W cTo identify the ideal weight vector of a neural network, is the approximate weight of the neural network, To identify the weight estimation error of the neural network, u j is the jth control input, d is the unknown, bounded input disturbance, and γ is a positive constant indicating the degree of disturbance attenuation.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] (1) The present invention is aimed at a multi-drive servo system with interference, and decouples the interference to ensure the H of the system. ∞ The performance index reaches the Nash equilibrium state, and the nonlinear modeling ability of the identification neural network is considered to be used to identify the dynamic characteristics of the multi-drive servo system to improve the accuracy of the system state prediction. At the same time, the critical neural network model is used to approximate the value function to solve the nonlinear solution problem. Compared with the prior art, the present invention improves the accuracy of the system state prediction, thereby achieving stable control of the system.

[0062] (2) The present invention utilizes an event-triggered control strategy to update the control input and interference strategy only when the system state changes significantly, thereby significantly reducing the waste of system controller computing resources and maintaining system stability.

[0063] (3) The present invention can be applied to edge computing systems such as gantry cranes, unmanned systems, robotic arms, energy storage, and industrial processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a schematic diagram of the method flow of the present invention. DETAILED DESCRIPTION

[0065] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0066] This embodiment provides a multi-drive servo system based on event triggering. ∞ The control method takes into account the problem that the state and parameters of the multi-drive servo system are difficult to predict accurately, and the time-triggered control input will lead to a waste of computing resources. This method ensures the H ∞ The performance index reaches the Nash equilibrium state. The nonlinear modeling ability of the neural network is used to identify the dynamic characteristics of the system, solving the problem of low accuracy in predicting the system state. Finally, by setting the threshold for event triggering, when the system state error exceeds the threshold, the event is triggered and the system controller is updated. Specifically, Figure 1 As shown, the method comprises the following steps:

[0067] Step 1: Build a multi-drive servo system model with disturbances and decouple the disturbances.

[0068] Introducing a multi-drive servo system model with disturbances

[0069] in, is the system status, They are drift system dynamics, input dynamics, and disturbance dynamics. represents the control input, is an unknown, bounded input disturbance, satisfying d≤d m , where d m is a normal number.

[0070] Step 2: Use the identification neural network to identify the system and estimate the dynamic characteristics of the system.

[0071] The nonlinear modeling capability of the identification neural network is applicable to the dynamic characteristics of various complex systems. Three identification neural networks are used to identify f(x), g of the nonlinear system respectively. j (x), k(x) (drift system dynamics, input dynamics and disturbance dynamics), the system can be expressed as:

[0072]

[0073] Where n a ,n b ,n c is the number of hidden neurons of the three neural networks, is a constant matrix, is the activation function, is the ideal weight vector of the neural network, ε a ,ε jb ,ε c is the residual of the neural network.

[0074] Using approximate weights Estimate the state variables x and the ideal weights W a ,W jb ,W c , then the system can be expressed as

[0075]

[0076] Weight updates in a neural network optimize network performance, gradually reducing the difference between the output and the expected output. Through repeated iterations and optimization, the neural network can gradually learn the inherent laws of the data and improve the accuracy and efficiency of recognition. The weight update rule of the recognition neural network is:

[0077]

[0078] Through the identification process of this step, a neural network-based identification system model is obtained.

[0079] Step 3: Construct the cost function of the multi-drive servo system and obtain the expressions of the nonlinear optimal control strategy and the worst interference strategy by solving the HJI equation under the event trigger mechanism.

[0080] Define the cost function of the multi-drive servo system to measure the system's effectiveness in balancing control performance and disturbance effects. By optimizing the cost function, the impact of disturbances on the system can be minimized while ensuring the basic performance of the system, thereby improving the overall performance of the system.

[0081]

[0082] in

[0083] Through interference decoupling, each independent input can effectively resist part of the external interference and make all H ∞ The performance index reaches the Nash equilibrium state.

[0084] d(τ)=d1(τ)+…d i (τ)+…d N (τ)

[0085] Calculate the optimal strategy sequence Make all H ∞ The performance indicators can all reach the overall optimal, and the optimal strategy {u1…u i …u N} will minimize the cost function, while the interference d * (x) will maximize it. Therefore, the optimal cost function for each input is described as:

[0086]

[0087] Define and solve the HJI equation for this system:

[0088]

[0089] The optimal strategy sequence When the saddle point solution of Nash equilibrium is reached, the benefits corresponding to the strategy combination of all participants are optimal overall, and the optimal control strategy is obtained by solving the HJB equation under the time trigger mechanism. and worst interference

[0090]

[0091] Since the control strategy and disturbance strategy solved by the HJI equation are nonlinear, a critical neural network is needed for approximation.

[0092] Step 4: Construct the value function and use the critical neural network to approximate it to design the event-triggered control law to obtain the final optimal control strategy and the worst interference.

[0093] This step combines the neural network identification system model and event triggering mechanism to use a critical neural network to approximate the optimal value function. The critical neural network can effectively approximate any complex value function by virtue of its nonlinear activation function and the complexity of the multi-layer network structure. use Estimating ideal weights Get the approximate value function

[0094] During the training process, the data input to the critical neural network is first normalized to ensure that each feature has the same importance in the model.

[0095] Next, the gradient descent method is used to iteratively update the weights in the critical neural network, which can gradually reduce the error between the predicted value and the actual value.

[0096] In addition, the input data is re-standardized each time the weight is updated to ensure that each feature contributes to the error in a balanced manner during the optimization process, thereby preventing some features from having too large weights and affecting the overall optimization effect.

[0097] The steps are as follows:

[0098] The approximate Hamiltonian function is:

[0099]

[0100] in for The estimated value of .

[0101] Choose the squared residuals:

[0102]

[0103] The gradient descent method is used to update the weights of the critical neural network until the approximation error is minimized to obtain an approximate value function. The expression for the weight update is:

[0104]

[0105] where η i is the learning rate,

[0106]

[0107] In the event-triggered mechanism, the controller state is updated only when an event is triggered, reducing the sampling frequency of the data and the number of controller updates. The sampling time of event-triggered control is expressed as λ0,λ1,λ2,…,λ k ,λ k+1 ,…, where λ0=0 is the initial sampling time, λ k is the kth sampling time, x k = x(λ k ) The state sequence under the sampling instance is x0,x1,x2,…,x k ,x k+1 ,…, then the error of event triggering is expressed as e(λ k )=x k -x(t). When the error e(λ k )Violation of threshold e T When the event is triggered and the data is transmitted to update the controller, the trigger instance e(λ k ) is reset to zero, that is, e(λ k )=0.

[0108] The final event-triggered control law is obtained and interference law for:

[0109]

[0110] The final control law calculated is input into the controller to deal with the disturbance and realize the H ∞ control.

[0111] Step 5: Use the Lyapunov function method to verify the system stability under the event-triggered strategy.

[0112] Select the corresponding Lyapunov function L. Under the control of event triggering, find the first-order derivative of L with respect to time, and bring it into the final event-triggered control law and interference law to derive the corresponding event triggering threshold e T When ||e(λ k )|| 2 <||e T || 2 , so that This means that the system with event-triggered control law is asymptotically stable.

[0113] The control and interference signals generated by the event trigger mechanism are updated when the event trigger conditions are met, ensuring that the system can still resist interference while minimizing the control law and maintaining system stability. In this way, the control signal will not be updated frequently, but will be adjusted at the appropriate time according to the changes in the system state, thereby achieving efficient and stable control.

[0114] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0115] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A H-based multi-drive servo system based on event triggering ∞ The control method is characterized in that The following steps are involved: A multi-drive servo system model with interference is established to decouple the interference and establish the optimal value function V of the system under the time trigger mechanism. i * (x); The identification neural network is used to identify the multi-drive servo system model with interference, and the neural network-based identification system model is obtained; Based on the event trigger mechanism, the error e(λ k ) Whether it violates the set threshold e T If not, the controller is not updated. If so, the controller is updated with the calculated optimal control strategy to cope with the worst-case disturbance. ∞ Control process; The process of obtaining the calculated optimal control strategy and the worst interference strategy includes: In combination with the neural network-based identification system model and event triggering mechanism, the optimal value function is approximated by the critical neural network to obtain the final control strategy and interference strategy.

2. The H of the event-triggered multi-drive servo system according to claim 1 ∞ The control method is characterized in that The expression of the multi-drive servo system model with interference is: In the formula, is a multi-drive servo system model with disturbance, x is the system state vector, f(x), g j (x), k(x) are the drift system dynamics, input dynamics and disturbance dynamics respectively, u j represents the control input, d is the unknown, bounded input disturbance, satisfying d≤d m , where d m is a normal number, and N is a normal number.

3. The H of the event-triggered multi-drive servo system according to claim 2 ∞ The control method is characterized in that The expression for decoupling interference is: d(τ)=d1(τ)+…d i (t)+…d N (t) Where d(τ) is the interference, d i (τ) is the i-th disturbance after decoupling.

4. The H of the event-triggered multi-drive servo system according to claim 1 ∞ The control method is characterized in that The step of obtaining the neural network-based identification system model comprises: The drift system dynamics, input dynamics and disturbance dynamics in the multi-drive servo system model with disturbance decoupling are identified using an identification neural network. The system is expressed as: Using approximate weights Estimate the state variables x and the ideal weights W a ,W jb ,W c , the system is expressed as: According to the weight update rule, the approximate weights in the identification neural network are updated, and after repeated iterative optimization, the final neural network-based identification system model is obtained; In the formula, is the multi-drive servo system model with disturbance, A is the constant matrix, W c T To identify the transpose of the ideal weight vector of a neural network, σ a (·),σ jb (·),σ c (·) is the activation function, ε a , ε jb , ε c is the residual of the neural network, u j is the jth control input, x is the system state vector, N is a positive integer, d is an unknown, bounded input disturbance, is the approximate multi-drive servo system model with disturbance, is the approximate system state vector, is the transpose of the approximate weights.

5. The H of the event-triggered multi-drive servo system according to claim 4 ∞ The control method is characterized in that The weight update rule is: In the formula, is the transpose of the approximate weight, α a , α jb , α c is the learning rate, σ a (·),σ jb (·),σ c (·) is the activation function, is the transpose of the state estimation error.

6. The H of the event-triggered multi-drive servo system according to claim 1 ∞ The control method is characterized in that The optimal value function V of the system under the time trigger mechanism is established i * The step (x) comprises: Based on the multi-drive servo system model after disturbance decoupling, the value function of the system is defined as follows: in: Based on the value function of the system, combined with the event trigger mechanism, a system H ∞ The optimal value function of the performance index reaching the overall optimal is expressed as: Where V i (x) is the value function, x is the system state vector, u i is the i-th control strategy, d is an unknown, bounded input disturbance, satisfying d≤d m , where d m is a normal number, u j represents the jth control input, Q i is a positive definite matrix, N is a positive integer, R ij is a symmetric positive definite matrix, w i (·) is the utility function, γ is a positive constant, indicating the degree of disturbance attenuation, V i * (x) is the optimal value function and T is the transpose of the matrix.

7. The H of the event-triggered multi-drive servo system according to claim 6. ∞ The control method is characterized in that According to the value function of the system, the HJI equation of the system is defined and solved, and the expression is: According to the solved HJI equation, the theoretically nonlinear time-triggered control strategy and interference strategy of the system are obtained, and the expressions are: Where x is the system state vector, R ij is a symmetric positive definite matrix, w i (·) is the utility function, V i * (x) is the optimal value function, T is the transpose of the matrix, is the optimal control strategy, is the matrix R ii The inverse matrix of is the function V i * The gradient operator with respect to the variable x, is the interference strategy for the ith input, k(x) is the interference dynamics, is the ith disturbance after decoupling, g i (x) is the ith input dynamics, g j (x) is the jth input dynamics.

8. The H of the event-triggered multi-drive servo system according to claim 1 ∞ The control method is characterized in that The error e(λ) triggered by the event k )for: e(λ k )=x k -x(t) In the formula, e(λ k ) is the error triggered by the event, λ k is the kth sampling time, x k is the sampling state, and x(t) is the state variable.

9. The H of the event-triggered multi-drive servo system according to claim 1 ∞ The control method is characterized in that The expressions of the control strategy and interference strategy obtained according to the optimal value function are: In the formula, R ij is a symmetric positive definite matrix, is the matrix R ii The inverse matrix of are the approximate weights of the identification neural network, T is the transpose of the matrix, σ a (·),σ ib (·),σ jb (·),σ c (·) is the activation function of the identification neural network, N is a positive integer, and γ is a positive constant, which indicates the degree of disturbance attenuation.

10. The H of the event-triggered multi-drive servo system according to claim 1 ∞ The control method is characterized in that In the process of approximating the optimal value function, the optimal value function is approximated by a critical neural network. use Estimating ideal weights Get the approximate value function The specific steps to obtain the final event-triggered control law and interference strategy include: The approximate Hamiltonian function is: The control law and interference law for: Select the residual square, the expression is: The gradient descent method is used to update the weights of the critical neural network to obtain an approximate optimal value function. The expression of the weight update is: Where η i is the learning rate, H i (·) is the Hamiltonian function, x is the system state vector, λ k is the kth sampling time, yes The estimated value of yes The estimated value of yes The estimated value of To critique the ideal weights of a neural network, Criticizing the estimated weights of the neural network, b i is the reconstruction error, To criticize the activation function of the neural network, For function The derivative of x, w i (·) is the utility function, N is a positive integer, are the approximate weights of the identification neural network, σ a (·),σ jb (·),σ c (·) is the activation function of the identification neural network, E c is the objective function, For function Derivative of x, T is the transpose of the matrix, W a , W jb , W c To identify the ideal weight vector of a neural network, is the approximate weight of the neural network, To identify the weight estimation error of the neural network, u j is the jth control input, d is the unknown, bounded input disturbance, and γ is a positive constant indicating the degree of disturbance attenuation.

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