Finite-time consensus control method for high-order all-wheel drive uncertain multi-agent systems

Abstract

The present invention provides a finite-time consistency control method for a high-order all-wheel drive uncertain nonlinear multi-agent system. First, a dynamic equation model of the high-order all-wheel drive uncertain nonlinear multi-agent system is constructed; then, a finite-time integral sliding surface is designed; based on the established multi-agent system dynamic equation model and the designed finite-time integral sliding surface, an adaptive control method is used to estimate the unknown parameters of the system and obtain an equivalent distributed adaptive finite-time integral sliding mode controller; based on the pole placement method, the finite-time integral sliding surface and the linearized parameters involved in the corresponding controller that meet the system performance requirements are obtained; the designed controller is introduced into the high-order all-wheel drive uncertain nonlinear multi-agent system to achieve the finite-time consistency control goal. This method not only fully demonstrates the advantages of high-order all-wheel drive theory in nonlinear system control, but also lays an important foundation for the integrated development of high-order all-wheel drive theory and traditional control theory.

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 consistency control method for a high-order all-wheel drive uncertain multi-agent system. Background Art

[0002] In practical applications, the rapid response capability of multi-agent systems is a crucial performance metric. Finite-time control methods offer significant advantages in improving system speed, as they enable the system state to converge to the ideal state within a preset time. However, real-world agent system models often exhibit nonlinear characteristics and uncertainties, which poses significant challenges to finite-time consensus control. Designing a consistent controller for complex nonlinear systems is inherently challenging within the framework of traditional state-space methods, and achieving finite-time convergence further increases the difficulty.

[0003] There are two major problems in designing consensus controllers for nonlinear multi-agent systems: 1) the model has strong specific nonlinear constraints, meaning that system performance analysis and controller design can only be performed for one or several types of nonlinear dynamics; and 2) the design process of nonlinear controllers is very complex. Summary of the Invention

[0004] To address the above problems, the present invention provides a finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system, which is characterized by comprising the following steps:

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

[0006] S2, designing a finite-time integral sliding surface based on the agent’s neighbor errors and their derivatives of various orders and linearized information terms;

[0007] S3, deriving the finite-time integral sliding mode surface and using adaptive control methods to estimate the unknown parameters of the system, thereby obtaining an equivalent distributed adaptive finite-time integral sliding mode controller;

[0008] S4, based on the pole placement method, obtain the finite time integral sliding mode surface and the linearization parameters involved in the corresponding controller that meet the system performance requirements;

[0009] S5, an adaptive finite-time integral sliding mode controller with determined linearization parameters is introduced into the high-order all-wheel drive uncertain nonlinear multi-agent system to achieve the finite-time consistency control goal.

[0010] Preferably, the high-order all-drive uncertain nonlinear multi-agent system in S1 is composed of It is composed of intelligent agents, of which the The dynamic equation of an agent is as follows:

[0011] ;

[0012] in:

[0013] It is The state input of each agent;

[0014] 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 and satisfies , is a positive real number;

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

[0022] Preferably, the specific process of S2 is:

[0023] S21, determine the finite-time consistency control objectives of the high-order all-wheel drive uncertain nonlinear multi-agent system, as follows:

[0024] For any two agents and agents , there is a time constant , so that for any , agent and agents The state and its derivatives of all orders can be consistent, that is:

[0025] ;

[0026] in, For the Agent state No. derivatives, For the Agent state No. order derivatives;

[0027] S22: Design a distributed adaptive finite-time integral sliding mode controller for the dynamic model of the multi-agent system in S1 and the finite-time consistency control objective in S21. , the specific form is as follows:

[0028] ;

[0029] in:

[0030] is the finite-time integral sliding mode controller to be designed;

[0031] is the finite-time adaptive controller to be designed;

[0032] S23, p. Finite-time integral sliding surface of an agent By its state Derivative , the integral of the linearized information term The integral of the sum of the error information of the neighbors The specific form is as follows:

[0033] ;

[0034] in:

[0035] is the graph adjacency matrix corresponding to Rank Column elements;

[0036] is the neighbor error information term coefficient, and satisfies ;

[0037] is a constant gain that scales the neighbor error term and satisfies , is a constant that adjusts the convergence characteristics of the system;

[0038] is the linearization parameter to be designed;

[0039] is the neighbor error information related item.

[0040] Preferably, the neighbor error information related items in S23 The specific form is:

[0041] ;

[0042] in, is the agent state dimension, is a symbolic function.

[0043] Preferably, the specific steps for designing the distributed adaptive finite-time integral sliding mode controller in S3 are:

[0044] S31, for the finite time integral sliding surface Take the derivative and get the corresponding derivative ;

[0045] S32, designed by nonlinear terms , linearization information item and neighbor error information and Finite-time integral sliding mode controller ;

[0046] S33, designed by switching control items and model uncertainty compensation Finite-time adaptive controller ,in:

[0047] The linearization control gain coefficient satisfies: , ;

[0048] Exponential power parameter satisfy: ;

[0049] The adaptive adjustment coefficient satisfies: ;

[0050] To address uncertainty An estimate of the unknown upper bound of ;

[0051] is a saturation function;

[0052] S34, based on the known system nonlinear information, linearization information term, neighbor error information, integral sliding mode surface and model uncertainty compensation information, design an adaptive finite time integral sliding mode controller consisting of a finite time integral sliding mode controller and a finite time adaptive controller ;

[0053] S35, for Unknown nonlinear information of the agent Upper bound of , based on the designed finite time integral sliding surface, the adaptive control method is used to obtain its estimated value online .

[0054] Preferably, the finite time adaptive controller The specific form of the saturation function in is as follows:

[0055] ;

[0056] in , To adjust the upper bound of uncertainty The decay rate, It is for uncertainty An estimate of the unknown upper bound of , and:

[0057] ;

[0058] in,

[0059] is the finite time integral sliding surface;

[0060] is the dimension of the agent’s state;

[0061] is a symbolic function.

[0062] Preferably, the specific process of S4 is:

[0063] S41, constructing an eigenvector matrix of finite relative eigenvalues and infinite relative eigenvalues of the closed-loop system based on a pole placement method, and verifying the non-singularity of the eigenvector matrix;

[0064] S42, adjusting the eigenvector matrix according to the system matrix type. If the system matrix is a unit matrix, eliminating the eigenvector component corresponding to the infinite eigenvalue;

[0065] S43, introduces a parameterized matrix set, configures the characteristic structure of the closed-loop system through the free parameter matrix, and finds a solution that meets the configuration conditions;

[0066] S44, decomposing the controller parameters into linear combination forms, combining with the adaptive adjustment matrix, and solving the linearization parameters of each order respectively;

[0067] S45, verify the reversibility of the parameter matrix and modify the configuration conditions according to the dynamic performance and stability requirements of the closed-loop system.

[0068] Preferably, the finite time integral sliding mode controller in S32 The specific form is:

[0069] ;

[0070] in:

[0071] is the linearization parameter to be designed;

[0072] is the related item of neighbor error information;

[0073] is the coefficient of the neighbor error information term;

[0074] For the known nonlinear information items of each agent;

[0075] is the graph adjacency matrix corresponding to Rank Column elements;

[0076] For the An intelligent agent in The state of the moment order derivatives;

[0077] For the An intelligent agent in The state of the moment order derivatives;

[0078] is a constant gain that scales the neighbor error term and satisfies , is a constant that adjusts the convergence characteristics of the system.

[0079] Preferably, the finite time adaptive controller in S33 , the specific form is as follows:

[0080] ;

[0081] in:

[0082] For the Unknown nonlinear information of the agent Upper bound of estimated value of;

[0083] The linearization control gain coefficient satisfies: , ;

[0084] is the finite time integral sliding surface;

[0085] is the dimension of the agent’s state;

[0086] The saturation function is the same as the above saturation function.

[0087] Preferably, the adaptive finite-time integral sliding mode controller in S34 is specifically in the following form:

[0088] ;

[0089] in:

[0090] is the control input matrix, and for any , ;

[0091] and They are The state variables and control inputs of each agent;

[0092] , for the An intelligent agent in The state of the moment order derivatives;

[0093] , for the An intelligent agent in The state of the moment order derivatives;

[0094] For the An intelligent agent in The 0th to the 1st order of the state at the moment The set of derivatives, namely:

[0095] ;

[0096] is the known nonlinear information of the system;

[0097] is the coefficient of the neighbor error information term;

[0098] is the number of agents;

[0099] The communication topology adjacency matrix corresponds to Rank Elements of the column;

[0100] is a constant gain that scales the neighbor error term and satisfies , is a constant that adjusts the convergence characteristics of the system;

[0101] is the linearization parameter to be designed;

[0102] The linearization control gain coefficient satisfies: , ;

[0103] Exponential power parameter satisfy: ;

[0104] The adaptive adjustment coefficient satisfies: .

[0105] Saturation function This is consistent with the saturation function mentioned above.

[0106] Compared with the prior art, the present invention has the following beneficial effects:

[0107] The present invention first transforms the nonlinear control problem into a linear control problem based on high-order all-wheel drive theory. At the same time, the design of the integral sliding surface achieves finite-time convergence of the system and makes the system robust.

[0108] Aiming at the uncertainty of the system, an adaptive control method is used to perform online estimation under the premise that there is an unknown upper bound.

[0109] Under the high-order all-wheel drive architecture, the controller parameters are designed based on the pole placement method, which improves the control performance of the entire system and ensures the operational efficiency of the multi-agent system. Finally, simulation experiments verify the effectiveness of the proposed control scheme.

[0110] Specifically, the high-order full-drive theory is first used to transform the nonlinear problem into a linear problem, which simplifies the controller design process.

[0111] Secondly, by designing an integral sliding surface, we ensure that the system state converges in a finite time while reducing controller chattering by introducing an integral term, thereby improving the robustness and speed of the system. In response to the uncertainty in the system, an adaptive method is used to estimate the upper bound of the uncertainty online.

[0112] The controller and the linearization parameters in the integral sliding surface are designed based on the pole placement method, which fully utilizes the advantages of high-order all-wheel drive theory in control. BRIEF DESCRIPTION OF THE DRAWINGS

[0113] Figure 1 It is a flow chart of the overall process of the present invention.

[0114] Figure 2 It is a directed topological graph of a multi-agent system.

[0115] Figure 3 This is a curve diagram of the position change of the multi-agent system.

[0116] Figure 4 This is the speed change curve of the multi-agent system.

[0117] Figure 5 This is the acceleration change curve of the multi-agent system.

[0118] Figure 6 It is the curve diagram of the integral sliding surface change.

[0119] Figure 7 It is the adaptive parameter change curve.

[0120] Figure 8 This is the position change curve of the multi-Eulerian-Lagrangian system.

[0121] Figure 9 This is the velocity change curve of the multi-Eulerian-Lagrangian system.

[0122] Figure 10 Control input variation curve diagram for multi-Euler-Lagrangian system.

[0123] Figure 11 This is the adaptive parameter change curve of the multi-Euler-Lagrangian system.

[0124] Figure 12 This is the curve diagram of the integral sliding surface change of the multi-Euler-Lagrangian system. DETAILED DESCRIPTION

[0125] The present invention provides a finite time consistency 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:

[0126] Step 1: Construct a dynamic equation model of a high-order all-wheel drive uncertain nonlinear multi-agent system;

[0127] Step 2: for the multi-agent system model established in step 1, design a finite-time integral sliding surface based on the agent neighbor errors and their derivatives of various orders and linearized information items;

[0128] Step 3: Based on the high-order nonlinear multi-agent model established in step 1 and the finite-time integral sliding mode surface obtained in step 2, an adaptive control method is used to estimate the unknown parameters of the system and obtain an equivalent distributed adaptive finite-time integral sliding mode controller;

[0129] Step 4: Based on the sliding mode controller of the adaptive integral sliding mode controller in step 3 and the high-order nonlinear multi-agent system in step 1, a finite-time integral sliding mode surface and linearization parameters involved in the corresponding controller that meet system performance requirements are obtained based on the pole placement method;

[0130] In step five, the linearized parameters determined in step four are substituted back into the adaptive finite-time integral sliding mode controller, and then the controller is introduced into the high-order all-wheel drive uncertain nonlinear multi-agent system to achieve the finite-time consistency control goal.

[0131] 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.

[0132] Example 1:

[0133] This embodiment uses a third-order nonlinear multi-agent model as an example. Assume that the multi-agent system consists of five agents, and the corresponding communication topology diagram is as follows: Figure 2 The corresponding Laplacian matrix is as follows:

[0134] .

[0135] Without loss of generality, assume that The specific form of the agent model is as follows:

[0136] ;

[0137] in:

[0138] Representing the An intelligent agent in Position, velocity and acceleration information at each moment;

[0139] For the The unmodeled part of the agent;

[0140] For the The control matrix items of each agent.

[0141] The control parameters in the sliding surface are designed based on the pole placement method as follows:

[0142] ;

[0143] The parameters in the controller are designed as follows:

[0144] , , ;

[0145] The adaptive update rate parameters are designed as:

[0146] , .

[0147] The initial state of the agent is set as follows:

[0148] .

[0149] Based on the above conditions and parameter settings, a simulation time of 60s was selected for the experiment. Figures 3 to 5 The simulation results clearly show that despite the presence of uncertainties in the agent model, the states of the five agents are able to achieve consistency within a finite timeframe. Specifically, as the simulation progresses, the positions, velocities, and accelerations of all agents gradually converge, demonstrating the system's excellent collaborative nature.

[0150] like Figure 6 As shown in the figure, based on the high-order all-wheel drive system theory method, the integral sliding mode surface can converge to 0 in a limited time and maintain its invariance. From the above simulation results, it can be seen that even if there are unmodeled uncertainties, the system maintains the ability to converge quickly. Figure 7 The effectiveness of adaptive gain was further verified, demonstrating its ability to effectively mitigate the impact of unmodeled uncertainty on system performance. By adjusting the adaptive gain, the system can dynamically adjust its control parameters in the face of unknown or changing environments, further improving system robustness and ensuring both stability and accuracy.

[0151] Example 2:

[0152] This embodiment addresses the problem of insufficient synchronization accuracy caused by dynamic load changes, joint friction differences, and external disturbances in the collaborative operation of multiple robotic arms. A robust adaptive control method based on high-order all-wheel drive logic is proposed. In industrial automation scenarios (such as multiple robotic arms collaboratively handling heavy parts in an automobile assembly line), it is necessary to ensure the consistency of the position and velocity of the five robotic arms under strongly coupled nonlinear dynamics. To this end, the system is modeled as a distributed control problem of a multi-Eulerian-Lagrangian system, and its dynamic equation is expressed as:

[0153] ;

[0154] in 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 term and friction term respectively, is the set of uncertainties and disturbances of the system.

[0155] The coefficients of the correlation matrix are chosen as:

[0156] ;

[0157] ;

[0158] ;

[0159] ;

[0160] ;

[0161] Its all-wheel drive form is:

[0162] ;

[0163] in:

[0164] ;

[0165] .

[0166] For the linearized parameters in the sliding surface, according to the design scheme given by the high-order full-drive theory, it is designed as follows:

[0167] .

[0168] The parameters in the controller are designed as follows:

[0169] , , .

[0170] The adaptive update rate parameters are designed as:

[0171] , .

[0172] The initial state is set as follows: .

[0173] On the basis of the above conditions and parameter settings, in order to further verify the effectiveness and robustness of the proposed control strategy, a simulation time of 60s was also selected for the experiment. The position and velocity change curves of each agent are shown in Figure 2. Figure 8 and Figure 9 As shown in the figure, it is not difficult to see that despite the increase in the system's dimensionality, all agents stabilize after about 10 seconds, and the states of each agent are consistent. This also shows the good collaborative properties of the system. Figure 10 The change curve of the control input is further shown. Figure 11 The variation curve of adaptive parameters is shown. Figure 12 The paper demonstrates that the integral sliding mode surface established based on high-order all-wheel drive system theory can converge to zero in a finite time while maintaining its invariance. The estimated parameters converged within a short period of time, demonstrating the successful multi-manipulator collaborative task.

[0174] 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.

[0175] 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 consensus control method for a high-order all-wheel drive uncertain multi-agent system, characterized in that: The following processes are included: S1, construct the dynamic equation model of high-order all-wheel drive uncertain nonlinear multi-agent system; S2, designing a finite-time integral sliding surface based on the agent’s neighbor errors and their derivatives of various orders and linearized information terms; S3, derive the finite-time integral sliding mode surface and use adaptive control methods to estimate the unknown system parameters, thereby obtaining an equivalent distributed adaptive finite-time integral sliding mode controller. The specific steps for designing the distributed adaptive finite-time integral sliding mode controller are as follows: S31, for the finite time integral sliding surface Take the derivative and get the corresponding derivative ; S32, designed by nonlinear terms , linearization information item and neighbor error information and Finite-time integral sliding mode controller ,in: is the coefficient of the neighbor error information term; is the neighbor error information related item; is a constant gain for scaling the neighbor error terms; It is The state variables of the agent order derivatives; It is The state variables of the agent order derivatives; S33, designed by switching control items and model uncertainty compensation Finite-time adaptive controller ,in: The linearization control gain coefficient satisfies: , ; Exponential power parameter satisfy: ; The adaptive adjustment coefficient satisfies: ; is a saturation function; It is for uncertainty An estimate of the unknown upper bound of ; S34, based on the known system nonlinear information, linearization information term, neighbor error information, integral sliding mode surface and model uncertainty compensation information, design an adaptive finite time integral sliding mode controller consisting of a finite time integral sliding mode controller and a finite time adaptive controller ; S35, for Unknown nonlinear information of the agent Upper bound of , based on the designed finite time integral sliding surface, the adaptive control method is used to obtain its estimated value online ; S4, based on the pole placement method, obtain the finite time integral sliding mode surface and the linearization parameters involved in the corresponding controller that meet the system performance requirements; S5, an adaptive finite-time integral sliding mode controller with determined linearization parameters is introduced into the high-order all-wheel drive uncertain nonlinear multi-agent system to achieve the finite-time consistency control goal.

2. The finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system according to claim 1, characterized in that: The high-order all-drive uncertain nonlinear multi-agent system in S1 is composed of It is composed of intelligent agents, of which the The dynamic equation of an agent is as follows: in: It is The state variables of each 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 and satisfies , is a positive real number; is the control input matrix of the system, and for any , .

3. The finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system according to claim 2, characterized in that: The specific process of S2 is: S21, determine the finite-time consistency control objectives of the high-order all-wheel drive uncertain nonlinear multi-agent system, as follows: For any two agents and agents , there is a time constant , so that for any , agent and agents The state and its derivatives of all orders can be consistent, that is: ； in, For the Agent state No. derivatives, For the Agent state No. order derivatives; S22: Design a distributed adaptive finite-time integral sliding mode controller for the dynamic model of the multi-agent system in S1 and the finite-time consistency control objective in S21. , the specific form is as follows: ； in: is the finite-time integral sliding mode controller to be designed; is the finite-time adaptive controller to be designed; S23, p. Finite-time integral sliding surface of an agent By its state Derivative , the integral of the linearized information term The integral of the sum of the error information of the neighbors The specific form is as follows: ； in: is the graph adjacency matrix corresponding to Rank Column elements; is the neighbor error information term coefficient, and satisfies ; is a constant gain that scales the neighbor error term and satisfies , is a constant that adjusts the convergence characteristics of the system; is the linearization parameter to be designed; is the neighbor error information related item.

4. A finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system as claimed in claim 3, characterized in that: The neighbor error information related items in S23 The specific form is: ； in, is a symbolic function.

5. The finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system according to claim 1, characterized in that: The finite time adaptive controller The specific form of the saturation function in is as follows: ； in , To adjust the upper bound of uncertainty The decay rate, It is for uncertainty An estimate of the unknown upper bound of , and: ； in, is the finite time integral sliding surface; is a symbolic function.

6. The finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system according to claim 1, characterized in that: The specific process of S4 is: S41, constructing an eigenvector matrix of finite relative eigenvalues and infinite relative eigenvalues of the closed-loop system based on a pole placement method, and verifying the non-singularity of the eigenvector matrix; S42, adjusting the eigenvector matrix according to the system matrix type. If the system matrix is a unit matrix, eliminating the eigenvector component corresponding to the infinite eigenvalue; S43, introduces a parameterized matrix set, configures the characteristic structure of the closed-loop system through the free parameter matrix, and finds a solution that meets the configuration conditions; S44, decomposing the controller parameters into linear combination forms, combining with the adaptive adjustment matrix, and solving the linearization parameters of each order respectively; S45, verify the reversibility of the parameter matrix and modify the configuration conditions according to the dynamic performance and stability requirements of the closed-loop system.

7. The finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system according to claim 5, characterized in that: The finite time integral sliding mode controller in S32 The specific form is: ； in: is the linearization parameter to be designed; is the related item of neighbor error information; is the coefficient of the neighbor error information term; For the known nonlinear information items of each agent; is the graph adjacency matrix corresponding to Rank Column elements; For the An intelligent agent in The state of the moment order derivatives; For the An intelligent agent in The state of the moment order derivatives; is a constant gain that scales the neighbor error term and satisfies , is a constant that adjusts the convergence characteristics of the system.

8. The finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system according to claim 1, characterized in that: The finite time adaptive controller in S33 , the specific form is as follows: ； in: For the Unknown nonlinear information of the agent Upper bound of estimated value of; The linearization control gain coefficient satisfies: , .

9. The finite-time consensus control method for a high-order all-wheel drive uncertain multi-agent system according to claim 5, characterized in that: The adaptive finite time integral sliding mode controller in S34 is specifically in the following form: ； in: is the control input matrix, and for any , ; and They are The state variables and control inputs of each agent; , for the An intelligent agent in The state of the moment order derivatives; , 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 coefficient of the neighbor error information term; is the number of agents; is the graph adjacency matrix corresponding to Rank Column elements; is a constant gain that scales the neighbor error term and satisfies , is a constant that adjusts the convergence characteristics of the system; is the linearization parameter to be designed; The linearization control gain coefficient satisfies: , ; Exponential power parameter satisfy: ; The adaptive adjustment coefficient satisfies: .

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