Finite time consistency control method for high-order all-drive uncertain multi-agent system

Abstract

The invention provides a finite time consistency control method for a high-order all-drive uncertain multi-agent system. The finite time consistency control method comprises the following steps: firstly, constructing a dynamic equation model of the high-order all-drive uncertain non-linear multi-agent system; designing a finite time integral sliding mode surface; according to the established multi-agent system dynamic equation model and the designed finite time integral sliding mode surface, adopting an adaptive control method to estimate unknown parameters of the system, and obtaining an equivalent distributed adaptive finite time integral sliding mode controller; based on a pole assignment method, linear parameters which meet system performance requirements and are involved in a finite time integral sliding mode surface and a corresponding controller are obtained; the designed controller is substituted into a high-order all-drive uncertain nonlinear multi-agent system, and the finite time consistency control target is achieved. The method not only fully reflects the advantages of the high-order all-drive theory in the aspect of nonlinear system control, but also lays an important foundation for the fusion development of the high-order all-drive theory and the traditional control theory.

Description

Technical Field

[0001] The present invention belongs to the technical field of networked multi-agent control strategies, and particularly relates to a finite-time consensus control method for a high-order fully actuated uncertain multi-agent system. Background Art

[0002] In practical applications, the fast response ability of a multi-agent system is a crucial performance index. The finite-time control method has shown significant advantages in improving the rapidity of the system because it can make the system state converge to the ideal state within a preset time. However, the agent system models in reality often have nonlinear characteristics and uncertainties, which pose severe challenges to finite-time consensus control. Especially within the framework of traditional state-space methods, it is already difficult to design a consensus controller for complex nonlinear systems, and the difficulty increases significantly if finite-time convergence is to be further achieved.

[0003] There are two major problems in the design of a consensus controller for a nonlinear multi-agent system: 1) The specific nonlinear constraints of the model are strong, that is, the system performance analysis and controller design can only be carried out for a certain class or several classes of nonlinear dynamics; 2) The design process of the nonlinear controller is very complex. Summary of the Invention

[0004] In view of the above problems, the present invention provides a finite-time consensus control method for a high-order fully actuated uncertain multi-agent system, which is characterized by including the following processes: S1. Construct a dynamic equation model of a high-order fully actuated uncertain nonlinear multi-agent system; S2. Design a finite-time integral sliding mode surface according to the agent neighbor error and its derivatives of each order, and the linearized information term; S3. Differentiate the finite-time integral sliding mode surface, and use an adaptive control method to estimate the unknown parameters of the system, and then obtain an equivalent distributed adaptive finite-time integral sliding mode controller; S4. Based on the pole placement method, obtain the linearized parameters that satisfy the system performance requirements involved in the finite-time integral sliding mode surface and the corresponding controller; S5. Substitute the adaptive finite-time integral sliding mode controller with determined linearized parameters into the high-order fully actuated uncertain nonlinear multi-agent system to achieve the finite-time consensus control goal.

[0005] Preferably, the high-order fully actuated uncertain nonlinear multi-agent system in the S1 consists of agents, and the dynamic equation of the th agent is as follows: ; Where: is the state input of the th agent; is the dimension of the agent state; is the control input of the th agent; is the th - order derivative of the state of the th agent at time ; is the set of the 0 - th to th - order derivatives of the state of the th agent at time , that is: ; is the known nonlinear - term information of the system; is the unknown nonlinear - term information of the system and satisfies , is a positive real number; is the large control - input matrix of the system, and for any , .

[0006] Preferably, the specific process of S2 is as follows: S21. Determine the finite - time consensus - control objective of the high - order fully - actuated uncertain nonlinear multi - agent system, specifically as follows: For any two agents and agent , there exists a time constant such that for any , the states and their respective derivatives of agent and agent can converge to be the same, that is: ; where, is the th - order derivative of the state of the th agent, is the th - order derivative of the state of the th agent; 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 consensus - control objective in S21 , in the following specific form: ; Wherein: is the finite-time integral sliding mode controller to be designed; is the finite-time adaptive controller to be designed; S23, the finite-time integral sliding mode surface of the th agent is composed of the th-order derivative of its state, the integral of the linearization information term and the integral of the sum of neighbor error information , in the following specific form: ; Wherein: is the element of the th row and th column corresponding to the graph adjacency matrix; is the coefficient of the neighbor error information term and satisfies ; is the constant gain for scaling the neighbor error term and satisfies , is the constant for adjusting the convergence characteristic of the system; is the linearization parameter to be designed; is the term related to neighbor error information.

[0007] Preferably, the term related to neighbor error information in the above S23 ; Wherein, is the dimension of the agent state, is the sign function.

[0008] Preferably, the specific steps for designing the distributed adaptive finite-time integral sliding mode controller in the above S3 are as follows: S31, take the derivative of the finite-time integral sliding mode surface to obtain the corresponding derivative ; S32, design the finite-time integral sliding mode controller composed of the non-linear term , the linearization information term and the sum of neighbor error information ; S33. Design a finite-time adaptive controller composed of a switching control term and a model uncertainty compensation term , where: The linearization control gain coefficient satisfies: ; , ; The exponential power parameter satisfies: ; The adaptive adjustment coefficient satisfies: ; is an estimated value of the unknown upper bound for the uncertainty ; is a saturation function; S34. According to 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 composed of a finite-time integral sliding mode controller and a finite-time adaptive controller ; S35. For the unknown upper bound of the unknown nonlinear term information of the th agent, based on the designed finite-time integral sliding mode surface, use an adaptive control method to obtain its estimated value online.

[0009] Preferably, the specific form of the saturation function in the finite-time adaptive controller is as follows: ; where , is the decay rate for adjusting the upper bound of the uncertainty , is an estimated value of the unknown upper bound for the uncertainty , and: ; where, is the finite-time integral sliding mode surface; is the dimension of the agent state; is the sign function.

[0010] Preferably, the specific process of S4 is: S41. Based on the pole placement method, construct the eigenvector matrices of the finite relative eigenvalues and infinite relative eigenvalues of the closed-loop system, and verify the non-singularity of the eigenvector matrices; S42. Adjust the eigenvector matrix according to the type of system matrix. If the system matrix is an identity matrix, eliminate the eigenvector components corresponding to the infinite eigenvalues; S43. Introduce a set of parameterized matrices, configure the eigenstructure of the closed-loop system through the free parameter matrices, and find the solutions that satisfy the configuration conditions; S44. Decompose the controller parameters into a linear combination form, and combine with the adaptive adjustment matrix to solve each order of linearized parameters respectively; S45. Verify the invertibility of the parameter matrix, and correct the configuration conditions according to the dynamic performance and stability requirements of the closed-loop system.

[0011] Preferably, the finite-time integral sliding mode controller in S32 The specific form is: ; Where: are the linearized parameters to be designed; are the relevant terms of the neighbor error information; are the coefficients of the neighbor error information terms; is the known non-linear information term of the th agent; is the element of the th column of the th row of the graph adjacency matrix corresponding to; is the th derivative of the th order of the state of the th agent at time; is the th derivative of the th order of the state of the th agent at time;

[0012] Preferably, the finite-time adaptive controller in S33 , the specific form is as follows: ; Where: The upper bound of the unknown non - linear term information for the th agent; The estimated value of The linearized control gain coefficient satisfies: , ; is the finite - time integral sliding mode surface; is the dimension of the agent state; The saturation function is the same as the above - mentioned saturation function.

[0013] Preferably, the adaptive finite - time integral sliding mode controller in S34 has the following specific form: ; Where: is the control input matrix, and for any , ; and are respectively the state variable and control input of the th agent; , is the th - order derivative of the state of the th agent at time ; , is the th - order derivative of the state of the th agent at time ; is the set of the 0 - th to th - order derivatives of the state of the th agent at time , that is: ; is the known non - linear term information of the system; is the coefficient of the neighbor error information term; is the number of agents; is the element in the th row and th column of the communication topology adjacency matrix; is the constant gain for scaling the neighbor error term and satisfies , is a constant for adjusting the system convergence characteristics; is a linearization parameter to be designed; The linearization control gain coefficient satisfies: , ; Exponential power parameter satisfies: ; The adaptive adjustment coefficient satisfies: .

[0014] Saturation function is consistent with the above saturation function.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The present invention first transforms the non-linear control problem into a linear control problem based on the high-order full-drive theory. At the same time, the design of the integral sliding surface realizes the finite-time convergence of the system and makes the system have a certain robustness.

[0016] Aiming at the uncertainty of the system, under the premise that there is an unknown upper bound, an adaptive control method is used for online estimation.

[0017] Under the high-order full-drive method framework, the design of the controller parameters is based on the pole-placement method, which will make the control performance of the whole system better and ensure the operation efficiency of the multi-agent system. Finally, the effectiveness of the proposed control scheme is verified through simulation experiments.

[0018] Specifically, first, the high-order full-drive theory is used to transform the non-linear problem into a linear problem, which simplifies the design process of the controller.

[0019] Secondly, by designing the integral sliding surface, while ensuring that the chattering of the controller is reduced by introducing the integral term, the system state can converge in finite time, improving the robustness and rapidity of the system. For the uncertainty existing in the system, an adaptive method is used to online estimate the upper bound of the uncertainty.

[0020] Based on the pole-placement method, the linearization parameters in the controller and the integral sliding surface are designed, giving full play to the advantages of the high-order full-drive theory in control. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is the overall process flow chart of the present invention.

[0022] Figure 2 is the directed topology graph of the multi-agent system.

[0023] Figure 3 is the curve graph of the position change of the multi-agent system.

[0024] Figure 4 It is the speed change curve graph of the multi-agent system.

[0025] Figure 5 It is the acceleration change curve graph of the multi-agent system.

[0026] Figure 6 It is the integral sliding mode surface change curve graph.

[0027] Figure 7 It is the adaptive parameter change curve graph.

[0028] Figure 8 It is the position change curve graph of the multi-Euler-Lagrange system.

[0029] Figure 9 It is the speed change curve graph of the multi-Euler-Lagrange system.

[0030] Figure 10 It is the control input change curve graph of the multi-Euler-Lagrange system.

[0031] Figure 11 It is the adaptive parameter change curve graph of the multi-Euler-Lagrange system.

[0032] Figure 12 It is the integral sliding mode surface change curve graph of the multi-Euler-Lagrange system. Detailed implementation manners

[0033] The present invention provides a finite-time consensus control method for a high-order fully actuated uncertain multi-agent system, and the overall process is as Figure 1 shown: including the following steps: Step 1, construct a dynamic equation model of a high-order fully actuated uncertain nonlinear multi-agent system; Step 2, for the multi-agent system model established in Step 1, design a finite-time integral sliding mode surface according to the agent neighbor error and its derivatives of each order, and the linearized information term; Step 3, according to the high-order nonlinear multi-agent model established in Step 1 and the finite-time integral sliding mode surface obtained in Step 2, use an adaptive control method to estimate the unknown parameters of the system, and obtain an equivalent distributed adaptive finite-time integral sliding mode controller; Step 4, according to 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, based on the pole placement method, obtain the linearized parameters that satisfy the system performance requirements involved in the finite-time integral sliding mode surface and the corresponding controller; Step 5: Substitute the linearization parameters determined in Step 4 back into the adaptive finite-time integral sliding mode controller, and then bring the controller into the high-order fully actuated uncertain nonlinear multi-agent system to achieve the finite-time consensus control objective.

[0034] The following further illustrates the present invention with reference to embodiments. Obviously, the described embodiments are part of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0035] Embodiment 1: In this embodiment, a third-order nonlinear multi-agent model is used as an example. Assume that the multi-agent system consists of five agents, and the corresponding communication topology diagram is as Figure 2 shown. The form of its corresponding Laplacian matrix is as follows: .

[0036] Without loss of generality, assume that the specific form of the -th agent model is as follows: ; where: respectively represent the position, velocity, and acceleration information of the -th agent at time; is the unmodeled part of the -th agent; is the control matrix term of the -th agent.

[0037] For the control parameters in the sliding mode surface, they are designed based on the pole placement method as: ; The parameters in the controller are designed as: , , ; The adaptive update rate parameters are designed as: , .

[0038] The initial states of the agents are set as follows: .

[0039] Based on the above conditions and parameter settings, a simulation time of 60 s was selected for the experiment. According toFigures 3 to 5 From the simulation results in , it can be clearly observed that although there are uncertain unmodeled factors in the agent model, the states of the five agents can still achieve consensus within a finite time. Specifically, as the simulation time progresses, the state variables such as the positions, velocities, and accelerations of all agents gradually tend to be consistent, demonstrating good cooperative characteristics of the system.

[0040] As Figure 6 shown, according to the theoretical method of the high-order fully actuated system, the integral sliding mode surface can converge to 0 within a finite time and maintain its invariance. It can be seen from the above simulation results that even in the presence of unmodeled uncertain terms, the system still maintains the ability of rapid convergence. And Figure 7 further verifies the effect of using the adaptive gain, which can effectively reduce the interference of the unmodeled uncertainty part on the system performance. By adjusting the adaptive gain, the system can dynamically adjust its control parameters when facing unknown or changing environments, thereby further improving the robustness of the system and ensuring the stability and accuracy of the system.

[0041] Example 2: In this example, aiming at the problem of insufficient synchronization accuracy caused by dynamic load changes, joint friction differences, and external disturbances in the cooperative operation of multiple robotic arms, a robust adaptive control method based on the high-order fully actuated theory is proposed. In industrial automation scenarios (such as the cooperative handling of heavy components by multiple robotic arms on an automotive assembly line), it is necessary to ensure the pose and velocity consistency of 5 robotic arms under strong coupling nonlinear dynamics. Therefore, the system is modeled as a distributed control problem of a multi-Euler-Lagrange system, and its dynamic equation is expressed as: ; where is the joint angle position vector (the state of the system) of the th robotic arm, are its first-order and second-order derivatives, is the control torque input (the control input of the system). is the inertia matrix of the system, and the Coriolis force matrix adopts an anti-symmetric structure, and its non-diagonal elements represent the inertial coupling effect between joints. and are the gravity term and friction term matrices respectively, is the set of uncertainties and disturbances of the system.

[0042] The coefficients of the relevant matrices are selected as: ; ; ; ; ; Its full drive form is: ; Wherein: ; .

[0043] For the linearized parameters in the sliding mode surface, according to the design scheme given by the high-order full drive theory, it is designed as: .

[0044] The parameters in the controller are designed as: , , .

[0045] The adaptive update rate parameter is designed as: , .

[0046] Set the initial state as follows: .

[0047] 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 60 s is also selected for the experiment. The change curves of the position and speed of each agent are as Figure 8 and Figure 9 shown. It is not difficult to see that although the dimension of the system increases, all agents tend to be stable after about 10 s, and the states of each agent are consistent. This also shows the good cooperative characteristics of the system. Figure 10 Further shows the change curve of the control input. Figure 11 Shows the change curve of the adaptive parameter. Figure 12 Shows that the integral sliding mode surface established according to the high-order full drive system theory method can converge to 0 in a finite time and maintain its invariance. It is not difficult to see that the estimated parameters converge in a short time, indicating that the cooperative operation task of multiple manipulators is completed.

[0048] The above is only the preferred embodiment of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

[0049] Although the specific embodiments of the present invention have been described above, they are not limitations on the protection scope of the present invention. Those skilled in the art should understand that various modifications or variations that can be made without creative efforts on the basis of the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A finite-time consistency control method for a high-order all-drive uncertain multi-agent system, characterized in that: The process includes: S1, construct the dynamic equation model of high-order all-wheel drive uncertain nonlinear multi-agent system; S2, design the finite time integral sliding surface according to the agent neighbor error and its derivatives of various orders and linearized information items; S3, deriving the finite-time integral sliding mode surface and using the adaptive control method to estimate the unknown parameters of the system, thereby obtaining an equivalent distributed adaptive finite-time integral sliding mode controller; 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 consistency control method of a high-order all-drive uncertain multi-agent system as claimed in claim 1, characterized in that: The high-order all-drive uncertain nonlinear multi-agent system in S1 is composed of It is composed of 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 Agents in The state of the moment Derivatives; For the Agents 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 term 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 consistency control method of a high-order all-drive uncertain multi-agent system as claimed in 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 Agent , there is a time constant , so that for any , Agent and Agent 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. 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 integrated sliding surface of an agent By its state Derivative , the integral of the linearized information term The integral of the sum of the neighbor error information The specific form is as follows: ； in: is the graph adjacency matrix corresponding to Line Column elements; is the coefficient of the neighbor error information term and satisfies ; is a constant gain that scales the neighbor error term and satisfies , A constant for adjusting the convergence characteristics of the system; is the linearization parameter to be designed; is the neighbor error information related item.

4. A finite-time consistency control method for a high-order all-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 consistency control method of a high-order all-wheel drive uncertain multi-agent system as claimed in claim 3, characterized in that: The specific steps of designing the distributed adaptive finite-time integral sliding mode controller in S3 are: 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 ; 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; 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, an adaptive finite time integral sliding mode controller consisting of a finite time integral sliding mode controller and a finite time adaptive controller is designed. ; S35, for Unknown nonlinear information of agents The upper bound of , based on the designed finite time integral sliding surface, the adaptive control method is used to obtain its estimated value online .

6. The finite-time consistency control method of a high-order all-wheel drive uncertain multi-agent system as claimed in claim 5, 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 of For uncertainty An estimate of the unknown upper bound of , and: ； in, is the finite time integral sliding surface; is a symbolic function.

7. The finite-time consistency control method of a high-order all-wheel drive uncertain multi-agent system as claimed in claim 5, characterized in that: The specific process of S4 is as follows: S41, constructing an eigenvector matrix of finite relative eigenvalues ​​and infinite relative eigenvalues ​​of a 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, and if the system matrix is ​​a unit matrix, eliminating the eigenvector component corresponding to the infinite eigenvalue; S43, introduce a parameterized matrix set, configure the characteristic structure of the closed-loop system through the free parameter matrix, and find 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.

8. The finite-time consistency control method of a high-order all-drive uncertain multi-agent system as claimed in claim 6, 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 The known nonlinear information items of each agent; is the graph adjacency matrix corresponding to Line Column elements; For the Agents in The state of the moment Derivatives; For the Agents in The state of the moment Derivatives; is a constant gain that scales the neighbor error term and satisfies , is a constant that adjusts the convergence characteristics of the system.

9. The finite-time consistency control method of a high-order all-drive uncertain multi-agent system as claimed in claim 5, characterized in that: The finite time adaptive controller in S33 , the specific form is as follows: ； in: For the Unknown nonlinear information of agents The upper bound of An estimated value of The linearization control gain coefficient satisfies: , .

10. The finite-time consistency control method of a high-order all-wheel drive uncertain multi-agent system according to claim 6, 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 state variables and control inputs for each agent; , for Agents in The state of the moment Derivatives; , for Agents in The state of the moment Derivatives; For the Agents 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 Line Column elements; is a constant gain that scales the neighbor error term and satisfies , A constant for adjusting 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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