A neural network-based consistency learning control method

Abstract

The application belongs to the technical field of intelligent control, and particularly relates to a consistency learning control method based on a neural network, which comprises the following steps: S1, constructing a linear parameterization model of consistency output of multiple intelligent agents; S2, designing a loss function by outputting relevant consistency output through a neural network, and obtaining a linear parameter update algorithm in the time and iteration directions through a gradient descent method; and S3, using the output of the neural network to design a controller, and constructing a consistency learning control scheme of the multiple intelligent agent system based on neural network approximation. The scheme updates parameters based on the time axis and the iteration axis, does not require a system model and strict matrix conditions, and realizes perfect tracking in the whole time period. The application breaks through the traditional cognition of taking error as an index parameter, directly fits equivalent parameters through a neural network, solves the problems of insufficient fitting capacity of a projection algorithm and nonlinear approximation error under a complex system, and significantly improves the convergence speed of the system and the adaptability of consistency control.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of intelligent control, and more particularly relates to a consistency learning control method based on a neural network. BACKGROUND

[0002] A multi-agent system is a network cluster composed of multiple intelligent individuals with communication, sensing, and execution capabilities, and capable of independent decision-making. Each robot arm in a complex multi-robot arm system can be regarded as an "intelligent agent" with physical execution capability. The consistency tracking control of a complex multi-robot arm system aims to ensure that multiple robot arms can synchronously track target trajectories or maintain a specific coordination relationship when working cooperatively. However, due to modeling errors of robot arm parameters (such as joint friction coefficients and link inertias), environmental disturbances (such as sudden changes in contact surface friction), and unknown dynamics of objects (such as changes in mass when grasping objects), existing control methods have many defects:

[0003] Comparative Document 1 CN119644756A proposes a multi-robot arm adaptive dynamic programming optimal sliding mode control method, which is based on communication topology constraint position error, self-adjusting performance function dynamic optimization convergence boundary, and combines sliding mode control with adaptive dynamic programming to realize multi-robot arm consistency and optimal control. The defects of this method are as follows: 1) Model dependency: this method needs to assume that the dynamic model ( , , ) is accurately known, and does not consider unmodeled dynamics or parameter uncertainties, which limits the robustness in practical applications. 2) Approximation error accumulation: the approximation error of the neural network directly affects the control law, and the control input containing the error acts on the robot arm dynamics, changing the state trajectory , and thus affecting the subsequent approximation target function , forming an error-state drift-greater error positive feedback cycle. 3) Limited scalability: verification is only for 2-DOF robot arms, and the applicability of multi-DOF (>2) or heterogeneous robot arm systems is not fully demonstrated.

[0004] Comparative Document 2 CN119292063B proposes an event-triggered iterative learning consistency control method for multi-agent systems under FDI attacks, which designs a target function through equivalent linearization model, and then obtains a parameter estimation algorithm through projection algorithm. This method requires the target function to satisfy the convexity or local linearity condition. When the multi-agent system has strong nonlinearity, linearization approximation will introduce large errors, leading to parameter estimation bias, and thus affecting the accuracy of consistency control. In addition, the consistency control of multi-agent systems often involves non-convex target functions, and the projection algorithm is prone to local optimization in non-convex scenarios, which cannot guarantee global convergence, and the error convergence speed is slow.

[0005] In view of the above, the present application aims to provide a novel iterative learning controller, and a data-driven control method with high accuracy and strong applicability for complex manipulator systems. SUMMARY

[0006] 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 networks is proposed.

[0007] The object of the present application can be achieved by the following technical solutions:

[0008] A consistency learning control method based on neural networks comprises the following steps:

[0009] S1, a linear parameterized model of multi-agent consistency output is constructed;

[0010] S2, the input of the previous time information and the consistency output are fitted by a neural network model to obtain linearization parameters, a loss function is designed from the consistency output, and a neural network parameter update algorithm along the time and iteration directions is obtained by gradient descent method;

[0011] S3, the output of the neural network is used to design a controller, and the linearization parameters obtained in step S2 are applied to the adjustable gain of the controller, and a consistency learning control scheme based on neural network approximation of the multi-agent system is constructed.

[0012] Further, the step S1 comprises:

[0013] Step S1-1, according to the topological structure information, the consistency output model of the multi-agent system is constructed as:

[0014] ;

[0015] Wherein, represents the system output of the jth agent at the kth iteration time;

[0016] represents the expected output at the kth iteration time;

[0017] represents the set of all neighbor agents of the kth agent;

[0018] An adjacency matrix is constructed for the topological structure of the multi-agent system;

[0019] represents the agent​ Communication state with virtual leader 0;

[0020] Step S1-2, construct the nonlinear dynamic relationship between ideal consistency error and input variables:

[0021] ;

[0022] wherein, represents the system input; represents the nonlinear function of the agent ; and respectively represent the order of the system consistency error and the output;

[0023] Step S1-3, combined with the state transition iterative dynamic linearization method, obtain the linear parameterization model between the consistency error and the input vector :

[0024] ;

[0025] wherein, is the equivalent linearization parameter vector, , represents the difference operator.

[0026] Further, the step S2 includes:

[0027] Step S2-1, introduce the radial basis neural network method along the iteration, construct the neural network output model as follows:

[0028] ;

[0029] wherein, is the weight vector;

[0030] is the hidden layer function vector; n is the number of hidden layer nodes;

[0031] Step S2-2, update the unknown parameters of the neural network, and design the following loss function:

[0032] ;

[0033] The linearization parameter estimation algorithm between the consistency output and the input vector is obtained by using the gradient descent method as follows:

[0034] ;

[0035] ;

[0036] ;

[0037] wherein, , and are the estimated values of , and respectively; , and denote step factors.

[0038] Further, the step S3 comprises: applying a neural network to output an iterative learning controller designed as follows:

[0039] ;

[0040] wherein, ; is a weight factor; is a step factor.

[0041] The beneficial effects of the present application are:

[0042] The application discloses a data-driven multi-robot system iterative learning consistency control method, and aims at the problems of model dependence, complex parameter adjustment and error accumulation in the prior art, and proposes a variable gain iterative learning scheme based on a neural network. The method skips the traditional input-output relationship, establishes an equation of consistency error and input variables, iteratively approximates equivalent linearization parameters by using a neural network, and acts on a controller gain, so that the whole scheme does not need to consider the influence of approximation error. Different from control along a time axis, the scheme updates parameters based on a time axis and an iterative axis, does not need a system model and strict matrix conditions, and realizes perfect tracking in a whole time period. The application breaks the traditional cognition that approximation error is an index parameter, directly fits equivalent parameters by using a neural network, solves the problems of insufficient fitting capacity of a projection algorithm and nonlinear approximation error, and significantly improves the convergence speed and control adaptability under a complex system. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a flow chart of the consistency learning control method based on the neural network;

[0044] Figure 2 is a principle block diagram of the consistency learning control method based on the neural network;

[0045] Figure 3 is a communication topology graph between the robots;

[0046] Figure 4 is an output comparison graph of the consistency learning control method under the multi-robot system;

[0047] Figure 5 The diagram shows the convergence performance of the consensus learning control method for multi-manipulator systems proposed in this invention.

[0048] Figure 6 This is a comparison chart of the outputs of four robotic arms between the consistency learning control method proposed in this invention and the method in a comparative patent.

[0049] Figure 7 This is a comparison chart of the convergence performance of four robotic arms using the consistency learning control method proposed in this invention and the method in a comparative patent. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0051] See Figure 1 , Figure 2 As shown in the figure, this embodiment discloses a consistency learning control method based on neural networks, which includes the following steps:

[0052] S1. Construct a linear parameterized model for the consistent output of multiple agents;

[0053] Consider an unknown discrete-time multi-agent system, where Indicates system output, Indicates system input; Indicates the number of iterations. Indicates the agent's ID number. Representing discrete time, T is a positive integer; Indicates the first The set of all neighboring agents of an agent; adjacency matrix ,and ; Represents intelligent agents and It is a neighboring intelligent agent, and vice versa. .

[0054] Based on topological information, a consensus output model for a multi-agent system is constructed as follows:

[0055] ;

[0056] in, express The expected output at any given moment, i.e., the output of the virtual leader;

[0057] Represents intelligent agents Communication status with virtual leader 0; This means that the agent can directly receive information from the leader 0, and vice versa. .

[0058] Constructing an ideal nonlinear dynamic relationship between consistency error and input variables:

[0059] ;

[0060] in, Represents intelligent agents Nonlinear functions; and Let represent the system consistency error and the order of the output, respectively, and both be unknown positive integers.

[0061] Assumption 1: The initial state for all iterations Same, that is: ;

[0062] Assumption 2: Nonlinear function Satisfying the global Lipschitz condition, i.e.

[0063] ;

[0064] in, and These are two Lipschitz constants.

[0065] Conventional techniques typically rely on nonlinear functions of the output, constructing an equivalent linearized model between input and output through complex mathematical derivations. This process not only requires a precise system mathematical model but also imposes stringent requirements on the model's applicability. This embodiment delves into the consistency error reflecting the communication relationship between agents and the intrinsic connection between input and output, directly constructing a linearized model for multi-agent systems. This method completely eliminates the dependence on system mathematical models, achieving effective adaptation regardless of whether the agent dynamics are linear or nonlinear, affine or non-affine, or homogeneous or heterogeneous. This breakthrough greatly broadens the application scenarios of the technology, overcomes the limitations of traditional models in the control of complex multi-agent systems, and provides a more universal and flexible solution for multi-domain dynamic collaborative control.

[0066] Specifically, by combining the state transition iterative dynamic linearization method, the consistency error is obtained. With input vector Linear parameterized model between:

[0067] ;

[0068] in,

[0069] ;

[0070] denotes the equivalent linearization parameter vector;

[0071] , , denotes the difference operator; subsequently, if not otherwise specified, have the meaning of the difference operator.

[0072] S2, estimate the linearization parameters between the consistency output and the input vector using neural networks;

[0073] Introduce the radial basis neural network method along the iteration, and establish the neural network output model as follows:

[0074] ;

[0075] wherein,

[0076] is the weight vector;

[0077] is the hidden layer function vector;

[0078] n is the number of hidden layer nodes;

[0079] The output of the lth hidden layer node is:

[0080] ;

[0081] wherein,

[0082] is the input vector, , , and are appropriate normal numbers;

[0083] is the center vector of the lth hidden node;

[0084] is the radius of the lth hidden node;

[0085] denotes the two-norm operator of the vector.

[0086] It is found in practice that the nonlinear fitting capability of the neural network is inherently contradictory to its estimation error: if the network output is directly used to compensate for the nonlinear term of the system, the approximation error will accumulate with the control loop; if an error compensation mechanism is introduced, the algorithm complexity will be significantly increased, which is difficult to meet the distributed computing requirements of multi-agent systems. The embodiment designs a loss function based on the consistent output of the neural network model, which retains the strong fitting capability of the neural network without considering the direct impact of the estimation error on the controller. Subsequently, combined with the control parameters, the gain can be varied over time and iteration, thereby improving the convergence effect of control and achieving faster tracking in iteration.

[0087] Specifically, the following loss function is designed to realize the weight update of unknown parameters of the neural network:

[0088] ;

[0089] The following parameter equation is constructed:

[0090] ;

[0091] ;

[0092] ;

[0093] wherein, , and denote the step factor.

[0094] To extend the neural network algorithm to the iteration axis, the gradient descent on the iteration axis needs to be considered, and then the above parameter equation is designed. Through the loss function, the partial derivatives of , and are calculated by using the derivative of the composite function in mathematics, and the coupling between multiple parameters is comprehensively considered to realize the comprehensive derivation of multiple types of parameters. When the neural network model is migrated to the iterative learning control scene, the dual dynamic characteristics of the time axis and the iteration axis need to be handled simultaneously: on the time axis, the parameters need to respond to the system state changes in real time; on the iteration axis, cross-period optimization needs to be performed based on historical batch data. The coupling characteristics of this dual-dimension make it difficult for the traditional single-axis parameter update mechanism to effectively model, and the embodiment constructs a dual-axis parameter update equation that takes into account dynamic response and historical experience reuse, realizing the comprehensive derivation of multiple types of parameters.

[0095] Specifically, the gradient descent method is used to obtain the neural network update equation between the consistent output and the input vector:

[0096] ;

[0097] ;

[0098] ;

[0099] in, , and They are , and The estimated value.

[0100] S3. Construct a consensus learning control scheme for multi-agent systems based on neural network approximation.

[0101] The criterion function for controlling the input based on the output of a neural network is:

[0102] ;

[0103] in, It is a weighting factor;

[0104] The iterative learning controller is obtained from the criterion function (a13) using the optimization method:

[0105] ;

[0106] in, ; It is the step size factor.

[0107] Combining the neural network parameter update equation and iterative learning controller designed above, the following consensus learning control scheme for a multi-agent system based on neural network approximation is constructed:

[0108] ;

[0109] in, for The estimated vector; It is a saturated function; the definitions of other symbols remain unchanged from those of the same symbols in the preceding steps.

[0110] If a multi-agent system satisfies Assumptions 1-2 and the controller parameters are adjusted within allowable ranges, then the proposed neural network-based iterative consensus learning control method can guarantee: consensus error... It is convergent and bounded; therefore, the tracking error of the system... It also converges to a bounded state.

[0111] To verify the method of the present application, the following simulation was performed on the method of the present application:

[0112] As shown in Figure 3 , consider the following multi-robot system consisting of four DC motor driven robotic arms, construct the dynamic model as:

[0113] ;

[0114] wherein,

[0115] , and represent the angular displacement, velocity and acceleration, respectively;

[0116] is the driving torque, ;

[0117] is the moment of inertia, , , , and represent the motor load, mass, length, damping coefficient and gravitational acceleration, respectively.

[0118] At the sampling time, , the desired velocity is:

[0119] ;

[0120] The controller parameters are set as , , , , , ; the initial values are taken as , , , , , , , , ; the consistency learning control method based on neural network is applied, the tracking performance of the system output at the 1st, 50th, 100th, 200th iteration is shown in Figure 4 ; the convergence of the tracking error is shown in Figure 5 , wherein the vertical axis represents the average tracking error (ATE), which is defined as . From Figure 4 andFigure 5 It can be seen that when model information is unknown and only I / O data is available, the proposed neural network-based consistency learning control method can effectively improve the control performance of the system and achieve the consistency tracking goal.

[0121] The control scheme for comparison document 2 is as follows:

[0122] ;

[0123] ,if or , ;

[0124] ;

[0125] Controller parameters are set to , , , , , , , , The control method proposed in this embodiment is compared with that in prior art document 2. Figure 6 The chart shows a comparison of the tracking performance outputs of the four agents in the 200th iteration; the chart showing the comparison of tracking errors is as follows. Figure 7 As shown. From Figures 6-7 It can be seen that for complex multi-manipulator systems, the proposed consensus control method based on neural network parameter estimation has a faster convergence speed and can achieve better control performance.

[0126] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A neural network-based consistency learning control method, characterized by, The method comprises the following steps: S1, constructing a linear parameterization model of multi-agent consensus output; S2, fitting the input of the previous moment information and the consensus output by a neural network model to obtain linearization parameters, designing a loss function from the consensus output, and obtaining a neural network parameter update algorithm along the time and iteration directions by gradient descent method; Step S2-1, a radial basis neural network method along the iteration is introduced, and the following neural network output model is constructed: wherein is a weight vector; is the hidden layer function vector; n is the number of hidden layer nodes; Step S2-2, the unknown parameters of the neural network are updated, and the following loss function is designed: The neural network parameter estimation algorithm between the consensus output and the input vector is obtained by gradient descent method as follows: wherein , , are the estimated values of , and ; , and denote step size factors, S3, using the output of the neural network to design a controller, and applying the linearization parameters obtained in step S2 to the adjustable gain of the controller, to construct a consensus learning control scheme of the multi-agent system based on neural network approximation.

2. The neural network-based consistency learning control method according to claim 1, characterized by, The step S1 comprises: Step S1-1, constructing a consensus output model of the multi-agent system according to the topological structure information as follows: Wherein, denotes the kth iteration the system output of the jth agent at time representing desired output at a time instant; represents a set of all neighbor agents of the th intelligent agent; constructing an adjacency matrix for the multi-agent system topology; representing an agent communication state with virtual leader 0; Step S1-2, constructing a nonlinear dynamic correlation between the ideal consensus error and the input variable: wherein, represents a system input; represents an agent nonlinear function; and respectively represent a system consensus error and an order of input; Step S1-3, get consistency error by combining state transition iterative dynamic linearization method Linear parameterization model between input vector ​ wherein is the equivalent linearized parameter vector, , denotes the difference operator.

3. The neural network-based consistency learning control method according to claim 1, characterized by, The step S3 comprises: using the neural network output to design the following iterative learning controller: wherein ; is a weight factor; is a step factor.

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