Fixed-time time-varying formation control method for disturbed nonlinear multi-agent system

Abstract

The invention provides a method for quickly realizing fixed-time time-varying formation control of a multi-agent system under a directed network. Wherein a topological graph formed by the N intelligent agents is directed and connected; a system composed of N intelligent agents has bounded disturbance and Lipscherz nonlinearity at the same time, modeling is carried out on the system, and a formation dynamics model is established; determining formation information and a control target of the system; the asymmetry of the graph and constraints existing in dynamics are overcome, and the formation error of the system is determined; according to formation errors, formation information and a control target of the system, a control protocol which is fast in convergence, high in precision and good in robustness is designed, the designed control protocol can enable the multi-agent system to achieve formation within finite time, convergence time does not depend on an upper bound of an initial value, and therefore the convergence time can be adjusted by adjusting control parameters; the invention also provides a strict theoretical proof of formation fixed time convergence, and the effectiveness of the algorithm is explained through a numerical simulation example.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-agent formation control and provides a new method for solving the problem of forming a time-varying formation control of a multi-agent system containing both nonlinear and uncertain interference within a fixed time. Background Art

[0002] In the context of the rapid development of science and technology today, multi-agent systems (MASs) have become a research hotspot in fields such as automation and robotics. A multi-agent system consists of multiple autonomous agents that can work together to complete complex tasks that a single agent cannot efficiently complete through mutual cooperation and information exchange. Formation control, as a key collaborative control behavior in a multi-agent system, aims to make all agents move according to a predetermined structure, requiring all agents to maintain a preset relative state with other agents, and allowing the agent system to move and operate according to a predetermined formation and strategy, which is crucial to improving the overall performance of the system. This capability is particularly important in practical applications. For example, drone swarms can achieve collaborative reconnaissance and attack through formation flight, improving combat effectiveness and survivability. This collaborative operation method not only improves the efficiency of task execution, but also enhances the reliability and autonomy of the system.

[0003] When modeling the dynamics of formation flying vehicles, technical challenges may be encountered, such as nonlinear systems and environmental interference. Each aircraft in formation flying has complex dynamic characteristics, including rotation, translation and other degrees of freedom. These dynamic characteristics are themselves nonlinear, causing the formation flying system to exhibit nonlinear characteristics. Formation flying will be affected by a variety of environmental factors, such as changes in wind speed and wind direction. These interference and uncertainty factors will also make the system unstable. Most previous studies only focus on one constraint condition in nonlinear systems or interferences. These research results are difficult to achieve time-varying formation control in the presence of both nonlinearity and interference.

[0004] A key issue in formation control is the speed of convergence. In early studies, the results on consistency and formation were mainly asymptotically convergent, that is, the states of the multi-agent system can only reach consistency or form a preset formation when time tends to infinity, and accurate and fast convergence cannot be achieved. Considering that some practical problems require the multi-agent system to complete the specified task within a finite convergence time that is bounded by the initial value, the researchers studied finite-time convergence. Compared with asymptotic convergence, finite-time convergence formation control is faster, but finite-time convergence formation control is related to the initial value of the system. When the initial value is large, the convergence time of the multi-agent system will also increase. Therefore, it is particularly important to further design a fixed-time convergence algorithm that is robust to the initial value. Summary of the invention

[0005] The purpose of the present invention is to solve the technical problems existing in the above-mentioned background technology, that is, to solve the problem of forming a time-varying formation control of a multi-agent system with both nonlinearity and interference within a fixed time when the communication topology graph is a directed graph. To this end, the present invention proposes a fixed-time time-varying formation control method for a nonlinear multi-agent system with interference. It includes: assuming that the topology graph composed of N agents is directed and connected; and the system composed of these N agents simultaneously has bounded disturbances and Lipschitz nonlinearity, modeling the above system, and establishing a formation dynamics model; determining the formation information and control objectives of the system; overcoming the asymmetry of the graph and the constraints existing in the dynamics, and determining the formation error of the system; according to the formation error, formation information and control objectives of the system, designing a formation control protocol with fast convergence, high precision and good robustness, the designed algorithm can enable the multi-agent system to realize formation within a limited time, and the convergence time has an upper bound that is not dependent on the initial value, so that the convergence time can be adjusted by adjusting the control parameters; the present invention also provides a strict theoretical proof of the fixed-time convergence of the formation, and illustrates the effectiveness of the algorithm through numerical simulation examples.

[0006] The fixed-time time-varying formation control method of a nonlinear multi-agent system with interference designed according to the present invention can be applied to the scene where nonlinearity and interference exist simultaneously in the directed communication network of the formation aircraft. Under the framework of distributed control and fixed-time control theory and Lyapunov stability theory, the dynamic model of the disturbed nonlinear multi-agent system is established according to the actual application scenario, the formation information and control target are determined, the asymmetry of the communication topology diagram and the constraints of the system are overcome, the formation error is determined, and the fixed-time time-varying formation control protocol is designed according to the formation error, the formation information and the formation control target. The designed control protocol can enable the multi-agent system to realize formation in a limited time, and the convergence time has an upper bound that is not dependent on the initial value. The formation error can accurately converge to 0 within a fixed time, and the control target of fast convergence, high precision and good robustness can be achieved. The method is suitable for the control task of the fixed-time time-varying formation of a nonlinear multi-agent system with interference, and has good practical value.

[0007] The design process of the algorithm for solving the distributed fixed-time formation control problem of multi-agent systems with nonlinear and uncertain disturbances mentioned above includes the following steps:

[0008] Step 1: Describe the communication topology graph composed of N intelligent agents and the related knowledge of the graph;

[0009] Step 2: Establish a dynamic model of the disturbed nonlinear multi-agent system;

[0010] Step 3: Determine formation information and formation control objectives;

[0011] Step 4: Overcome the asymmetry of the graph and the constraints of the system to determine the formation error;

[0012] Step 5: Design a fixed-time time-varying formation control protocol based on formation error, formation information and formation control objectives;

[0013] Step 6: Prove the convergence and effectiveness of the fixed-time time-varying formation control protocol.

[0014] As an improvement of the present invention, the communication topology graph composed of N intelligent agents and the related knowledge of the graph in step 1 are described as follows:

[0015] Assumptions is a weighted directed graph, where V = {v1,v1…,v N} is a node set, is a directed edge set. is the adjacency matrix of ij ≥ 0. The number of directed edges ε in G k Represents an ordered pair of nodes (v i ,v j )∈ε, indicating that there exists a j to v i The directed information flow of v i Can receive v j Information, where v i and v j They are called child nodes and parent nodes respectively. And assume that there is no self-loop in the directed graph. There are different nodes in the directed graph So that from node v i To node v j There exists a directed path whose directed sequence is The directed spanning tree of a directed graph G contains all the nodes of G and has at least one root node, and the root node satisfies that there is a unique directed path from this node to any other node in G. The Laplace matrix L of the graph G is defined as: L = (l ij ) N×N , when i≠j, l ij =-a ij ; when i = j, and are the incoming neighbors and outgoing neighbors of agent i, respectively.

[0016] The present invention assumes that the topological graph of the agent is a strongly connected directed graph. The Laplacian matrix of the graph G satisfies L1 N = 0, and assume that L has an eigenvector ξ = (ξ1, ..., ξ N ) T satisfy and i >0, i=1, ..., N, such that ξ T L = 0. In addition, there exists a matrix Γ = diag(ξ) such that set up is any positive vector that satisfies in yes The second smallest eigenvalue of .

[0017] As an improvement of the present invention, the dynamic model of the disturbed nonlinear multi-agent system established in step 2 is as follows:

[0018] Consider a first-order multi-agent system with N agents and nonlinear and uncertain interference as follows, referred to as model (1).

[0019]

[0020] in is the state of the ith agent, let x = [x1, x2, ..., x N ] T . is the control input of the ith agent, represents the Lipschitz nonlinearity, Unknown external interference.

[0021] f(x) in model (1) i (t), t) is a Lipschitz continuous function, there exists a Lipschitz constant β>0, Satisfies: |f(ω, t)-f(ω′, t)|≤β|ω-ω′|. External disturbance d i (x i (t), t) is bounded, that is, there exists a positive scalar So that: |d i (x i (t), t)|≤ε, i=1, 2,...,N.

[0022] As an improvement of the present invention, the step 3 of determining the formation information and the formation control target is specifically as follows:

[0023] First, we give the definition of fixed-time formation: Let h(t) = [h1(t), h2(t), ...h N (t)] T Describing the formation structure of the agent system in the reference coordinate system, for model (1), if for any initial values ​​x1(0), x2(0), ..., x N (0), there exists a control protocol ui , i = 1, 2, ..., N, and a bounded positive scalar T that does not depend on the initial value, such that: If it holds, then model (1) can realize fixed-time formation. The vector h(t) defines the basic framework of the desired formation formed by N agents. Assume that h i (t) and is bounded, that is, satisfies

[0024] As an improvement of the present invention, according to the steps 1, 2 and 3, the asymmetry of the graph and the constraints of the system in step 4 can be overcome to determine the formation error as follows:

[0025] Let x i (t)-h i (t) = z i (t), l∈1,2,...,N. Let Represents the relative error of the ith agent, then the dynamic equation of the error can be obtained:

[0026]

[0027] where e=[e1,e2,…,e N ] T , z=[z1,z2,…,z N ] T , F=[f(x1(t),t),f(x2(t),t),…,f(x N (t), t)] T , D=[d(x1(t),t),d(x2(t),t),…,d(x N (t), t)] T , remember That is

[0028] As an improvement of the present invention, according to steps 1, 2, 3 and 4, the fixed-time time-varying formation control protocol is designed according to the formation error, formation information and formation control target in step 5 as follows:

[0029] Design a distributed formation control protocol as shown below:

[0030]

[0031] Where μ>1, and the control parameters k1 and k2 are both positive numbers. and This control protocol can realize fixed-time time-varying formation control of disturbed multi-agent systems, and can make the system have the advantages of high precision, fast convergence and good robustness.

[0032] As an improvement of the present invention, the proof of convergence and effectiveness of the fixed-time time-varying formation control protocol in step 6 is specifically as follows:

[0033] Let the Lyapunov function be:

[0034]

[0035] The first-order derivative of V with respect to time is:

[0036]

[0037] Pick Known e i [0] and e i [μ] have the same sign, when e i =0, yes When e i ≠0 yes

[0038] For |(k1e [0] +k2e [μ] ) T ΓLF| is estimated as:

[0039]

[0040] in: is any positive real number, θ=[θ1,θ2,…,θ N ] T =(e [0] +e [μ] ).

[0041] Remember L T The eigenvalues ​​of L are λ1≤λ2≤...≤λ N . Where λ2>0, in 1 N YesL T L corresponds to the eigenvector of λ1=0. Since μ>1, |e i |≤|e i | 0 +|e i | μ , that is |e i | 2 ≤(ei [0] +e i [μ] ) 2 :

[0042]

[0043] right Estimated to be:

[0044]

[0045] Where L i represents the i-th row of L.

[0046] right have:

[0047]

[0048] so

[0049] Combining formulas (6)-(9), we have:

[0050]

[0051] make when When H>0, let but Right now

[0052] where ||θ|| 2 for:

[0053]

[0054] in when|e i |≥1, there is when|e i When |≤1, there is When p>1, And known We can get:

[0055]

[0056] In addition, if the formation is not achieved, there is at least one e i ≠0, so that |sign(e i )|=1, therefore,

[0057] on the other hand:

[0058]

[0059] Right now

[0060] Combining (11), (12) and (13) above, we can obtain:

[0061]

[0062] We can get:

[0063]

[0064] in According to the fixed-time stability theorem, the realization of the fixed-time formation of model (1) can be guaranteed by the protocol (3). Its convergence time T max Depend on Given.

[0065] Compared with the prior art, the advantages of the present invention are as follows:

[0066] 1. Aiming at a multi-agent formation system with nonlinear and uncertain interference, the present invention proposes a new distributed formation control algorithm with the characteristics of high precision, fast convergence and good robustness.

[0067] 2. The control protocol proposed in the present invention designs a formation control algorithm on the basis of ensuring consistent tracking, allowing the intelligent system to move and operate according to a predetermined formation and strategy.

[0068] 3. The method proposed by the present invention for forming a formation of multiple agents at a fixed time in the presence of both nonlinear and uncertain bounded interference includes the design of distributed architecture collaborative control and the design of formation control protocol. By adjusting each control gain in the control protocol, the tracking error can be converged to 0 in a finite time, and the convergence time T is obtained according to the proof of the convergence of the controller. max It only depends on the size of the control gain and has nothing to do with the initial state of the system. This algorithm not only improves the efficiency of task execution but also ensures the stability, reliability and autonomy of the multi-agent system in forming formation control, realizes the consistency-based formation control goal of the present invention, and meets the practical application of the multi-agent system in forming fixed-time time-varying formation control in the presence of nonlinearity and interference, and has extremely high practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flow chart of the control method in the present invention;

[0070] Figure 2It is a communication topology diagram of the intelligent agent system in the present invention;

[0071] Figure 3 A motion trajectory diagram of the intelligent agent of the present invention;

[0072] Figure 4 This is a formation tracking error trajectory diagram of the present invention. DETAILED DESCRIPTION

[0073] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0074] The present invention proposes a method for forming a formation of multiple agents at a fixed time in the presence of nonlinear and uncertain bounded interference, including the design of distributed architecture cooperative control and formation control protocol. Under the framework of fixed-time stability theorem and Lyapunov stability theory, the present invention designs a distributed formation control algorithm to achieve the formation control goal based on consistency. Each agent can realize the cooperative control of the entire system according to its own and neighbor's state information, and exchange information through the protocol to maintain the desired formation structure.

[0075] The multi-agent formation control method of the present invention is not only innovative in theory, but also has wide applicability and important practical value in practical applications, especially in scenarios where multiple constraints exist simultaneously and require fast response and high stability.

[0076] The design process of the algorithm for solving the distributed fixed-time formation control problem of multi-agent systems with nonlinear and uncertain disturbances mentioned above includes the following steps:

[0077] Step 1: Describe the communication topology graph composed of N intelligent agents and the related knowledge of the graph;

[0078] Step 2: Establish a dynamic model of the disturbed nonlinear multi-agent system;

[0079] Step 3: Determine formation information and formation control objectives;

[0080] Step 4: Overcome the asymmetry of the graph and the constraints of the system to determine the formation error;

[0081] Step 5: Design a fixed-time time-varying formation control protocol based on formation error, formation information and formation control objectives;

[0082] Step 6: Prove the convergence and effectiveness of the fixed-time time-varying formation control protocol.

[0083] Furthermore, the communication topology graph composed of N intelligent agents and the related knowledge of the graph in step 1 are described as follows:

[0084] Assumptions is a weighted directed graph, where V = {v1, v1..., v N} is a node set, is a directed edge set. is the adjacency matrix of ij ≥ 0. The number of directed edges ε in G k Represents an ordered pair of nodes (v i , v j )∈ε, indicating that there exists a j to v i The directed information flow of v i Can receive v j Information, where v i and v j They are called child nodes and parent nodes respectively. And assume that there is no self-loop in the directed graph. There are different nodes in the directed graph So that from node v i To node v j There exists a directed path whose directed sequence is The directed spanning tree of a directed graph G contains all the nodes of G and has at least one root node, and the root node satisfies that there is a unique directed path from this node to any other node in G. The Laplace matrix L of the graph G is defined as: L = (l ij ) N×N , when i≠j, l ij =-a ij ; when i = j, and are the incoming neighbors and outgoing neighbors of agent i, respectively.

[0085] The present invention assumes that the topological graph of the agent is a strongly connected directed graph. The Laplacian matrix of the graph G satisfies L1 N = 0, and assume that L has an eigenvector ξ = (ξ1, ..., ξ N ) T satisfy and i >0, i=1, ..., N, such that ξ T L = 0. In addition, there exists a matrix Γ = diag(ξ) such that set up is any positive vector that satisfies in yes The second smallest eigenvalue of .

[0086] Furthermore, the dynamic model of the disturbed nonlinear multi-agent system established in step 2 is as follows:

[0087] Consider a first-order multi-agent system with N agents and nonlinear and uncertain interference as follows, referred to as model (1).

[0088]

[0089] in is the state of the ith agent, let x = [x1, x2, ..., x N ] T . is the control input of the ith agent, represents the Lipschitz nonlinearity, Unknown external interference.

[0090] f(x) in model (1) i (t), t) is a Lipschitz continuous function, there exists a Lipschitz constant β>0, Satisfies: |f(ω, t)-f(ω′, t)|≤β|ω-ω′|. External disturbance d i (x i (t), t) is bounded, that is, there exists a positive scalar So that: |d i (x i (t), t)|≤ε, i=1, 2,...,N.

[0091] Furthermore, the step 3 determines the formation information and the formation control target as follows:

[0092] First, we give the definition of fixed-time formation: Let h(t) = [h1(t), h2(t), ...h N (t)] T Describing the formation structure of the agent system in the reference coordinate system, for model (1), if for any initial values ​​x1(0), x2(0), ..., x N (0), there exists a control protocol u i , i = 1, 2, ..., N, and a bounded positive scalar T that does not depend on the initial value, such that: If it holds, then model (1) can realize fixed-time formation. The vector h(t) defines the basic framework of the desired formation formed by N agents. Assume that h i (t) and is bounded, that is, satisfies

[0093] Furthermore, according to steps 1, 2 and 3, the asymmetry of the graph and the constraints of the system in step 4 can be overcome, and the formation error is determined as follows:

[0094] Let x i (t)-h i (t) = z i (t), i∈1,2,...,N. Let Represents the relative error of the ith agent, then the dynamic equation of the error can be obtained:

[0095]

[0096] where e=[e1,e2,…,e N ] T , z=[z1,z2,…,z N ] T , F=[f(x1(t),t),f(x2(t),t),…,f(x N (t), t)] T , D=[d(x1(t),t),d(x2(t),t),…,d(x N (t), t)] T , remember That is

[0097] Further, according to steps 1, 2, 3 and 4, the fixed-time time-varying formation control protocol is designed according to the formation error, formation information and formation control target in step 5 as follows:

[0098] Design a distributed formation control protocol as shown below:

[0099]

[0100] Where μ>1, and the control parameters k1 and k2 are both positive numbers. Head This control protocol can realize fixed-time time-varying formation control of disturbed multi-agent systems, and can make the system have the advantages of high precision, fast convergence and good robustness.

[0101] Furthermore, the proof of convergence and effectiveness of the fixed-time time-varying formation control protocol in step 6 is as follows:

[0102] Let the Lyapunov function be:

[0103]

[0104] The first-order derivative of V with respect to time is:

[0105]

[0106] Pick k =min{k1,k2}, Known e i [0] and e i [μ] have the same sign, when e i =0, yes When e i ≠0 yes

[0107] For |(k1e [0] +k2e [μ] ) T ΓLF| is estimated as:

[0108]

[0109] in: is any positive real number, θ=[θ1,θ2,…,θ N ] T =(e [0] +e [μ] ).

[0110] Remember L T The eigenvalues ​​of L are λ1≤λ2≤...≤λ N . Where λ2>0, in 1N is L T L corresponds to the eigenvector of λ1=0. Since μ>1, |e i |≤|e i | 0 +|e i | μ , that is |e i | 2 ≤(e i [0] +e i [μ] ) 2 :

[0111]

[0112] right Estimated to be:

[0113]

[0114] Where L i represents the i-th row of L.

[0115] right have:

[0116]

[0117] so

[0118] Combining formulas (6)-(9), we have:

[0119]

[0120] make when When H>0, let but Right now

[0121] where ||θ|| 2 for:

[0122]

[0123] in when|e i |≥1, there is when|e i When |≤1, there is When p>1, And known We can get:

[0124]

[0125] In addition, if the formation is not achieved, there is at least one e i ≠0, so that |sign(e i )|=1, therefore,

[0126] on the other hand:

[0127]

[0128] Right now

[0129] Combining (11), (12) and (13) above, we can obtain:

[0130]

[0131] We can get:

[0132]

[0133] in According to the fixed-time stability theorem, the realization of the fixed-time formation of model (1) can be guaranteed by the protocol (3) proposed in the present invention. Its convergence time T max Depend on Given.

[0134] Example 1

[0135] The technical solution of the present invention is further described according to the accompanying drawings and in combination with specific numerical simulation implementation methods. The present invention uses a Matlab platform for simulation and provides a numerical example to demonstrate the performance of the proposed distributed formation control algorithm.

[0136] Consider a MASs with 6 agents, where The topology of the intelligent system is as follows: Figure 2 As shown, its adjacency matrix is: A = [0 1 0 0 0 0; 0 0 0 1 0 0; 1 1 0 0 0 0; 0 0 0 0 1 0; 0 0 0 0 0 1; 0 01 0 0 0]. The parameters of controller (3) are selected as: k1 = 2, k2 = 2, μ = 1.2.

[0137] Let a = 0.8, where the required dynamic formation format is:

[0138]

[0139] The expected formation is a regular hexagon.

[0140] Under controller (2), the motion trajectory of the multi-agent system is as follows: Figure 3 As shown. Figure 3 It can be seen that the intelligent agents can still form a formation within a fixed time under complex constraints. The formation is a regular hexagon and changes over time. The formation tracking error trajectory is shown in the figure Figure 4 shown. Figure 4 It shows that the formation tracking error can quickly reach a consensus, that is, multiple agents complete the formation.

[0141] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Equivalent replacements or substitutions made on the basis of the above technical solutions all fall within the protection scope of the present invention.

Claims

1. A method for controlling a fixed-time time-varying formation of a disturbed nonlinear multi-agent system, characterized in that: The method comprises the following steps: Step 1: Describe the communication topology graph composed of N intelligent agents and the related knowledge of the graph; Step 2: Establish a dynamic model of the disturbed nonlinear multi-agent system; Step 3: Determine formation information and formation control objectives; Step 4: Overcome the asymmetry of the graph and the constraints of the system to determine the formation error; Step 5: Design a fixed-time time-varying formation control protocol based on formation error, formation information and formation control objectives; Step 6: Prove the convergence and effectiveness of the fixed-time time-varying formation control protocol.

2. The method for controlling a fixed-time time-varying formation of a disturbed nonlinear multi-agent system according to claim 1, characterized in that: The communication topology graph composed of N intelligent agents and the related knowledge of the graph in step 1 are described as follows: Assumptions is a weighted directed graph, where V = {v1,v1…,v N } is a node set, is a directed edge set, is the adjacency matrix of ij ≥0, directed edges ε in G k Represents an ordered pair of nodes (v i ,v j )∈ε, indicating that there exists a j to v i The directed information flow of v i Can receive v j Information, where v i and v j They are called child nodes and parent nodes respectively, and their weights And assuming that there are no self-loops in the directed graph, there are different nodes in the directed graph So that from node v i To node v j There exists a directed path whose directed sequence is The directed spanning tree of a directed graph G contains all the nodes of G and has at least one root node, and the root node satisfies the unique directed path from the node to any other node in G. The Laplace matrix L of the graph G is defined as: L = (l ij ) N×N , when i≠j, l ij =-a ij ; when i = j, and are the incoming neighbors and outgoing neighbors of agent i respectively; Assume that the topological graph of the agent is a strongly connected directed graph, and the Laplacian matrix of graph G satisfies L1 N = 0, and assume that L has an eigenvector ξ = (ξ1,...,ξ N ) T satisfy and i >0,i=1,…,N, such that ξ T L = 0, and there exists a matrix Γ = diag(ξ) such that set up is any positive vector that satisfies in yes The second smallest eigenvalue of .

3. The method for controlling a fixed-time time-varying formation of a disturbed nonlinear multi-agent system according to claim 1, characterized in that: The dynamic model of the disturbed nonlinear multi-agent system established in step 2 is as follows: Consider a first-order multi-agent system with N agents and nonlinear and uncertain interference as follows, referred to as model (1). in is the state of the ith agent, let x = [x1, x2, …, x N ] T , is the control input of the ith agent, represents the Lipschitz nonlinearity, For unknown external interference; f(x) in model (1) i (t),t) is a Lipschitz continuous function, there exists a Lipschitz constant β>0, Satisfies: |f(ω,t)-f(ω′,t)|≤β|ω-ω′|, external disturbance d i (x i (t),t) is bounded, that is, there exists a positive scalar So that: |d i (x i (t),t)|≤ε,i=1,2,…,N.

4. The method for controlling a fixed-time time-varying formation of a disturbed nonlinear multi-agent system according to claim 1, characterized in that: The step 3 of determining the formation information and formation control target is as follows: First, we give the definition of fixed-time formation: Let h(t) = [h1(t), h2(t), …h N (t)] T Describe the formation structure of the intelligent system in the reference coordinate system. For model (1), if for any initial values ​​x1(0), x2(0), ..., x N (0), there exists a control protocol u i , i = 1, 2, ..., N, and a bounded positive scalar T that does not depend on the initial value, such that: If it holds, then model (1) can realize fixed-time formation. The vector h(t) defines the basic framework of the desired formation formed by N agents. Assume that h i (t) and is bounded, that is, satisfies 5. The method for controlling a fixed-time time-varying formation of a disturbed nonlinear multi-agent system according to claim 1, characterized in that: According to the steps 1, 2 and 3, the formation error determined in step 4 to overcome the asymmetry of the graph and the constraints of the system is as follows: Let x i (t)-h i (t) = z i (t),i∈1,2,...,N, let represents the relative error of the formation of the i-th agent, then the dynamic equation of the formation error can be obtained: where e=[e1,e2,…,e N ] T ,z=[z1,z2,…,z N ] T , F=[f(x1(t),t),f(x2(t),t),…,f(c N (t),t)] T , D=[d(x1(t),t),d(x2(t),t),…,d(x N (t),t)] T , remember That is 6. The method for controlling a fixed-time time-varying formation of a disturbed nonlinear multi-agent system according to claim 1, characterized in that: According to steps 1, 2, 3 and 4, the fixed-time time-varying formation control protocol is designed according to the formation error, formation information and formation control target in step 5 as follows: Design a distributed formation control protocol as shown below, referred to as protocol (3): Where μ>1, where the control parameters k1 and k2 are both positive numbers, where s [j] =sign(s)|s| k , and 7. The method for controlling a fixed-time time-varying formation of a disturbed nonlinear multi-agent system according to claim 1, characterized in that: The proof of convergence and effectiveness of the fixed-time time-varying formation control protocol in step 6 is as follows: Let the Lyapunov function be: The first-order derivative of V with respect to time is: Pick k =min{k1,k2}, Known e i [0] and e i [μ] have the same sign, when e i =0, yes When e i ≠0 yes For |(k1e [0] +k2e [ξ] ) T ΓLF| is estimated as: in: k a is any positive real number, θ=[θ1,θ2,…,θ N ] T =(e [0] +e [μ] ), Remember L T The eigenvalues ​​of L are λ1≤λ2≤...≤λ N , where λ2>0, in YesL T L corresponds to the eigenvector of λ1=0, because ξ>1, so |e i |≤|e i | 0 +|e i | μ , that is |e i | 2 ≤(e i [0] +ei [μ] ) 2 : right Estimated to be: Where L i represents the i-th row of L; right have: so Combining formulas (6)-(9), we have: make when When H>0, let but Right now where ∥θ∥ 2 for: in when|e i When |≥1, there is when|e i When |≤1, there is When p>1, And known We can get: In addition, if the formation is not achieved, there is at least one e i ≠0, so that |sign(e i )|=1, therefore, on the other hand: Right now Combining (11), (12) and (13) above, we can get: You can get: in According to the fixed-time stability theorem, the realization of fixed-time formation for model (1) can be guaranteed by the protocol (3), and its convergence time T max Depend on Given.

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