Finite-time cooperative tracking control method based on adaptive RBF neural network

Abstract

The present invention provides a finite-time cooperative tracking control method based on an adaptive RBF neural network, belonging to the technical field of networked multi-agent control strategies. The method comprises the following steps: constructing a dynamic mathematical model of a high-order all-wheel drive uncertain nonlinear multi-agent system including a virtual leader and followers; constructing an error dynamic system including an adaptive RBF neural network estimation compensation term according to a cooperative tracking control target and uncertain terms in the system; designing a finite-time integral sliding mode surface based on the theory of a high-order all-wheel drive system; designing linearization parameters of the finite-time integral sliding mode surface based on a pole configuration method according to the dynamic performance of the system and the finite-time convergence requirement, and obtaining a finite-time integral sliding mode controller; designing an adaptive update law for the RBF neural network weight and the upper bound of the approximate error, introducing the network weight and the approximate error into the finite-time integral sliding mode controller, and realizing finite-time cooperative tracking control.

Description

Technical Field

[0001] The present invention belongs to the technical field of networked multi-agent control strategies, and in particular relates to a finite-time collaborative tracking control method for a high-order all-wheel drive uncertain nonlinear multi-agent system based on an adaptive RBF neural network. Background Art

[0002] With the rapid development of artificial intelligence and automation technologies, collaborative tracking control of nonlinear multi-agent systems has attracted significant attention from control experts and scholars due to its wide application in path planning, smart transportation, smart grids, and other fields. However, traditional nonlinear control schemes are based on first-order state-space methods, resulting in complex controller designs, difficult implementation, and unsatisfactory control performance. Furthermore, considering model uncertainty and the goal of rapid convergence, in light of objective conditions and practical needs, poses even greater challenges to the design of nonlinear control schemes. Summary of the Invention

[0003] To address these issues, the present invention employs an adaptive RBF neural network algorithm to estimate and compensate for system model uncertainty in nonlinear multi-agent systems with high-order all-wheel drive uncertainty. Unlike traditional state-space methods, this invention optimizes the design of a collaborative tracking control scheme based on high-order all-wheel drive theory, ultimately achieving finite-time collaborative tracking control of uncertain nonlinear multi-agent systems.

[0004] The present invention provides a finite-time cooperative tracking control method for a high-order all-wheel drive uncertain multi-agent system based on an adaptive RBF neural network, comprising the following steps:

[0005] S1, construct the dynamic equation model and error system of high-order all-wheel drive uncertain nonlinear multi-agent system;

[0006] S2, uses the adaptive RBF neural network to estimate the uncertainties, and compensates for any uncertainties to obtain the compensated error system;

[0007] S3, based on the high-order all-wheel drive system theory, designs a finite-time integral sliding surface including neighbor error correlation terms and linearization terms;

[0008] S4, according to the system dynamic characteristics and finite time convergence requirements, the linearization parameters are obtained based on the pole placement method, and a finite time integral sliding mode controller is designed;

[0009] S5, based on the finite-time integral sliding surface, designs an adaptive update law for the upper bound of the RBF neural network weights and approximate errors, brings the network weights and approximate errors into the controller, and integrates the controller into the multi-agent system to achieve finite-time collaborative tracking control.

[0010] Preferably, the specific process of S1 is:

[0011] S11, determine the dynamic mathematical model of the follower, where the high-order all-drive uncertain nonlinear multi-agent system is composed of Follower agents, The specific form of the dynamic mathematical model of a follower is as follows:

[0012] ;

[0013] in:

[0014] It is The state variables of an agent, is the dimension of the agent’s state;

[0015] It is Control input for each agent;

[0016] For the An intelligent agent in The state of the moment order derivatives;

[0017] For the An intelligent agent in The 0th to the 1st order of the state at the moment The set of derivatives, namely:

[0018] ;

[0019] is the known nonlinear information of the system;

[0020] is the unknown nonlinear information of the system;

[0021] is the control input matrix of the system, and for any , ,have ;

[0022] S12, determine the dynamic mathematical model of the virtual leader, the specific form is as follows:

[0023] ;

[0024] in Is a virtual leader in Time status Step to The set of derivatives, is the state variable of the virtual leader, is the state variable of the virtual leader derivatives, Nonlinear information for virtual leaders, is the control input matrix of the virtual leader, is the control input of the virtual leader;

[0025] S13, determine the finite-time cooperative tracking control objective of the high-order all-wheel drive uncertain nonlinear multi-agent system, as follows:

[0026] For any agent , there is a time constant , so that for any And any system initial state, we have:

[0027] ;

[0028] in For the An intelligent agent in The state of the moment derivatives, For the virtual leader agent The state of the moment Derivatives.

[0029] Preferably, the specific steps of S2 are:

[0030] S21, definition Neighborhood error of each agent , the specific form is as follows:

[0031] ;

[0032] in, is the graph adjacency matrix corresponding to Rank Column elements, For nodes The containment gain;

[0033] S22, construct an error dynamic system based on the dynamic mathematical model of the follower, the dynamic mathematical model of the virtual leader, and the neighbor error, The specific form of the error dynamic system of an agent is as follows:

[0034] ;

[0035] definition , then:

[0036] ;

[0037] in is the graph Laplacian matrix, is the pinning gain matrix, and:

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] in, for Unit column vector of order; for The unit matrix of order;

[0043] S23, construct an error dynamic system including an adaptive RBF neural network estimation compensation term, the specific form is as follows:

[0044] ;

[0045] in represents the network weight matrix, Indicates the number of neurons in the network; represents the output vector of the Gaussian basis function; represents the approximation error of the neural network;

[0046] represents the input signal of the neural network, and Should meet , is the upper bound of the approximation error.

[0047] Preferably, the finite time integral sliding mode surface described in S3 is specifically in the form of:

[0048] ;

[0049] in:

[0050] ;

[0051] is a hyperparameter, and ;

[0052] ;

[0053] ;

[0054] ;

[0055] is a positive definite diagonal matrix, ;

[0056] ;

[0057] and, is the linearization parameter to be designed;

[0058] ;

[0059] ;

[0060] is a symbolic function.

[0061] Preferably, the specific steps of S4 include:

[0062] S41, according to the system dynamic characteristics and finite time convergence requirements, the linearization parameters are obtained based on the pole placement method;

[0063] S42, based on the linearization parameters and the finite time integral sliding mode surface obtained in S41, a finite time integral sliding mode controller is obtained, which is specifically in the following form:

[0064] ;

[0065] in, is the sum of the known nonlinear information of the system, and , for The identity matrix of order, and are two positive definite diagonal matrices, is the upper bound of the approximation error The estimated value of is the RBF neural network weight The estimated value of and is a positive hyperparameter.

[0066] Preferably, the specific steps of S5 are:

[0067] S51, determine the RBF neural network weight Adaptive update law of ;

[0068] S52, determining an adaptive update law for an upper bound of the approximation error;

[0069] S53, weight and the upper bound of the approximation error Substitute it into the finite-time integral sliding mode controller to realize finite-time cooperative tracking control.

[0070] Preferably, the weight in S51 The adaptive update law is as follows:

[0071] ;

[0072] in, is a positive definite matrix, Weight The derivative of the weighted estimate of .

[0073] Preferably, the adaptive update law of the upper bound of the approximate error in S52 is specifically in the form of:

[0074] ;

[0075] in, is a positive hyperparameter, is the estimated value of the upper bound of the approximation error, for The derivative of .

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] Overall beneficial effects:

[0078] Solve the finite-time cooperative tracking control problem of high-order full-drive uncertain nonlinear multi-agent system: The present invention proposes a finite-time cooperative tracking control method based on an adaptive RBF neural network. Compared with the traditional state-space method, the controller designed by this method is simple and practical, and the control effect is better. Specifically, based on the adaptive RBF neural network, the compensation control of arbitrary model uncertainty is realized, and the finite-time convergence is achieved by constructing a finite-time integral sliding mode controller. At the same time, the high-order full-drive theory is integrated, and the controller linearization parameter items are obtained based on the pole configuration method to achieve the optimization of control performance. It is worth mentioning that the control scheme designed by this invention is applicable to general directed communication topology structures, and has broad application prospects in practical fields such as industrial manufacturing, smart transportation, and smart grids;

[0079] Specific beneficial effects:

[0080] Small model uncertainty restrictions: Use adaptive RBF neural networks to approximate arbitrary model uncertainty online. There is no need to know the upper bound of model uncertainty in advance, which makes it more applicable and has a wider range of applications.

[0081] Simple and practical controller design: Based on high-order all-wheel drive theory, complex nonlinear control problems are transformed into linear control problems, making the corresponding finite-time cooperative controller design simpler and more practical;

[0082] Better collaborative control: The linearization parameters in the controller are obtained based on the pole placement method, which further optimizes the performance indicators of the entire system while achieving finite-time convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a flow chart of the overall process of the present invention.

[0084] Figure 2 It is a directed topological graph of a multi-agent system.

[0085] Figure 3 This is the RBF neural network architecture diagram.

[0086] Figure 4 This is the position error change curve of the multi-agent system.

[0087] Figure 5 This is the speed error change curve of the multi-agent system.

[0088] Figure 6 This is the acceleration error change curve of the multi-agent system.

[0089] Figure 7 This is the position error change curve of the multi-Euler-Lagrangian system.

[0090] Figure 8 This is the velocity error change curve of the multi-Euler-Lagrangian system. DETAILED DESCRIPTION

[0091] The present invention provides a finite time cooperative tracking control method for a high-order all-wheel drive uncertain multi-agent system. The overall process is as follows: Figure 1 As shown, the following steps are included.

[0092] Step 1: Determine the dynamic mathematical model of the follower, where the high-order all-drive uncertain nonlinear multi-agent system is composed of Follower agents, The specific form of the dynamic mathematical model of a follower is as follows:

[0093] ;

[0094] in:

[0095] It is The state variables of an agent, is the dimension of the agent’s state;

[0096] It is Control input for each agent;

[0097] For the An intelligent agent in The state of the moment order derivatives;

[0098] For the An intelligent agent in The 0th to the 1st order of the state at the moment The set of derivatives, namely:

[0099] ;

[0100] is the known nonlinear information of the system;

[0101] is the unknown nonlinear information of the system;

[0102] is the control input matrix of the system, and for any , ,have ;

[0103] Determine the dynamic mathematical model of the virtual leader, the specific form is as follows:

[0104] ;

[0105] in Is a virtual leader in Time status Step to The set of derivatives, is the state variable of the virtual leader, is the state variable of the virtual leader derivatives, Nonlinear information for virtual leaders, is the control input matrix of the virtual leader, is the control input of the virtual leader.

[0106] Step 2: Determine the finite-time cooperative tracking control objective of the high-order all-wheel drive uncertain nonlinear multi-agent system, as follows:

[0107] For any agent , there is a time constant , so that for any And any system initial state, we have:

[0108] ;

[0109] in For the An intelligent agent in The state of the moment derivatives, For the virtual leader agent The state of the moment order derivatives;

[0110] Definition Neighborhood error of each agent , the specific form is as follows:

[0111] ;

[0112] in, is the graph adjacency matrix corresponding to Rank Column elements, For nodes The pinning gain; taking the nth derivative of the neighbor error, we get:

[0113] ;

[0114] Substitute the virtual leader model and follower model into the neighbor error In the derivative, the error system is determined as:

[0115] ;

[0116] definition , then:

[0117] ;

[0118] in is the graph Laplacian matrix, is the pinning gain matrix, and:

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] in, for Unit column vector of order; for The unit matrix of order;

[0124] For unknown uncertainties in the error system , let the total set of uncertain terms be .

[0125] Step 3: Use RBF neural network to An estimate will be made, which will be of the form:

[0126] ;

[0127] in represents the network weight matrix, Indicates the number of neurons in the network, that is, the number of nodes. represents the output vector of the Gaussian basis function; represents the approximation error of the neural network;

[0128] represents the input signal of the neural network, and Should meet , is the approximate error;

[0129] Will Substituting into the error system, the compensated error system is:

[0130] ;

[0131] Build the The high-order full-drive integral sliding surface of an agent is in the form of:

[0132] ;

[0133] in, is the linearization parameter to be designed, is a positive definite diagonal matrix, is a positive constant hyperparameter and , and ;

[0134] make , rewrite the integral sliding surface as:

[0135] ;

[0136] in:

[0137] ;

[0138] is a hyperparameter, and ;

[0139] ;

[0140] ;

[0141] ;

[0142] is a positive definite diagonal matrix, ;

[0143] ;

[0144] and, is the linearization parameter to be designed;

[0145] ;

[0146] ;

[0147] is a symbolic function;

[0148] Taking the derivative of the integral sliding surface, we get:

[0149] ;

[0150] The Substituting into the derivative of the integral sliding surface, we get:

[0151] ;

[0152] Among them, the total set of known nonlinear terms of the system .

[0153] Step 4: According to the system dynamic characteristics and finite time convergence requirements, the linearization parameters are obtained based on the pole placement method;

[0154] According to the linearization parameters, the integral sliding mode control protocol is designed as follows:

[0155] ;

[0156] in and are two positive definite diagonal matrices, is the upper bound of the approximation error, is an estimate of the upper bound of the approximation error Weight The estimated value of and is a positive constant hyperparameter.

[0157] Step 5: Determine the weight The adaptive update law is as follows:

[0158] ;

[0159] in, is a positive definite matrix, Weight The derivative of the estimate of .

[0160] Determine the upper bound of the approximation error The adaptive update law is as follows:

[0161] ;

[0162] in, is a positive constant hyperparameter, is the upper bound of the approximation error The derivative of the estimate of .

[0163] The weight and the upper bound of the approximation error Substitute it into the integral sliding mode control protocol, and then apply the control protocol to the system to achieve finite-time consistency control.

[0164] The present invention will be further described below with reference to the following embodiments. It should be understood that the embodiments described are only a portion of the present invention, not all of the embodiments. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0165] Example 1:

[0166] This embodiment uses a third-order nonlinear multi-agent system model to simulate and verify the effectiveness of the proposed control scheme. The interaction topology diagram of the multi-agent system is shown in Figure 2. Figure 2 As shown, number 0 is the virtual leader and numbers 1-5 are followers. The RBF neural network used to estimate the uncertainty is as follows Figure 3 As shown;

[0167] No. i The dynamic mathematical model of a follower agent is as follows:

[0168] ;

[0169] in:

[0170] ;

[0171] ;

[0172] ;

[0173] The dynamic model of the virtual leader is expressed as:

[0174] ;

[0175] according to Figure 2 Get its corresponding Laplacian matrix and containment gain The matrix has the following form:

[0176] ;

[0177] The controller parameters are designed as follows: , , , , . The integral sliding surface Select as ,parameter , the linearization parameters are: ;

[0178] The initial states of the virtual leader and follower are as follows:

[0179] ;

[0180] Figures 4 to 6 The error curve of the high-order all-wheel drive multi-agent system during the control process is further demonstrated. This curve clearly shows that the system error gradually converges to zero within a finite time, exhibiting a relatively stable trend during the convergence process. This demonstrates that, under the action of the cooperative tracking controller, the system can effectively overcome initial errors and ultimately reach the desired stable state, meeting the basic requirements of cooperative tracking control. Throughout the simulation process, even when the system may be subject to external disturbances or contain certain model uncertainties, the proposed control method maintains high robustness, ensuring that the states of each agent converge within a finite time.

[0181] Example 2:

[0182] The core difference from Example 1 is that the controlled object considered in this embodiment is a multi-manipulator system in an industrial automation scenario. During the collaborative operation process, there are problems such as dynamic load changes, joint friction, and external interference. The corresponding dynamic mathematical model can be modeled as an uncertain multi-Eulerian-Lagrangian system, which is specifically in the following form:

[0183] ;

[0184] in ,when When , it is the dynamic mathematical model of the virtual leader, otherwise it is the dynamic mathematical model of the follower. The interactive topology diagram is as follows Figure 2 shown. For the The robot arm joint angle position vector (the state of the system), Its first and second order derivatives, is the control torque input (the control input of the system). is the inertia matrix of the system, the Coriolis force matrix An antisymmetric structure is used, and its non-diagonal elements represent the inertial coupling effect between joints. and are the matrices of gravity and friction respectively, is the set of uncertainties and disturbances of the system;

[0185] The coefficients of the correlation matrix are chosen as:

[0186] ;

[0187] ;

[0188] ;

[0189] ;

[0190] ;

[0191] Its all-wheel drive form is:

[0192] ;

[0193] in:

[0194] ;

[0195] ;

[0196] The controller parameters are designed to be , , , , . The integral sliding surface Select as ,parameter For the linearization parameters, the high-order full drive method can be designed as:

[0197] .

[0198] The initial state of the system is set as follows: .

[0199] Figure 7 and Figure 8The changing curves of the position and velocity errors of the multi-Euler-Lagrangian system are further demonstrated. The figure shows that the system errors converge to 0 in a relatively fast time, that is, under the action of the collaborative tracking control scheme of the present invention, the multi-agent system can quickly realize collaborative tracking control.

[0200] The above description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

[0201] Although the above describes the specific implementation methods of the present invention, it does not limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A finite time cooperative tracking control method based on an adaptive RBF neural network, characterized in that: The following processes are included: S1, construct a dynamic mathematical model of a high-order all-drive uncertain nonlinear multi-agent system including virtual leaders and followers; S2, based on the collaborative tracking control objectives and the uncertainties in the system, an error dynamic system including an adaptive RBF neural network estimation compensation term is constructed; S3, based on the high-order all-wheel drive system theory, designs a finite-time integral sliding surface including neighbor error correlation terms and linearization terms; S4, according to the system dynamic performance and finite time convergence requirements, the linearization parameters of the finite time integral sliding mode surface are designed based on the pole placement method to obtain the finite time integral sliding mode controller; The specific steps include: S41, according to the system dynamic characteristics and finite time convergence requirements, the linearization parameters are obtained based on the pole placement method; S42, based on the linearization parameters and the finite time integral sliding mode surface obtained in S41, a finite time integral sliding mode controller is obtained, which is specifically in the following form: ； in, is the sum of the known nonlinear information of the system, and , is the Laplace matrix, is the pinning gain matrix; for The unit matrix of order; ； for -dimensional unit vector; ； is a positive definite diagonal matrix, ; is a hyperparameter, ; ； and are two positive definite diagonal matrices respectively; is the upper bound of the approximation error estimated value of; is the number of agents; is the RBF neural network weight estimated value of; and is a positive hyperparameter; For the agent state n order derivatives; ； ； is a symbolic function; ； Represents the input signal of the neural network; S5, based on the finite-time integral sliding mode surface, designs an adaptive update law for the RBF neural network weights and the upper bound of the approximate error, introduces the network weights and approximate error into the finite-time integral sliding mode controller, and realizes finite-time cooperative tracking control; the specific steps are: S51, determine the RBF neural network weight The adaptive update law is as follows: ； in, is a positive definite matrix, Weight The derivative of the weighted estimate of ; S52, determine the adaptive update law of the upper bound of the approximate error, the specific form is: ； in is a positive hyperparameter, is the estimated value of the upper bound of the approximation error, for The derivative of S53, weight and the upper bound of the approximation error Substitute it into the finite-time integral sliding mode controller to realize finite-time cooperative tracking control.

2. The finite-time cooperative tracking control method based on an adaptive RBF neural network according to claim 1, characterized in that: The specific process of S1 is as follows: S11, determine the dynamic mathematical model of the follower, where the high-order all-drive uncertain nonlinear multi-agent system is composed of Follower agents, The specific form of the dynamic mathematical model of a follower is as follows: ； in: It is The state variables of an agent, is the dimension of the agent’s state; It is Control input for each agent; For the An intelligent agent in The state of the moment order derivatives; For the An intelligent agent in The 0th to the 1st order of the state at the moment The set of derivatives, namely: ； is the known nonlinear information of the system; is the unknown nonlinear information of the system; is the control input matrix of the system, and for any , have ; S12, determine the dynamic mathematical model of the virtual leader, the specific form is as follows: ； in Is the virtual leader in Time status Step to The set of derivatives, is the state variable of the virtual leader, is the state variable of the virtual leader derivatives, Nonlinear information for virtual leaders, is the control input matrix of the virtual leader, is the control input of the virtual leader; S13, determine the finite-time cooperative tracking control objective of the high-order all-wheel drive uncertain nonlinear multi-agent system, as follows: For any agent , there is a time constant , so that for any And any system initial state, we have: ； in, For the An intelligent agent in The state of the moment derivatives, For the virtual leader agent The state of the moment Derivatives.

3. The finite time cooperative tracking control method based on an adaptive RBF neural network according to claim 2, characterized in that: The specific steps of S2 are: S21, definition Neighborhood error of each agent , the specific form is as follows: ； in is the graph adjacency matrix corresponding to Rank Column elements, For nodes The containment gain; S22, construct an error dynamic system based on the dynamic mathematical model of the follower, the dynamic mathematical model of the virtual leader, and the neighbor error, The specific form of the error dynamic system of an agent is as follows: ； definition , then: ； in is the graph Laplacian matrix, is the pinning gain matrix, and: ； ； ； ； in, for Unit column vector of order; for The unit matrix of order; S23, construct an error dynamic system including an adaptive RBF neural network estimation compensation term, the specific form is as follows: ； in represents the network weight matrix, Indicates the number of neurons in the network; represents the output vector of the Gaussian basis function; represents the approximation error of the neural network; represents the input signal of the neural network, and Should meet , is the upper bound of the approximation error.

4. The finite-time cooperative tracking control method based on an adaptive RBF neural network according to claim 3, characterized in that: The specific form of the finite time integral sliding mode surface described in S3 is: ； in: ； is a hyperparameter, and ; ； ； ； is a positive definite diagonal matrix, ; ； and, is the linearization parameter to be designed; ； ； is a symbolic function.

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