Consistency learning control method based on neural network

Abstract

The invention belongs to the technical field of intelligent control, and particularly relates to a consistency learning control method based on a neural network, and the method comprises the steps: S1, constructing a linear parameterization model of multi-agent consistency output; s2, a loss function is designed by outputting related consistency output through a neural network, and a linear parameter updating algorithm in the time direction and the iteration direction is obtained through a gradient descent method; and S3, designing a controller by using the output of the neural network, and constructing a consistency learning control scheme of the multi-agent system based on neural network approximation. According to the scheme, the parameters are updated based on the time axis and the iteration axis, a system model and strict matrix conditions are not needed, and full-time-period perfect tracking is achieved. According to the method, the traditional cognition that errors serve as index parameters is broken through, equivalent parameters are directly fitted through the neural network, the problems of insufficient fitting capacity and nonlinear approximation errors of a projection algorithm under a complex system are solved, and the convergence speed of the system and the adaptability of consistency control are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent control technology, and more specifically, relates to a consistency learning control method based on neural network. Background Art

[0002] A multi-agent system is a network cluster composed of multiple intelligent individuals with communication, sensing, execution capabilities, and independent decision-making capabilities. Each robot in a complex multi-manipulator system can be regarded as an "agent" with physical execution capabilities. The consistency tracking control of complex multi-manipulator systems aims to ensure that multiple robots can synchronously track the target trajectory or maintain a specific coordination relationship when working together. However, due to modeling errors in robot parameters (such as joint friction coefficient and link inertia), environmental interference (such as sudden changes in contact surface friction), and the unknown dynamic characteristics of objects (such as mass changes when grasping objects), existing control methods have many drawbacks: Comparative Document 1 CN119644756A proposes an optimal sliding mode control method for multi-manipulator adaptive dynamic programming. It is based on the communication topology constraint position error and the self-adjusting performance function to dynamically optimize the convergence boundary. It combines sliding mode control with adaptive dynamic programming to achieve consistency and optimal control of multi-manipulators. The defects of this method are as follows: 1) Model dependence: This method requires the assumption of a dynamic model ( , , ) is precisely known, without considering unmodeled dynamics or parameter uncertainty, and its robustness is limited in practical applications. 2) Approximation error accumulation: the approximation error of the neural network Directly affects the control law, control input containing error Act on the dynamics of the robotic arm to change the state trajectory , which in turn affects the subsequent approximation objective function , forming a positive feedback loop of error-state drift-larger error. 3) Scalability limitations: The validation was limited to 2-DOF manipulators; the applicability to multi-DOF (>2) or heterogeneous manipulator systems has not been fully demonstrated.

[0003] Comparative Document 2, CN119292063B, proposes an event-triggered iterative learning consistency control method for a multi-agent system under FDI attack. This method designs the objective function through an equivalent linearization model and then obtains the parameter estimation algorithm through a projection algorithm. This method requires the objective function to satisfy convexity or local linearity conditions. When the multi-agent system has strong nonlinearity, the linear approximation will introduce large errors, resulting in parameter estimation deviations, which in turn affects the accuracy of consistency control. In addition, the consistency control of multi-agent systems often involves non-convex objective functions, and the projection algorithm is prone to falling into local optimality in non-convex scenarios, unable to guarantee global convergence, and the error convergence speed is slow.

[0004] In view of the above, a novel iterative learning controller is proposed, which can perform more accurate trajectory tracking of complex robotic arm systems and a data-driven control method with strong applicability, which is the subject faced by the present invention. Summary of the Invention

[0005] In order to solve the problems of strong model dependence, nonlinear approximation error accumulation and slow error convergence in the existing consistency control of multi-manipulator systems, a consistency learning control method based on neural network is proposed.

[0006] The purpose of the present invention can be achieved through the following technical solutions: A neural network-based consistency learning control method comprises the following steps: S1. Construct a linear parameterized model of multi-agent consensus output; S2. Using a neural network model, we fit the input and consistency output of previous time information to obtain linearized parameters. We then design a loss function based on the consistency output and use the gradient descent method to obtain a neural network parameter update algorithm along both time and iteration directions. S3. Use the output of the neural network to design a controller, and apply the linearization parameters obtained in step S2 to the adjustable gain of the controller to construct a consistency learning control scheme for the multi-agent system based on neural network approximation.

[0007] Furthermore, the step S1 includes: Step S1-1: Based on the topological structure information, the consistency output model of the multi-agent system is constructed as follows: ; in, Indicates the kth iteration The system output of the jth agent at time instant; express Expected output at the moment; Indicates the The set of all neighboring agents of an agent; Constructing an adjacency matrix for the topology of a multi-agent system; Representing an agent Communication status with virtual leader 0; Step S1-2: Construct an ideal nonlinear dynamic correlation between consistency error and input variables: ; in, Represents system input; Representing an agent Nonlinear function of and Represent the order of system consistency error and output respectively; Step S1-3: Combine the state transfer iterative dynamic linearization method to obtain the consistency error With the input vector A linear parameterized model between: ; in, is the equivalent linearization parameter vector, , represents the difference operator.

[0008] Furthermore, the step S2 includes: Step S2-1: Introduce the iterative radial basis neural network method to construct the following neural network output model: ; in, is the weight vector; is the hidden layer function vector; n is the number of hidden layer nodes; Step S2-2: Update the unknown parameters of the neural network and design the following loss function: ; The linear parameter estimation algorithm between the consistent output and the input vector is obtained using the gradient descent method as follows: ; ; ; in, , and They are , and estimated value of; , and Represents the step size factor.

[0009] Furthermore, step S3 includes: using the neural network output to design the following iterative learning controller: ; in, ; is the weight factor; is the step size factor.

[0010] Beneficial effects of the present invention: The present invention discloses a data-driven iterative learning consistency control method for a multi-manipulator system. In response to the problems of model dependence, complex parameter adjustment and error accumulation in the prior art, a variable gain iterative learning scheme based on a neural network is proposed. This method skips the traditional input-output relationship, establishes an equation for the consistency error and the input variable, and uses a neural network to iteratively approximate the equivalent linearization parameters and act on the controller gain. The entire scheme does not need to consider the influence of the approximation error. Different from the control along the time axis, this scheme updates the parameters based on the time axis and the iteration axis, does not require a system model and strict matrix conditions, and achieves perfect tracking of the entire time period. The present invention breaks through the traditional cognition of approximation error as an indicator parameter, directly fits the equivalent parameters through a neural network, solves the problem of insufficient fitting ability of the projection algorithm and nonlinear approximation error, and significantly improves the convergence speed and control adaptability under complex systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 This is a flow chart of a neural network-based consistency learning control method proposed by the present invention; Figure 2 This is a principle block diagram of a neural network-based consistency learning control method proposed in the present invention; Figure 3 It is the communication topology diagram between the robotic arms; Figure 4 This is an output comparison diagram of the consistency learning control method for the multi-manipulator system proposed by the present invention; Figure 5 This is a graph showing the convergence performance of the consistency learning control method for the multi-manipulator system proposed in the present invention; Figure 6 A comparison chart of the outputs of four robotic arms using the consistency learning control method proposed by the present invention and the comparative patent method; Figure 7 A comparison chart of the convergence performance of four robotic arms using the consistency learning control method proposed in this invention and the comparative patent method. DETAILED DESCRIPTION

[0012] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0013] See also Figure 1 、 Figure 2 As shown, the present embodiment discloses a neural network-based consistency learning control method, comprising the following steps: S1. Construct a linear parameterized model of multi-agent consensus output; Consider an unknown discrete-time multi-agent system where Indicates the system output, Represents system input; represents the number of iterations, represents the number of the agent, represents discrete time, T is a positive integer; Indicates the The set of all neighboring agents of an agent; the adjacency matrix ,and ; Representing an agent and is a neighbor agent, otherwise, .

[0014] Based on the topological structure information, the consistency output model of the multi-agent system is constructed as follows: ; in, express The desired output at the moment, i.e. the output of the virtual leader; Representing an agent Communication status with virtual leader 0; Indicates that the agent can directly receive information from leader 0, otherwise, .

[0015] Construct an ideal nonlinear dynamic relationship between consistency error and input variables: ; in, Representing an agent Nonlinear function of and They represent the system consistency error and the output order respectively, which are two unknown positive integers; Assumption 1: The initial state of all iterations The same, that is: ; Assumption 2: Nonlinear Function Satisfies the global Lipschitz condition, that is, ; in, and are two Lipschitz constants.

[0016] Conventional technologies usually rely on nonlinear functions of the output, and construct an equivalent linearization model between input and output through complex mathematical derivation. This process not only requires a precise system mathematical model as support, but also places strict requirements on the applicability of the model. This embodiment deeply explores the intrinsic connection between the consistency error and the input and output that reflects the communication relationship between the intelligent agents, and directly constructs a linearization model for the multi-agent system. This method completely gets rid of the dependence on the mathematical model of the system, and can achieve effective adaptation regardless of whether the dynamic characteristics of the intelligent agent are linear or nonlinear, affine or non-affine, or homogeneous or heterogeneous. This breakthrough has greatly broadened the application scenarios of the technology, broken the limitations of traditional models in the control of complex multi-agent systems, and provided a more universal and flexible solution for dynamic collaborative control in multiple fields.

[0017] Specifically, combined with the state transfer iterative dynamic linearization method, the consistency error is obtained With the input vector A linear parameterized model between: ; in, ; represents the equivalent linearization parameter vector; , , Represents the difference operator; unless otherwise specified, The meanings of both represent difference operators.

[0018] S2, using a neural network to estimate the linearization parameters between the consistency output and the input vector; The iterative radial basis neural network method is introduced to establish the following neural network output model: ; in, is the weight vector; is the hidden layer function vector; n is the number of hidden layer nodes; The output of the lth hidden layer node is: ; in, is the input vector, , , and is a suitable positive constant; is the center vector of the lth hidden node; is the radius of the lth hidden node; Represents the vector binorm operator.

[0019] Practice has found that the nonlinear fitting ability of neural networks is inherently contradictory to their estimation errors: if the network output is directly used to compensate for the nonlinear terms of the system, the approximation error will accumulate with the control loop; if an error compensation mechanism is introduced, the algorithm complexity will increase significantly, making it difficult to meet the distributed computing requirements of multi-agent systems. This embodiment designs the loss function through the consistent output of the neural network model. While retaining the strong fitting ability of the neural network, it does not need to consider the direct impact of the estimation error on the controller. It is subsequently combined with the control parameters to achieve variable gain over time and iterations, thereby improving the convergence of the control and achieving faster tracking in iterations.

[0020] Specifically, the following loss function is designed to update the weights of the unknown parameters of the neural network: ; Construct the following parametric equation: ; ; ; in, , and Represents the step size factor.

[0021] To extend the neural network algorithm to the iterative axis, it is necessary to consider the gradient descent on the iteration and then design the above parameter equations. Through the loss function, the composite function in mathematics is used to derive the , and When calculating partial derivatives, the coupling between multiple parameters is comprehensively considered to achieve comprehensive derivation of multiple types of parameters. When migrating the neural network model to the iterative learning control scenario, it is necessary to simultaneously deal with the dual dynamic characteristics of the time axis and the iteration axis: on the time axis, the parameters need to respond to changes in the system state in real time; on the iteration axis, cross-cycle optimization is required based on historical batch data. This dual-dimensional coupling characteristic makes it difficult to effectively model the traditional single-axis parameter update mechanism. This embodiment constructs a dual-axis parameter update equation that takes into account both dynamic response and historical experience reuse, achieving comprehensive derivation of multiple types of parameters.

[0022] Specifically, the gradient descent method is used to obtain the neural network update equation between the consistent output and the input vector: ; ; ; in, , and They are , and estimated value.

[0023] S3. Construct a consensus learning control scheme for multi-agent systems based on neural network approximation.

[0024] The criterion function for designing control input based on neural network output is: ; in, is the weight factor; By using the optimization method, the iterative learning controller is obtained from the criterion function (a13): ; in, ; is the step size factor.

[0025] Combining the neural network parameter update equations and iterative learning controller designed above, the following consensus learning control scheme for multi-agent systems based on neural network approximation is constructed: ; in, for The estimated vector of ; is a saturation function; the definitions of other symbols remain unchanged from the previous steps.

[0026] Considering that the multi-agent system satisfies assumptions 1-2 and the controller parameters are adjusted within the allowable range, the proposed iterative consistency learning control method based on neural networks can ensure that: the consistency error Is convergent and bounded; thus the tracking error of the system It is also convergent and bounded.

[0027] In order to verify the method of the present invention, the following simulations were performed on the method of the present invention: like Figure 3As shown, consider the following multi-manipulator system consisting of four DC motor-driven manipulators, and construct the dynamic model as follows: ; in, , and denote angular displacement, velocity, and acceleration respectively; is the driving torque, ; is the moment of inertia, , , , and They represent motor load, mass, length, damping coefficient and acceleration due to gravity respectively.

[0028] exist At the sampling time, the expected speed is: ; The controller parameters are set to , , , , , ; The initial value is , , , , , , , , ; Using the neural network-based consistency learning control method, the tracking performance of the system output at the 1st, 50th, 100th, and 200th iterations is as follows Figure 4 As shown in the figure; the convergence of the tracking error is as follows Figure 5 As shown, the vertical axis represents the average tracking error (ATE), which is defined as .from Figure 4 and Figure 5 It can be seen that when the model information is unknown and only I / O data can be obtained, the proposed neural network-based consistency learning control method can effectively improve the control performance of the system and achieve the consistency tracking goal.

[0029] The control scheme of comparative document 2 is as follows: ; ,if or , ; ; The controller parameters are set to , , , , , , , , ; Apply the control method proposed in this embodiment to compare with the comparative document 2, Figure 6 The tracking performance comparison chart of the four agents at the 200th iteration is shown in the figure below. The tracking error comparison chart is shown in the figure below. Figure 7 As shown. Figure 6-Figure 7 It can be seen that for complex multi-robotic arm systems, the proposed consistency control method based on neural network parameter estimation has a faster convergence speed and can achieve better control performance.

[0030] The above is a detailed description of an embodiment of the present invention. However, the content described is only a preferred embodiment of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A consistency learning control method based on neural network, characterized in that: The following steps are involved: S1. Construct a linear parameterized model of multi-agent consensus output; S2. Using a neural network model, we fit the input and consistency output of previous time information to obtain linearized parameters. We then design a loss function based on the consistency output and use the gradient descent method to obtain a neural network parameter update algorithm along both time and iteration directions. S3. Use the output of the neural network to design a controller, and apply the linearization parameters obtained in step S2 to the adjustable gain of the controller to construct a consistency learning control scheme for the multi-agent system based on neural network approximation.

2. The neural network-based consistency learning control method according to claim 1, characterized in that: The step S1 comprises: Step S1-1: Based on the topological structure information, the consistency output model of the multi-agent system is constructed as follows: in, y k,j (t+1) represents the system output of the jth agent at time t+1 of the kth iteration; y d (t+1) represents the expected output at time t+1; N j represents the set of all neighboring agents of the jth agent; a j,i Constructing an adjacency matrix for the topology of a multi-agent system; a j,0 represents the communication status between agent j and virtual leader 0; Step S1-2: Construct an ideal nonlinear dynamic correlation between consistency error and input variables: ε k,j (t+1)=f j (ε k,j (t),L,ε k,j (t-n ε ),u k,j (t),L,u k,j (t-n u )) Among them, u k,j (t)∈R represents the system input; f j (g) represents the nonlinear function of agent j; n ε and n u Represent the order of system consistency error and output respectively; Step S1-3: Combine the state transfer iterative dynamic linearization method to obtain the consistency error ε k,j (t+1) and the input vector u k,j (t) linear parameterized model: No k,j (t+1)=Θ k,j (t)D k,j (t) Among them, Θ k,j (t)=[θ k,j (0),L,θ k,j (t)]∈R 1×(t+1) is the equivalent linearization parameter vector, u k,j (t)=[u k,j (0),L,u k,j (t)] T ∈R t+1 , Δ represents the difference operator.

3. The neural network-based consistency learning control method according to claim 1, characterized in that: The step S2 comprises: Step S2-1: Introduce the iterative radial basis neural network method to construct the following neural network output model: Among them, w k,j (t)=[w 1,k,j (t),K,w n,k,j (t)] T is the weight vector; is the hidden layer function vector; n is the number of hidden layer nodes; Step S2-2: Update the unknown parameters of the neural network and design the following loss function: The neural network parameter estimation algorithm between the consistent output and input vectors using the gradient descent method is as follows: in, and They are w k,j (t), r l,k,j (t) and c l,k,j Estimated value of (t); η w , η r and η c Represents the step size factor.

4. The neural network-based consistency learning control method according to claim 1, characterized in that: The step S3 includes: using the neural network output to design the following iterative learning controller: in, λ>0 is the weight factor; 0<ρ≤1 is the step size factor.

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