Heterogeneous multi-agent system formation control method based on specified time observer

Abstract

The invention relates to a heterogeneous multi-agent system formation control method based on a specified time observer, and the method comprises the steps: building a dynamic model for each agent for a heterogeneous multi-agent system, taking each agent as a communication node, and building a communication topology; the intelligent agent collects state information of neighbor nodes, and constructs an error system to estimate a state matrix and an output matrix of a leader; setting a self-adaptive observer, and estimating a convex hull of a leader state by combining a state matrix and an output matrix of the leader according to real-time state information of neighbor nodes; constructing a time-varying formation tracking control protocol based on an output result of the self-adaptive observer in combination with a time scaling function; initializing a time-varying formation tracking control protocol according to an expected formation structure of the multi-agent system, and updating the state of each agent according to the time-varying formation tracking control protocol through a consistency controller to enable all agents to reach a preset formation; according to the invention, on the premise of not introducing global information, an expected formation shape can be completed within specified time.

Description

Technical Field

[0001] The present invention relates to the field of cooperative control of multi-agent systems, and particularly to a formation control method for heterogeneous multi-agent systems based on a specified-time observer. Background Art

[0002] In the research field of multi-agent systems, formation control technology has become a widely concerned research hotspot. A multi-agent system is a system composed of multiple interacting agents, which usually have sensing, computing, and decision-making capabilities, and achieve the overall tasks of the system through communication and cooperation. In the fields of aviation, unmanned driving, marine monitoring, and military, etc., the application scenarios of multi-agent formation control technology are extremely extensive. Through effective formation control methods, multiple agents can move collaboratively in space to complete complex tasks, such as target tracking, environmental monitoring, and rescue operations, etc.

[0003] Traditional formation control methods are mostly based on the assumption of homogeneous agents, that is, it is assumed that the agents in the system have the same dynamic model and sensing capabilities. However, in practical applications, agents usually exhibit heterogeneous characteristics, and there are differences in aspects such as the dynamic models, motion performances, and observation accuracies of agents. This heterogeneity has restricted the application of traditional formation control methods in heterogeneous multi-agent systems. Therefore, heterogeneous multi-agent formation control methods have become the research focus in recent years. To solve the control problems brought by heterogeneity, many new control strategies have been proposed, including methods based on leader-following, cooperative learning, and optimal control, etc., to meet the dynamic requirements of different agents.

[0004] In addition, in practical applications, due to the global network topology structure or task time factors, the information between agents may not be transmitted in real time, thus resulting in problems such as communication delays or data loss. And the design of an observer based on a specified time can achieve the desired observation accuracy within a limited time, enabling the formation control system to still achieve effective cooperation without global network topology information. This control strategy based on a specified-time observer can improve the robustness and response speed of the formation control system.

[0005] Therefore, in view of the challenges of heterogeneous multi-agent system formation control, combining the method of a specified-time observer, designing a new formation control strategy has important research significance and practical value. This method can improve the control accuracy and stability of multi-agent systems under the influence of heterogeneity and uncertainty factors, thereby promoting the application of multi-agent formation technology in complex environments. Summary of the Invention

[0006] To solve the problems in the above background art, the present invention provides a formation control method for heterogeneous multi-agent systems based on a specified-time observer, including the following steps:

[0007] S1: For a heterogeneous multi-agent system, establish a dynamic model for each agent, regard each agent as a communication node, and build a communication topology;

[0008] S2: The agent collects the state information of its neighbor nodes, and constructs an error system to estimate the state matrix and output matrix of the leader;

[0009] S3: Set an adaptive observer, which estimates the convex hull of the leader state based on the real-time state information of the neighbor nodes, combined with the state matrix and output matrix of the leader;

[0010] S4: Based on the output result of the adaptive observer, and combined with a time scaling function, construct a time-varying formation tracking control protocol;

[0011] S5: According to the expected formation structure of the multi-agent system, initialize the time-varying formation tracking control protocol, and update the states of each agent through a consensus controller according to the time-varying formation tracking control protocol, so that all agents reach the preset formation.

[0012] The present invention has at least the following beneficial effects:

[0013] The present invention proposes a formation control method for a heterogeneous multi-agent system based on a specified-time observer to achieve specified-time tracking of a time-varying formation of a heterogeneous multi-agent system. The proposed observer does not rely on global network topology information, and can enable each agent to estimate the state and system matrix of the leader within a specified time based on neighbor information. The formation tracking control protocol dynamically adjusts control parameters through the observer and by introducing a time scaling function, is not affected by the initial state of the system, nor by the upper limit of the settling time, and ensures that the output of the multi-agent system converges within a preset time. Brief Description of the Drawings

[0014] Figure 1 is a flowchart of the method of the present invention;

[0015] Figure 2 is a formation communication topology diagram of an embodiment of the present invention;

[0016] Figure 3 is an observer observation error diagram of an embodiment of the present invention;

[0017] Figure 4 is an output trajectory diagram of each agent of an embodiment of the present invention;

[0018] Figure 5 is an output formation tracking error diagram of each agent of an embodiment of the present invention;

[0019] Figure 6 is a formation tracking error diagram under different initial conditions of an embodiment of the present invention. Detailed implementation manners

[0020] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all 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 shall fall within the protection scope of the present invention.

[0021] There is a constraint condition for the topological structure in the multi-agent system referred to in the present invention, that is, each follower communicates with all leaders or none of the leaders. In the case where a follower does not communicate with any leader, it can be ensured that at least one other follower establishes communication with all leaders and has a directed path connecting to the above-mentioned follower.

[0022] Please refer to Figure 1 , the present invention provides a formation control method for a heterogeneous multi-agent system based on a specified-time observer, and the method includes but is not limited to the following steps:

[0023] S1: For the heterogeneous multi-agent system, establish a dynamic model for each agent, regard each agent as a communication node, and build a communication topology;

[0024] Considering that the multi-agent system consists of M followers and N leaders, the dynamic model of the followers includes:

[0025]

[0026] where i = 1, 2,..., M, represents the state of follower i, and n i represents the dimension of x i (t), represents the output of follower i, p represents the dimension of y i (t), u i (t) represents the control input of follower i, A i , B i and C i represent constant matrices with compatible dimensions, and B i is a row full-rank matrix; represents the rate of change of the state of follower i; t represents the time at t;

[0027] The dynamic model of the leaders includes:

[0028]

[0029] where k = M + 1, M + 2,..., M + N, Denotes the state of leader k, n i Denotes x k (t) dimension; Denotes the output of leader k, p denotes y k (t) dimension, S and R respectively denote the state matrix and output matrix of the leader, and have compatible dimensions.

[0030] Set the communication topology graph to meet some specific conditions, such as Figure 2 As shown, that is, each follower communicates with all leaders or none of the leaders. In the case where a follower does not communicate with any leader, it can be guaranteed that at least one other follower establishes communication with all leaders and has a directed path connecting to the above-mentioned follower. In Figure 2 7, 8, and 9 are leaders, and 1 - 6 are followers.

[0031] S2: The agent collects the state information of neighbor nodes and constructs an error system to estimate the state matrix and output matrix of the leader;

[0032] Given that the relative information of the leader cannot be directly available to all followers, an observer is established to obtain the state information of the leader using the relative information of neighbors. The following is the real-time observation of the leader system matrix:

[0033] S21: According to the state information of neighbor nodes collected by the agent, construct an error system:

[0034]

[0035] Among them, α and γ represent positive parameters selected by the user, T s Denotes the estimation time of matrix S; T R Denotes the estimation time of matrix R; μ() represents the time scaling function; Denotes the derivative of the time scaling function; I q Denotes the q-order identity matrix; T denotes matrix transpose; Denotes the state matrix estimation error of leader i, S i Denotes the estimation matrix of agent i for the leader state matrix; Denotes the output matrix estimation error of leader i, R i Denotes the estimation matrix of agent i for the leader output matrix; Denotes matrix Rate of change; Denotes matrix Rate of change; Denotes the Kronecker product operation;

[0036] S22: Estimate the state matrix and output matrix of the leader according to the constructed error system:

[0037]

[0038] Among them, S j represents the estimation matrix of agent j for the leader state matrix, and R j represents the estimation matrix of agent j for the leader output matrix; represents the rate of change of matrix S i ; represents the rate of change of matrix R i ;

[0039] S3: Set an adaptive observer, which estimates the convex hull of the leader state based on the real-time state information of neighbor nodes and combines the state matrix and output matrix of the leader;

[0040] The adaptive observer includes:

[0041]

[0042] Among them, represents the observation error between agent i and agent j; ξ i represents the estimated value of agent i for the convex hull of the leader state, ν i is the coupling gain, ν i0 is the initial value of the coupling gain, and α and γ are positive parameters selected by the user; T 1 represents the observation time preset by the adaptive observer; T represents the transpose.

[0043] It can be clearly seen from the expression of the adaptive observer that the time scaling function μ(t, T u ) plays a crucial role in accelerating the convergence speed. However, when , tends to infinity, indicating that the observer uses a relatively high gain. In this case, even a slight disturbance will have a significant impact on the system. To solve this problem, choosing an observation time greater than the actual engineering time is a simple and effective solution.

[0044] Preferably, the time scaling function includes:

[0045]

[0046]

[0047] Among them, s > 0 represents a parameter greater than 0, and T u represents the preset time selected by the user.

[0048] S4: Based on the output results of the adaptive observer and combined with the time-scaling function, construct a time-varying formation tracking control protocol;

[0049] Preferably, the time-varying formation tracking control protocol of the heterogeneous multi-agent system includes:

[0050]

[0051] where K 1i satisfies A i + B i K 1i is a Hurwitz matrix, and K 2i (t) = Ψ i (t) - K 1i Φ i (t), K 3i (t) = K 2i (t) + K 4i (t). To ensure that the desired formation is completed within the specified time, when t ∈ (0, T max ), T max = max{T S , T R}), by calculating through Lemma 1, (Φ i (t), Ψ i (t)) can be obtained. Lemma 1 is defined as follows: For any initial state If ∈> 0 is large enough, the following system

[0052]

[0053] has a unique bounded solution, and

[0054]

[0055] where represents 's rate of change; vec() represents the operation of converting a matrix into a vector, represents the corresponding inverse operation; q represents the dimension of the leader state; n i represents the dimension of the follower state; m i represents the dimension of the follower input;

[0056] When t ∈ [T max , +∞), directly solve the regulator equation to obtain (Φ i , Ψ i );

[0057]

[0058] K 4i (t) is the solution of the following equation:

[0059]

[0060] where A i , B i , C i are known constant matrices with compatible dimensions, S and R are the system matrices of the leader, S i is the estimated matrix of S, K i is the transition matrix.

[0061] S5: According to the expected formation structure of the multi-agent system, initialize the time-varying formation tracking control protocol, and update the states of all agents through the consensus controller according to the time-varying formation tracking control protocol, so that all agents reach the preset formation.

[0062] Preferably, the time-varying formation tracking control protocol includes:

[0063]

[0064] where K 1i satisfies the Hurwitz matrix of A i + B i K 1i , x i represents the state of agent i, ξ i represents the output result of the adaptive observer, φ i represents the offset of agent i relative to the leader, and is the n i th order identity matrix, represents the Moore-Penrose pseudoinverse matrix of matrix B i , K 2i (t) = Ψ i (t) - K 1i Φ i (t) represents the observer gain matrix, K 3i (t) = K 2i (t) + K 4i (t) represents the formation gain matrix, (Ψ i , Φ i ) represents the solution of the regulator, K 4i (t) is the formation compensation amount, K i is the transition matrix, T 2 represents the formation convergence time preset by the user.

[0065] Preferably, when the following conditions are met, all agents reach the preset formation:

[0066]

[0067] where y i (t) is the output of agent i at the current moment, and φ yi (t) is the output offset of the desired formation, and β k (k = M + 1, M + 2, …, M + N) satisfies represents the convex hull of N leaders.

[0068] The desired formation is represented by a time-varying vector where is piecewise continuously differentiable. The corresponding output formation offset is φ yi (t) = Rφ i (t).

[0069] N agents cooperate with each other to achieve and maintain an expected formation. The formation of a multi-agent system refers to a model in which a group of agents can satisfy certain geometric constraints or shapes. In the present invention, the formation is described based on the relative position vectors between the agents. A time-varying vector φ i (t) is set to represent the desired state formation of each agent, and this vector changes with time, indicating the characteristics of the time-varying formation.

[0070] Furthermore, it is explained that the condition for achieving a consensus formation is that as time progresses, the convex hull of the states of the agents and the leaders and the error of the expected formation can finally reach 0, that is:

[0071]

[0072] This embodiment considers a heterogeneous multi-agent system composed of 9 agents, where the follower subset and the leader subset The dynamics of followers 1, 3, and 5 are: The dynamics of followers 2, 4, and 6 are: The dynamics of leaders 7, 8, and 9 are: In addition, an expected formation structure is designed:

[0073]

[0074] where i = 1, 2, …, 6.

[0075] To verify the effectiveness of the proposed time-varying formation based on the specified-time observer, Matlab is used for simulation verification. This embodiment uses Figure 2It is an experimental topology diagram. Eventually, six follower agents will finally form a regular hexagon shape. Regarding the parameter values in the system, s = 3, α = 3, γ = 2, ∈ = 15, and each parameter matrix Randomly select the initial position state x of the agent 1 (0) = [1, 1] T , x 2 (0) = [-1, 1, 0] T , x 3 (0) = [0, 1] T , x 4 (0) = [1, 2, 1] T , x 5 (0) = [3, 0] T , x 6 (0) = [1, -1, -1] T , x 7 (0) = [0, 1, 0, 1] T , x 8 (0) = [1, 1, 0, 1] T , x 9 (0) = [0, 1, 1, 1] T , and they move in the 2-D plane;

[0076] Select T S = T R = 1s, T 1 = 2s, T 2 = 5s. From the simulation results, it can be obtained that, as Figure 3 shown, it represents the error between the observed value and the convex hull of the actual leader. We can see that an accurate estimate can be obtained within T 1 . Figure 4 Shows snapshots of the output trajectories at different times within t = 30s, showing that before T 2 , the followers have formed a rotating hexagon around the leader center. Figure 5 Also indicates that the output tracking error of each agent has become zero before T 2 , further indicating that the expected formation has been successfully achieved. In addition, Figure 6 Shows the variation of the tracking error under different initial states, which highlights the advantage of our method in maintaining the convergence speed while dealing with the initial state.

[0077] Verified by simulation experiments, according to the new adaptive specified-time observer and control protocol, without relying on global network topology information, it can achieve stable tracking of the formation within the preset time through neighbor interactions. Compared with the existing control methods, the proposed method has time controllability, distributed implementation, and adaptability to unknown system matrices, making up for the deficiencies of current technologies in the application of complex systems.

[0078] It should be noted that those of ordinary skill in the art can understand that all or part of the processes in the above method embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the above method embodiments. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), or the like.

[0079] The above are only specific implementation manners of the present application. It should be pointed out that for those of ordinary skill in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirits of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A formation control method for a heterogeneous multi-agent system based on a specified time observer, characterized in that: The following steps are involved: S1: For heterogeneous multi-agent systems, a dynamic model is established for each agent, each agent is regarded as a communication node, and a communication topology is constructed; S2: The agent collects the state information of neighbor nodes and constructs the error system to estimate the state matrix and output matrix of the leader; S3: Set an adaptive observer, which estimates the convex hull of the leader's state based on the real-time state information of neighbor nodes and the leader's state matrix and output matrix; S4: Based on the output of the adaptive observer and combined with the time scaling function, a time-varying formation tracking control protocol is constructed; S5: According to the expected formation structure of the multi-agent system, the time-varying formation tracking control protocol is initialized, and the state of each agent is updated according to the time-varying formation tracking control protocol through the consistency controller, so that all agents reach the preset formation.

2. According to claim 1, a heterogeneous multi-agent system formation control method based on a designated time observer is characterized in that: The process of building a communication topology includes: Constructing a directed graph Contains M followers and N leaders, where represents a node set, represents the edge set, It is a picture The adjacency matrix, w ij represents the edge weight from communication node i to communication node j, where i ,s j )∈ε when w ij =1, otherwise w ij =0; node s i Neighborhood collection Represents; the Laplacian matrix is ​​defined as in diag() represents a diagonal matrix function; assuming that all leaders have no neighbors, then in, Represents the Laplacian matrix of the subgraph composed of M follower nodes, Represents the portion of the Laplacian matrix determined by the connection relationship from M follower nodes to N leader nodes.

3. The method for controlling a formation of a heterogeneous multi-agent system based on a designated time observer according to claim 2, characterized in that: The dynamic model of the agent is a heterogeneous multi-agent system, including M followers and N leaders; wherein the dynamic model of the followers includes: Where i = 1, 2, ..., M, represents the state of follower i, n i Represents x i The dimension of (t), represents the output of follower i, and p represents y i The dimension of (t), u i (t) represents the control input of follower i, A i , B i and C i represents a constant matrix with compatible dimensions, and B i is a full row rank matrix; represents the state change rate of follower i; t represents time t; The leader dynamics model includes: Where k = M+1, M+2, …, M+N, represents the state of leader k, and q represents x k (t) dimension; represents the output of leader k, and p represents y k The dimensions of (t), S and R represent the state matrix and output matrix of the leader, respectively, and have compatible dimensions.

4. According to the method for controlling a formation of a heterogeneous multi-agent system based on a designated time observer according to claim 3, the step S2 comprises: S21: Construct an error system based on the state information of neighbor nodes collected by the agent: Among them, α and γ represent positive parameters selected by the user, T s represents the estimated time of matrix S; T R represents the estimated time of the matrix R; μ() represents the time scaling function; represents the derivative of the time scaling function; I q represents the q-order identity matrix; T represents matrix transpose; represents the state matrix estimation error of leader i, S i Represents the estimation matrix of agent i on the leader's state matrix; represents the output matrix estimation error of leader i, R i Represents the estimation matrix of agent i for the leader's output matrix; Representation Matrix The rate of change of Representation Matrix The rate of change of represents the Kronecker product operation; S22: Estimate the state matrix and output matrix of the leader based on the constructed error system: Among them, S j represents the estimation matrix of agent j for the leader's state matrix, R j Represents the estimation matrix of agent j for the leader's output matrix; Represents the matrix S i The rate of change of Represents the matrix R i The rate of change.

5. The method for controlling a formation of a heterogeneous multi-agent system based on a designated time observer according to claim 4, characterized in that: The adaptive observer comprises: in, represents the observation error between agent i and agent j; ξ i represents the estimate of the convex hull of the leader’s state by agent i, v i is the coupling gain, v i0 is the initial value of the coupling gain, α and γ are positive parameters selected by the user; T1 represents the observation time preset by the adaptive observer; T represents the transpose.

6. A method for controlling a formation of a heterogeneous multi-agent system based on a designated time observer according to claim 5, characterized in that: The time scaling function comprises: Among them, s>0 means the parameter is greater than 0, T u Indicates a preset time selected by the user.

7. The method for controlling a formation of a heterogeneous multi-agent system based on a designated time observer according to claim 6, characterized in that: The time-varying formation tracking control protocol includes: Among them, K 1i Satisfy A i +B i K 1i The Hurwitz matrix, x i represents the state of agent i, ξ i represents the output of the adaptive observer, φ i represents the offset of agent i relative to the leader, and n i The unit matrix, Represents the matrix B i The Moore-Penrose pseudo-inverse matrix, K 2i (t) = Ψ i (t)-K 1i Φ i (t) represents the observer gain matrix, K 3i (t) = K 2i (t)+K 4i (t) represents the formation gain matrix, (Φ i ,Ψ i ) represents the solution of the regulator, K 4i (t) is the formation compensation, K i is the transition matrix, and T2 represents the formation convergence time preset by the user.

8. The method for controlling a formation of a heterogeneous multi-agent system based on a designated time observer according to claim 7, characterized in that: When the following conditions are met, all agents reach the preset formation: Among them, y i (t) is the output of agent i at the current moment, φ yi (t) is the output offset of the desired formation, β k (k=M+1,M+2,…,M+N) satisfies Represents the convex hull of the N leaders.

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