A hierarchical formation control method for linear multi-agent systems

Abstract

The present invention discloses a hierarchical formation control method for a linear multi-agent system, comprising the following steps: establishing a state-space equation for the multi-agent system to construct a disturbance system; decomposing the multi-agent formation instructions into a global anchor point instruction and a local deviation instruction; defining a multi-agent error tracking strategy; establishing a communication network between the multi-agent system and the global anchor point system using a directed graph; utilizing neighboring information in the communication network to establish a distributed observer to enable each agent to estimate the global anchor point system; utilizing the estimated information from the distributed observer to establish a dynamic gain compensator to obtain an asymptotic solution to a regulator equation associated with the global anchor point system; solving the regulator equation associated with the disturbance system and the local deviation system; and combining the solutions to the regulator equation to establish a collaborative output regulation controller. The present invention reduces the amount of global formation instruction data transmitted, reduces the computational load of local agents, and improves system operational efficiency and stability.

Description

Technical Field

[0001] The present invention relates to the technical field of collaborative control of multi-agent systems, and in particular to a hierarchical formation control method for linear multi-agent systems. Background Art

[0002] In the past decade or so, inspired by the behavior of animal swarms in nature, people have paid great attention to the formation control problem of multi-agent systems. The mathematical models of the agents range from single integrators, double integrators, general linear systems, and other complex nonlinear systems.

[0003] Formation control strategies can be broadly categorized into three categories: leader-follower strategies, behavior-based strategies, and virtual structure strategies. Existing technologies often require frequent data exchange and complex computation between agents when implementing formation control. This not only increases the communication burden but also increases system energy consumption and latency. Therefore, developing a control method that can effectively reduce communication and computational requirements while ensuring formation performance is crucial for improving the efficiency and reliability of multi-agent systems.

[0004] In the existing research on multi-agent formation control based on adaptive dynamic programming, an adaptive control method using neural networks is proposed for the formation control problem of multi-agent systems (Research on Multi-agent Formation Control Based on Adaptive Dynamic Programming, Wang Jingxu, North China University of Technology). However, there are stability and reliability issues caused by communication constraints, as well as problems with neural network learning efficiency. To this end, this patented technology proposes a hierarchical formation control method for linear multi-agent systems. By splitting the formation instructions into global anchor instructions and local deviation instructions, and using distributed observers, it effectively reduces the transmission volume of global formation instruction data and reduces the computational load of local agents, which is of great significance in practical applications. Summary of the Invention

[0005] The purpose of the present invention is to reduce the communication and computational complexity in the collaborative control process of a multi-agent system, and to propose a hierarchical formation control method for a linear multi-agent system.

[0006] The present invention is achieved through at least one of the following technical solutions.

[0007] A hierarchical formation control method for a linear multi-agent system includes the following steps:

[0008] S1. Establish the state space equation of the multi-agent system and construct the disturbance system;

[0009] S2. Decompose the agent's formation command into global anchor point command and local deviation command according to the global anchor point system and the local deviation system;

[0010] S3. Establish an error tracking strategy for the agent;

[0011] S4. Use directed graphs to establish a communication network between the multi-agent system and the global anchor system;

[0012] S5. Using the neighboring information in the communication network, a distributed observer is established to enable each agent to estimate the global anchor system;

[0013] S6. Using the estimated information of the distributed observer, a dynamic gain compensator is established to obtain the asymptotic solution of the regulator equation related to the global anchor point system;

[0014] S7, solving the regulator equations related to the disturbance system and the local deviation system;

[0015] S8. Combined with the solution of the regulator equation, a collaborative output regulation controller is established to generate the control signal of the intelligent agent to achieve the desired formation control effect.

[0016] Furthermore, in step S1, a multi-agent system containing N agents is considered, and the state space equation of the i-th agent is:

[0017]

[0018] y mi (t) = C mi x i (t)+D mi u i (t)+F mdi d i (t) (1b);

[0019] y i (t) = C i x i (t) (1c);

[0020] Where i=1,...,N, Represents the i-th agent n i The system status of the dimension, Represents the i-th agent m i Dimensional control input, Represents the i-th agent p mi Dimensional measurement output, represents the p-dimensional output of the i-th agent, Represents the i-th agent q di dimensional external disturbance, represents the field of real numbers; is the system state x i (t) derivative with respect to time t; A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, C i The output matrix of the i-th agent; t represents time;

[0021] The external disturbance d of the i-th agent i (t) is generated by the following perturbation system:

[0022]

[0023] d i (t) = φ di ω di (t) (2b);

[0024] in, Represents the i-th agent n di dimensional perturbation system state, is the disturbance state ω di (t) The derivative with respect to time t, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system.

[0025] Furthermore, in step S2, the global anchor point system is:

[0026]

[0027] y0(t)=ψ0v0(t) (3b);

[0028] in, is the global anchor instruction, is the field of real numbers in p-dimensional space, represents the q-dimensional system state of the global anchor point system, is the field of real numbers in q-dimensional space, is the derivative of the global anchor system state v0(t) with respect to time t, Ψ0 is the modal matrix of the global anchor system, and ψ0 is the output matrix of the global anchor system.

[0029] Furthermore, in step S2, the local deviation system is:

[0030]

[0031] y bi (t) = φ bi ω bi (t) (4b);

[0032] in, The local deviation instruction of the i-th agent, i=1,...,N, where N is the total number of agents, n represents the local deviation system bi Maintain system status, For n bi The field of real numbers in dimensional space, is the local deviation system state ω bi (t) The derivative with respect to time t, Φ bi is the modal matrix of the local deviation system, φ bi is the output matrix of the local deviation system.

[0033] Furthermore, in step S3, the tracking error e of the i-th agent is i (t) is defined as:

[0034] e i (t) = y i (t)-y0(t)-y bi (t)

[0035] =C i x i (t)-ψ0v0(t)-φ bi ω bi (t) (5);

[0036] in, represents the p-dimensional output of the i-th agent, C i is the output matrix of the i-th agent.

[0037] Furthermore, in step S4, a directed graph is used to establish a communication network between the multi-agent system and the global anchor system. The multi-agent system contains N agents, and its communication network is a directed graph. Description, where the node set Edge Set Node 0 represents the global anchor system, i represents the i-th agent, and j represents the j-th agent; directed graph The weighted adjacency matrix of a ij is a matrix The element in row i+1 and column j+1 is used to indicate whether the i-th agent can receive the information of the j-th agent. ii =0; when When , it means that the i-th agent can receive the information of the j-th agent. At this time, a ij >0, otherwise a ij =0.

[0038] Furthermore, in step S5, the distributed observer of the i-th agent is:

[0039]

[0040] Where N is the total number of agents, Ψ0 is the modal matrix of the global anchor system, ψ0 is the output matrix of the global anchor system, and v0(t) is the state of the global anchor system; i (t) is the estimated value of the modal matrix Ψ0 of the global anchor system by the i-th agent distributed observer, ψ i (t) is the estimated value of the global anchor system output matrix ψ0 by the i-th agent distributed observer, η i (t) is the estimated value of the global anchor system state v0(t) by the i-th agent distributed observer; Ψ j (t) is the estimated value of the global anchor system modal matrix Ψ0 by the j-th agent distributed observer, ψ j (t) is the estimated value of the global anchor system output matrix ψ0 by the j-th agent distributed observer, η j (t) is the estimated value of the global anchor system state v0(t) by the j-th agent distributed observer. is η i (t) The derivative with respect to time t, η0(t) = v0(t), μ ψ 、μ Ψ 、μ η >0 is the gain coefficient of the observer.

[0041] Furthermore, in step S6, the design of the dynamic gain compensator includes:

[0042] Define the related operator symbols col, vec and M:

[0043] Suppose there are m column vectors β1,...,β m , define the operator col(β1, ..., β m )=[β1 T ,...,β m T ]T,β1 T ,...,β m T denote β1, ..., β m The transpose of

[0044] Suppose there is an m×n dimensional matrix Y, and the operator vec(Y)=col(γ1,...,γ n ),γ1,...,γ n are the 1st, ..., nth columns of the matrix Y respectively;

[0045] Suppose there is an mn-dimensional column vector Defining operators in Are all n-dimensional column vectors and satisfy column vector

[0046] The dynamic gain compensator of the i-th agent is:

[0047]

[0048]

[0049]

[0050] Among them, ξ i (t) is the state of the dynamic gain compensator, is the coefficient matrix, Ψ i (t) is the ith agent’s estimate of Ψ0 in the global anchor system, represents the Kronecker product of matrices, and I q n i The identity matrix of dimensions A and q, i 、B i 、C i is the system matrix of the ith agent, is the coefficient vector of the dynamic gain compensator, ψ i (t) is the i-th agent’s estimate of ψ0 in the global anchor system, for ξ i (t) The derivative with respect to time t, μ ξ >0 is the gain coefficient of the dynamic gain compensator; let is the asymptotic state solution of the regulator equation associated with the global anchor system in the ith agent, is the asymptotic input solution of the regulator equation associated with the global anchor system in the ith agent, is the operator, n i is the dimension of the system state of the i-th agent, m i is the dimension of the control input of the i-th agent, and q is the dimension of the global anchor system state.

[0051] Furthermore, in step S7, in the i-th agent, the regulator equation related to the disturbance system and the local deviation system is:

[0052] X di Φ di =A i X di +B i U di +E di φ di (8a);

[0053] 0=C i X di (8b);

[0054] X bi Φ bi =A i X bi +B i U bi (9a);

[0055] 0=C i X bi -φ bi (9b);

[0056] Among them, X di is the state solution of the regulator equation associated with the disturbance system, U di Enter the solution to the regulator equation associated with the perturbed system, A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C i The output matrix of the i-th agent, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system, X bi is the state solution of the regulator equation associated with the local deviation system, U bi Enter the solution to the regulator equation associated with the local deviation system, Φ bi is the modal matrix of the local deviation system, φ bi is the output matrix of the local deviation system.

[0057] Furthermore, in step S8, for the i-th agent, the state feedback gain matrix K is set xi Make A i +B i K xi is the Hurwitz matrix, set the gain matrix L of the Lumberg observer i Make is the Hurwitz matrix, the cooperative output regulation controller u of the i-th agent i (t) is:

[0058]

[0059] Among them, A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system, z i (t) is the state vector of the Lumberg observer, satisfying is the i-th agent's response to the system state x i The estimated value of (t), is the perturbation of the system state ω by the i-th agent di The estimated value of (t), For z i The derivative of (t) with respect to time t, Represents the i-th agent m i Dimensional control input, Represents the i-th agent p mi Dimensional measurement output, K di =U di -K xi X di For the estimated state The associated feedforward gain matrix, X di is the state solution of the regulator equation associated with the disturbance system, U di Enter the solution to the regulator equation associated with the perturbation system, K bi =U bi -K xi X bi is the system state ω with local deviation bi (t) The associated feedforward gain matrix, X bi is the state solution of the regulator equation associated with the local deviation system, U bi Enter the solution for the regulator equation associated with the local deviation system, is the state η of the distributed observer i (t) The associated feedforward gain matrix, is the asymptotic state solution of the regulator equation associated with the global anchor system in the ith agent, Be the asymptotic input solution to the regulator equation associated with the global anchor system in the ith agent.

[0060] Compared with the existing technology, the beneficial effects of the present invention are:

[0061] This method decomposes the desired path of each agent in the formation into a global anchor point command and a local deviation command. This decomposition eliminates the need for each agent to pre-master the trajectory characteristics and motion modal information of the entire multi-agent system. Instead, each agent can achieve fast and efficient formation control by relying solely on neighborhood information from the communication network and combining it with locally solved observer and regulator equations. This method further enhances the distributed performance of the multi-agent system, reduces the computational burden on individual agents, and improves the scalability of the multi-agent system. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 To implement a hierarchical formation control method for a linear multi-agent system;

[0063] Figure 2 is a directed graph of a multi-agent system communication network in an embodiment of the present invention;

[0064] Figure 3 This is a diagram of the formation movement trajectory of multiple intelligent agents in three-dimensional space in an embodiment of the present invention;

[0065] Figure 4 is the tracking error curve of each agent in the x direction;

[0066] Figure 5 is the tracking error curve of each agent in the y direction;

[0067] Figure 6 is a graph of the tracking error of each agent in the z direction. DETAILED DESCRIPTION

[0068] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the specific implementation of the present invention will be clearly and completely described below in conjunction with the embodiments and drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0069] like Figure 1 A hierarchical formation control method for a linear multi-agent system in this embodiment includes the following steps:

[0070] S1. Define the state space equation of the multi-agent system and construct the perturbation system. Consider a multi-agent system with N agents. The state space equation of the i-th agent is:

[0071]

[0072] y mi (t) = C mi x i (t)+D mi u i (t)+F mdi d i (t) (1b);

[0073] y i (t) = C i x i (t) (1c);

[0074] Where i=1,...,N, Represents the i-th agent n i The system status of the dimension, Represents the i-th agent m i Dimensional control input, Represents the i-th agent p mi Dimensional measurement output, represents the p-dimensional output of the i-th agent, represents the external disturbance of the qdi dimension of the i-th agent, represents the field of real numbers; is the system state x i (t) derivative with respect to time t; A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, C i The output matrix of the i-th agent; t represents time;

[0075] The external disturbance d of the i-th agent i (t) is generated by the following perturbation system:

[0076]

[0077] d i (t) = φ di ω di (t) (2b);

[0078] in, Represents the i-th agent n di dimensional perturbation system state, is the disturbance state ωdi (t) The derivative with respect to time t, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system.

[0079] S2. Decompose the multi-agent formation instructions into global anchor point instructions and local deviation instructions based on the global anchor point system and the local deviation system;

[0080] The global anchor system is:

[0081]

[0082] y0(t)=ψ0v0(t) (3b);

[0083] in, is the global anchor instruction, is the field of real numbers in p-dimensional space, represents the q-dimensional system state of the global anchor point system, is the field of real numbers in q-dimensional space, is the derivative of the global anchor system state v0(t) with respect to time t, Ψ0 is the modal matrix of the global anchor system, and ψ0 is the output matrix of the global anchor system.

[0084] The local deviation system is:

[0085]

[0086] y bi (t) = φ bi ω bi (t) (4b);

[0087] in, The local deviation instruction of the i-th agent, i=1,...,N, where N is the total number of agents, n represents the local deviation system bi Maintain system status, For n bi The field of real numbers in dimensional space, is the local deviation system state ω bi (t) The derivative with respect to time t, Φ bi is the modal matrix of the local deviation system, φ bi is the output matrix of the local deviation system.

[0088] S3. Define the error tracking strategy of the agent, the tracking error e of the i-th agent i (t) is defined as:

[0089] e i (t) = y i(t)-y0(t)-y bi (t)

[0090] =C i x i (t)-ψ0v0(t)-φ bi ω bi (t) (5);

[0091] in, represents the p-dimensional output of the i-th agent, C i is the output matrix of the i-th agent.

[0092] S4. Use directed graph to establish the communication network between the multi-agent system and the global anchor system. The multi-agent system contains N agents, and its communication network uses directed graph. Description, where the node set Edge Set Node 0 represents the global anchor system, i represents the i-th agent, and j represents the j-th agent; directed graph The weighted adjacency matrix of a ij is a matrix The element in row i+1 and column j+1 is used to indicate whether the i-th agent can receive the information of the j-th agent. ii =0; when When , it means that the i-th agent can receive the information of the j-th agent. At this time, a ij >0, otherwise a ij =0.

[0093] S5. Using the neighboring information in the communication network, a distributed observer is established to realize each agent’s estimation of the global anchor point system. The distributed observer of the i-th agent is:

[0094]

[0095] Where N is the total number of agents, Ψ0 is the modal matrix of the global anchor system, ψ0 is the output matrix of the global anchor system, and v0(t) is the state of the global anchor system; i (t) is the estimated value of the modal matrix Ψ0 of the global anchor system by the i-th agent distributed observer, ψ i (t) is the estimated value of the global anchor system output matrix ψ0 by the i-th agent distributed observer, η i (t) is the estimated value of the global anchor system state v0(t) by the i-th agent distributed observer; Ψ j (t) is the estimated value of the global anchor system modal matrix Ψ0 by the j-th agent distributed observer, ψ j(t) is the estimated value of the global anchor system output matrix ψ0 by the j-th agent distributed observer, η j (t) is the estimated value of the global anchor system state v0(t) by the j-th agent distributed observer. is η i (t) The derivative with respect to time t, η0(t) = v0(t), μ ψ 、μ Ψ 、μ η >0 is the gain coefficient of the observer.

[0096] S6. Using the estimated information of the distributed observer, a dynamic gain compensator is established to obtain the asymptotic solution of the regulator equation related to the global anchor point system:

[0097] First, define the relevant operator symbols col, vec and M:

[0098] Suppose there are m column vectors β1,...,β m , define the operator col(β1, ..., β m )=[β1 T ,...,β m T ] T , β1 T ,...,β m T denote β1, ..., β m The transpose of

[0099] Suppose there is an m×n dimensional matrix Y, and the operator vec(Y)=col(γ1,...,γ n ),γ1,...,γ n are the 1st, ..., nth columns of the matrix Y respectively;

[0100] Suppose there is an mn-dimensional column vector Defining operators in Are all n-dimensional column vectors and satisfy column vector

[0101] The dynamic gain compensator of the i-th agent is:

[0102]

[0103]

[0104]

[0105] Among them, ξ i (t) is the state of the dynamic gain compensator, is the coefficient matrix, Ψ i (t) is the ith agent’s estimate of Ψ0 in the global anchor system, represents the Kronecker product of matrices, and I q n i The identity matrix of dimensions A and q, i 、B i 、C i is the system matrix of the ith agent, is the coefficient vector of the dynamic gain compensator, ψ i (t) is the i-th agent’s estimate of ψ0 in the global anchor system, for ξ i (t) The derivative with respect to time t, μ ξ >0 is the gain coefficient of the dynamic gain compensator; let is the asymptotic state solution of the regulator equation associated with the global anchor system in the ith agent, is the asymptotic input solution of the regulator equation associated with the global anchor system in the ith agent, is the operator, n i is the dimension of the system state of the i-th agent, m i is the dimension of the control input of the i-th agent, and q is the dimension of the global anchor system state.

[0106] S7. Solve the regulator equation related to the disturbance system and the local deviation system. In the i-th agent, the regulator equation related to the disturbance system and the local deviation system is:

[0107] X di Φ di =A i X di +B i U di +E di φ di (8a);

[0108] 0=C i X di (8b);

[0109] X bi Φ bi =A i X bi +B i U bi (9a);

[0110] 0=C i X bi -φ bi (9b);

[0111] Among them, X di is the state solution of the regulator equation associated with the disturbance system, U di Enter the solution to the regulator equation associated with the perturbed system, A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C i The output matrix of the i-th agent, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system, X bi is the state solution of the regulator equation associated with the local deviation system, U bi Enter the solution to the regulator equation associated with the local deviation system, Φ bi is the modal matrix of the local deviation system, φ bi is the output matrix of the local deviation system.

[0112] S8. Combine the solutions of the regulator equations to establish a cooperative output regulation controller.

[0113] For the i-th agent, set the state feedback gain matrix K xi Make A i +B i K xi is the Hurwitz matrix, setting the gain matrix L of the Lumberg observer i Make is the Hurwitz matrix, the cooperative output regulation controller u of the i-th agent i (t) is:

[0114]

[0115] Among them, A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system, z i (t) is the state vector of the Lumberg observer, satisfying is the i-th agent's response to the system state x i The estimated value of (t), is the perturbation of the system state ω by the i-th agent di The estimated value of (t), For z i The derivative of (t) with respect to time t, Represents the i-th agent m i Dimensional control input, Represents the i-th agent p mi Dimensional measurement output, K di =U di -K xi X di For the estimated state The associated feedforward gain matrix, X di is the state solution of the regulator equation associated with the disturbance system, U di Enter the solution to the regulator equation associated with the perturbation system, K bi =U bi -K xi X bi is the system state ω with local deviation bi (t) The associated feedforward gain matrix, X bi is the state solution of the regulator equation associated with the local deviation system, U bi Enter the solution for the regulator equation associated with the local deviation system, is the state η of the distributed observer i (t) The associated feedforward gain matrix, is the asymptotic state solution of the regulator equation associated with the global anchor system in the ith agent, Be the asymptotic input solution to the regulator equation associated with the global anchor system in the ith agent.

[0116] As a specific embodiment, this embodiment uses Matlab for simulation verification. Considering that a multi-agent system includes N agents, the system matrix in the state space equation of the i-th, i=1,..., N agents is:

[0117] C mi =[1 1 1];

[0118] D mi =0, F mdi =[1 0],

[0119] where i=1,...,N,N=10, the system constant matrix Φ of the system perturbed by the i-th agent di 、φ di With the initial state W di (0) is:

[0120] w di (0) = col(0,1);

[0121] It is expected that the multi-agent system will form a five-pointed star shape, moving along the y-axis at a speed of θ = 1 m / s while rotating on the xoZ plane at an angular velocity of Ω = 0.5 rad / s. The system constant matrices Ψ0 and ψ0 of the global anchor system and the initial state v0(0) are set as:

[0122]

[0123] The system constant matrix Φ of the local deviation system of the i-th agent bi 、φ bi With the initial state ω bi (0) is set to:

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] As an embodiment, the initial state of the system of each agent is: x1(0) = col(0, 2, 25), x2(0) = col(0, 4, 20), x3(0) = col(0, 6, 15), x4(0) = col(0, 8, 10), x5(0) = col(0, 10, 5), x6(0) = col(0, 12, -5), x7(0) = col(0, 14, -10), x8(0) = col(0, 16, -15), x9(0) = col(0, 18, -20), x 10 (0) = col(0, 20, -25). The gain coefficient of the i-th (i = 1, ..., 10) agent observer is: μ ψ =10,μ Ψ =10,μ η =10, the initial state is: i (0)=0,ψ i (0) = 0, η i (0) = 0. The gain coefficient of the i-th (i = 1, ..., 10) agent dynamic gain compensator is: μ ξ =50, the initial state is ξ i(0) = 0. Take the state feedback gain matrix of the i-th (i = 1, ..., 10) agent Lumberg observer gain matrix L i =col(-35.25,63.75,16.25,-67.5,12.5).

[0131] Figure 2 Use a directed graph for the communication network of 10 agents, Figure 3 This is the trajectory of the formation operation of 10 intelligent agents in three-dimensional space. The 10 intelligent agents formed a five-pointed star shape in the space and moved forward in a spiral, achieving the desired control goal. Figure 4 、 Figure 5 、 Figure 6 These are the tracking error curves of each agent in the x, y, and z directions respectively. The tracking error of each agent asymptotically tends to 0.

[0132] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, numerous modifications and variations are possible based on the contents of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art can better understand and utilize the present invention.

Claims

1. A hierarchical formation control method for linear multi-agent systems, characterized in that: The following steps are involved: S1. Establish the state space equation of the multi-agent system and construct the disturbance system; S2. Decompose the agent's formation command into global anchor point command and local deviation command according to the global anchor point system and the local deviation system; S3. Establish an error tracking strategy for the agent; S4. Use directed graphs to establish a communication network between the multi-agent system and the global anchor system; S5. Using the neighboring information in the communication network, a distributed observer is established to enable each agent to estimate the global anchor system; S6. Using the estimated information of the distributed observer, a dynamic gain compensator is established to obtain the asymptotic solution of the regulator equation related to the global anchor point system; S7, solving the regulator equations related to the disturbance system and the local deviation system; S8. Combined with the solution of the regulator equation, a collaborative output regulation controller is established to generate the control signal of the intelligent agent to achieve the desired formation control effect.

2. A hierarchical formation control method for a linear multi-agent system according to claim 1, characterized in that: In step S1, consider a multi-agent system with N agents, and the state space equation of the i-th agent is: y mi (t)=C mi x i (t)+D mi u i (t)+F mdi d i (t)(1b); y i (t)=C i x i (t)(1c); Where i = 1,…,N, Represents the i-th agent n i The system status of the dimension, Represents the i-th agent m i Dimensional control input, Represents the i-th agent p mi Dimensional measurement output, represents the p-dimensional output of the i-th agent, Represents the i-th agent q di dimensional external disturbance, represents the field of real numbers; is the system state x i (t) derivative with respect to time t; A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, C i The output matrix of the i-th agent; t represents time; The external disturbance d of the i-th agent i (t) is generated by the following perturbation system: d i (t)=φ di ω di (t)(2b); in, Represents the i-th agent n di dimensional perturbation system state, is the disturbance state ω di (t) The derivative with respect to time t, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system.

3. The hierarchical formation control method for a linear multi-agent system according to claim 1, characterized in that: In step S2, the global anchor point system is: y0(t)=ψ0v0(t)(3b); in, is the global anchor instruction, is the field of real numbers in p-dimensional space, represents the q-dimensional system state of the global anchor point system, is the field of real numbers in q-dimensional space, is the derivative of the global anchor system state υ0(t) with respect to time t, Ψ0 is the modal matrix of the global anchor system, and ψ0 is the output matrix of the global anchor system.

4. A hierarchical formation control method for a linear multi-agent system according to claim 3, characterized in that: In step S2, the local deviation system is: y bi (t)=φ bi oh bi (t)(4b); in, The local deviation instruction of the i-th agent, i = 1, ..., N, N is the total number of agents, n represents the local deviation system bi Maintain system status, For n bi The field of real numbers in dimensional space, is the local deviation system state ω bi (t) The derivative with respect to time t, Φ bi is the modal matrix of the local deviation system, φ bi is the output matrix of the local deviation system.

5. The hierarchical formation control method for a linear multi-agent system according to claim 4, characterized in that: In step S3, the tracking error e of the i-th agent is i (t) is defined as: e i (t)=y i (t)-y0(t)-y bi (t) =C i x i (t)-ψ0υ0(t)-φ bi oh vi (t) (5); in, represents the p-dimensional output of the i-th agent, C i is the output matrix of the i-th agent.

6. The hierarchical formation control method for a linear multi-agent system according to claim 1, characterized in that: In step S4, a directed graph is used to establish a communication network between the multi-agent system and the global anchor system. The multi-agent system contains N agents, and its communication network is a directed graph. Description, where the node set Edge Set Node 0 represents the global anchor system, i represents the i-th agent, and j represents the j-th agent; directed graph The weighted adjacency matrix of a ij is a matrix The element in row i+1 and column j+1 is used to indicate whether the i-th agent can receive the information of the j-th agent. ii =0; when When , it means that the i-th agent can receive the information of the j-th agent. At this time, a ij >0, otherwise a ij =0.

7. The hierarchical formation control method for a linear multi-agent system according to claim 6, characterized in that: In step S5, the distributed observer of the i-th agent is: Where N is the total number of agents, Ψ0 is the modal matrix of the global anchor system, ψ0 is the output matrix of the global anchor system, and v0(t) is the state of the global anchor system; i (t) is the estimated value of the modal matrix Ψ0 of the global anchor system by the i-th agent distributed observer, ψ i (t) is the estimated value of the global anchor system output matrix ψ0 by the i-th agent distributed observer, η i (t) is the estimated value of the global anchor system state v0(t) by the i-th agent distributed observer; Ψ j (t) is the estimated value of the global anchor system modal matrix Ψ0 by the j-th agent distributed observer, ψ j (t) is the estimated value of the global anchor system output matrix ψ0 by the j-th agent distributed observer, η j (t) is the estimated value of the global anchor system state v0(t) by the j-th agent distributed observer; is η i (t) The derivative with respect to time t, η0(t) = υ0(t), μ ψ 、μ Ψ 、μ η >0 is the gain coefficient of the observer.

8. The hierarchical formation control method for a linear multi-agent system according to claim 1, characterized in that: In step S6, the design of the dynamic gain compensator includes: Define the related operator symbols col, vec and M: Suppose there are m column vectors β1,…,β m , define the operator col(β1,…,β m )=[β1 T ,…,β m T ] T , β1 T ,…,β m T denote β1,…,β m The transpose of Suppose there is an m×n dimensional matrix Υ, and the operator vec(Υ)=col(γ1,…,γ n ),γ1,…,γ n are the 1st,…,nth columns of the matrix Y respectively; Suppose there is an mn-dimensional column vector Defining operators in Are all n-dimensional column vectors and satisfy column vector The dynamic gain compensator of the i-th agent is: Among them, ξ i (t) is the state of the dynamic gain compensator, is the coefficient matrix, Ψ i (t) is the ith agent’s estimate of Ψ0 in the global anchor system, represents the Kronecker product of matrices, and I q n i The identity matrix of dimensions A and q, i 、B i 、C i is the system matrix of the ith agent, is the coefficient vector of the dynamic gain compensator, ψ i (t) is the i-th agent’s estimate of ψ0 in the global anchor system, for ξ i (t) The derivative with respect to time t, μ ξ >0 is the gain coefficient of the dynamic gain compensator; is the asymptotic state solution of the regulator equation associated with the global anchor system in the ith agent, is the asymptotic input solution of the regulator equation associated with the global anchor system in the ith agent, is the operator, n i is the dimension of the system state of the i-th agent, m i is the dimension of the control input of the i-th agent, and q is the dimension of the global anchor system state.

9. The hierarchical formation control method for a linear multi-agent system according to claim 1, characterized in that: In step S7, in the i-th agent, the regulator equation related to the disturbance system and the local deviation system is: X di Φ di =A i X di +B i U di +E di φ di (8a); 0=C i X di (8b); X bi Φ bi =A i X bi +B i U bi (9a); 0=C i X bi -φ bi (9b); Among them, X di is the state solution of the regulator equation associated with the disturbance system, U di Enter the solution to the regulator equation associated with the perturbed system, A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C i The output matrix of the i-th agent, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system, X bi is the state solution of the regulator equation associated with the local deviation system, U bi Enter the solution to the regulator equation associated with the local deviation system, Φ bi is the modal matrix of the local deviation system, φ bi is the output matrix of the local deviation system.

10. The hierarchical formation control method for a linear multi-agent system according to claim 1, characterized in that: In step S8, for the i-th agent, set the state feedback gain matrix K xi Make A i +B i K xi is the Hurwitz matrix, setting the gain matrix L of the Lumberg observer i Make is the Hurwitz matrix, the cooperative output regulation controller u of the i-th agent i (t) is: Among them, A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, Φ di is the modal matrix of the disturbance system, φ di is the output matrix of the perturbation system, z i (t) is the state vector of the Lumberg observer, satisfying is the i-th agent's response to the system state x i The estimated value of (t), is the perturbation of the system state ω by the i-th agent di The estimated value of (t), For z i The derivative of (t) with respect to time t, Represents the i-th agent m i Dimensional control input, Represents the i-th agent p mi Dimensional measurement output, K di =U di -K xi X di For the estimated state The associated feedforward gain matrix, X di is the state solution of the regulator equation associated with the disturbance system, U di Enter the solution to the regulator equation associated with the perturbation system, K bi =U bi -K xi X bi is the system state ω with local deviation bi (t) The associated feedforward gain matrix, X bi is the state solution of the regulator equation associated with the local deviation system, U bi Enter the solution for the regulator equation associated with the local deviation system, is the state η of the distributed observer i (t) The associated feedforward gain matrix, is the asymptotic state solution of the regulator equation associated with the global anchor system in the ith agent, Be the asymptotic input solution of the regulator equation associated with the global anchor system in the ith agent.

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