A model-unknown multi-agent consensus cooperative control method

Abstract

The application provides a model-unknown multi-agent consensus collaborative control method, comprising the following steps: constructing a communication topology by taking each agent in a multi-agent system as a communication node; constructing a dynamic model of the agent in a second-order system according to algebraic graph theory and control theory, and initializing the system; estimating unknown parts and external disturbances in the multi-agent system by using a fuzzy logic control algorithm; restraining the convergence time of the multi-agent system by setting a time scale function; setting a second-order consensus control protocol to update the position and speed information of each agent in the system within a specified time according to the time scale function, the unknown parts and the external disturbances in the multi-agent system; and constructing an error system according to the state information of each agent and its neighbor agents, so that each agent reaches the second-order consensus when the error system is stable, and the application can solve the consensus problem of the system model unknown and with unmatched disturbances.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control technology, and in particular relates to a multi-agent consensus cooperative control method with an unknown model. Background Technology

[0002] In recent years, research on multi-agent systems (MASs) has attracted much attention, with their wide applications in areas such as cooperative robot control, distributed sensor networks, swarming phenomena in biological and social systems, and chaotic circuit networks generating considerable interest. The core of MASs lies in the collaborative cooperation among agents, achieving effective information exchange by following specific topological rules, thereby accomplishing shared tasks under well-designed control laws.

[0003] In this field, the choice of control strategy is crucial for the cooperative control process of multi-agent networks, directly affecting the system's performance and efficiency when performing cooperative tasks. To achieve cooperative tasks in multi-agent systems, researchers have proposed various cooperative control schemes, including adaptive control, event-triggered control, and model predictive control. These strategies aim to meet the control requirements of different application scenarios, thereby improving the robustness and adaptability of the system. In time-critical applications, such as automotive parts assembly, spacecraft docking, and target interception, achieving ideal tracking accuracy in a short time is critical. Finite-time control, fixed-time control, and predefined / specified-time control play key roles in this regard and have received widespread attention. However, these algorithms generally require prior knowledge of the system's initial conditions, leading to the development of specified-time consistency algorithms. Specified-time control inherits the advantages of specified-time control, fixed-time control, and predefined-time control, and allows for precise pre-setting of settling times.

[0004] Current research in control theory is typically based on known models, where the system's dynamic equations and model parameters are known in advance. However, in many practical applications, the interactions and dynamics between agents may be unknown or difficult to model due to complexity. Many real-world problems involve the cooperative behavior of multiple agents, such as drone swarms, robot teams, and transportation systems. These systems often have highly complex dynamics and interactions, making accurate modeling difficult. Furthermore, the environment in which the agents operate may be uncertain, exhibiting various changes and stochasticities. On the other hand, model uncertainties may also arise from sensor noise, external disturbances, or unknown system characteristics, requiring researchers to design different control algorithms to address these uncertainties. Therefore, accurate modeling of multi-agent system environments in complex settings is a challenge, making the study of cooperative control problems under fuzzy models of significant practical importance.

[0005] Currently, research on time consistency of known systems has a relatively mature foundation. This invention utilizes these control theories and methods, applies them to time consistency of unknown systems, and creates a conservative control algorithm to reduce computational complexity, thereby solving the control problems of most systems in the real world. This is of great significance for multi-agent cooperative control. Summary of the Invention

[0006] To address the problems existing in the background technology, this invention provides a multi-agent consensus cooperative control method with an unknown model, comprising:

[0007] S1: Construct a communication topology by treating each agent in a multi-agent system as a communication node;

[0008] S2: Construct a dynamic model of the agent in a second-order system based on algebraic graph theory and cybernetics, and initialize the system;

[0009] S3: Use fuzzy logic control algorithms to estimate the unknown parts and external disturbances in a multi-agent system;

[0010] S4: Constrain the convergence time of the multi-agent system by setting a time scale function;

[0011] S5: Based on the time scale function, the unknown parts of the multi-agent system and external disturbances, set a second-order consensus control protocol to update the position and velocity information of each agent in the system within a specified time.

[0012] S6: Construct an error system based on the state information of each agent and its neighboring agents. When the error system is stable, all agents achieve second-order consistency.

[0013] Preferably, the process of constructing the communication topology includes:

[0014] Let G = (V, E, A) be an N-order directed graph. Let V = {1, 2, ..., N} represent the set of nodes, where N is the total number of nodes in the multi-agent system. The directed graph has a weighted adjacency matrix A = (a...). ij ) N×N a ij Let a be the weight of the ordered edges from node i to node j, and let a be the weight of the edges if and only if there are no edges between nodes i and j. ij =0; Based on the degree matrix D and the adjacency matrix B of the leader node in the directed graph, B = diag{b1,...,b...} i ,...,b n}; `deg(.)` represents the diagonalization operation; if follower node i has obtained information from the leader node, then `b`... i=1, otherwise b i =0.

[0015] Preferably, the dynamic model representation of the agent in the second-order system includes:

[0016]

[0017] Where, x i (t) represents the position of the i-th agent, v i (t) represents the velocity of the i-th agent; f i (x i (t),v i (t)) and g i (x i (t),v i (t) represents the unknown part of the i-th agent in a multi-agent system, d i1 (t) and d i2 (t) represents the external disturbance experienced by the i-th agent in a multi-agent system, u i (t) represents the control input of the multi-agent system.

[0018] Preferably, the estimation of unknown components and external disturbances in a multi-agent system using a fuzzy logic control algorithm includes:

[0019] The fuzzy logic control system is defined as follows:

[0020]

[0021] make The fuzzy logic control system is then represented as:

[0022]

[0023] in,

[0024] Define any continuous function on the compact set Ω W * Let f be the ideal value of W. * (x) represents h(m) i The ideal value of ); let F i2 =g i +d i2 Then the unknown parts and external disturbances in a multi-agent system are represented as:

[0025]

[0026]

[0027]

[0028]

[0029] in, Let ε represent the set of neighboring agents of the i-th agent. i1 With ε i2 x is an unknown constant greater than 0. j Let m represent the location information of the j-th neighboring agent of the i-th agent. i h(m) represents the input of the fuzzy logic control system. i ) represents the output of a fuzzy logic control system; The output h(m) of the fuzzy logic control system i The fuzzy membership function of ) reaches its maximum value h(m) under certain rules. i The value of ); G l These are fuzzy sets of linguistic variables; represents the membership function with respect to the input in a fuzzy logic control system; n represents the total number of agents in a multi-agent system; M represents the total number of rules in the fuzzy rule base; z i1 (t) represents the positional error between the i-th agent and the leader agent, z i2 (t) represents the indirect velocity error of the i-th agent, x d (t) represents the location information of the leading agent, d i1 (t), d i2 (t) represents the external disturbance experienced by the i-th agent.

[0030] Preferably, the time scale function is expressed as:

[0031]

[0032]

[0033]

[0034] Where ξ(t) represents the time gain function, t0 represents the initial time of the multi-agent system, T represents the convergence time of the multi-agent system, m is a variable factor parameter, h is a constant parameter, and ψ(t) is the time scale function.

[0035] Preferably, the second-order consistency control protocol is expressed as:

[0036]

[0037]

[0038] in, Let u represent the set of neighbor nodes of the i-th agent. i (t) represents the control input of the multi-agent system. and Indicates W i1 and W i2 The estimated value, ρ i1 With ρ i2 z is a constant parameter greater than 1. i1 This represents the state error between the i-th agent and the leader agent. z represents the rate of change of the intermediate control law of the i-th agent. i2 Let α represent the indirect velocity error of the i-th agent. i Φ(X) represents the intermediate control law of a multi-agent system, where k is a constant parameter greater than 0. i1 (t) represents the intermediate parameter about position in the fuzzy logic system, Φ(X i2 (t) represents the intermediate parameter of velocity in the fuzzy logic system, expressed as:

[0039]

[0040]

[0041] Where tanh(.) is the hyperbolic tangent function, with a range of [-1, 1]. and They represent ε respectively i1 and ε i2 In the ideal state, θ represents a constant parameter. This indicates the rate of change of the leader agent's position.

[0042] Preferably, the W i1 and W i2 The estimated values ​​include: real-time estimation of W by designing an adaptive control law. i1 and W i2 The estimated adaptive control law is as follows:

[0043]

[0044]

[0045] in, and express and Adaptive control law, Indicates W i1 The estimation error, Indicates W i2 The estimation error, γ i1η i1 γ i2 and η i2 This represents a constant parameter.

[0046] Preferably, the error system is represented as:

[0047] z i1 (t)=b i (x i (t)-x d (t))

[0048]

[0049] Where, x i (t) represents the position of the i-th agent, x d (t) represents the position of the leader agent, b i z represents the weight between followers and leaders. i1 Let a represent the positional error between the i-th agent and the leader. ij z represents the weights between the various agents. i2 This represents the indirect velocity error of the i-th agent.

[0050] The present invention has at least the following beneficial effects

[0051] This invention utilizes a fuzzy logic control algorithm combined with a specified time scale function to derive a specified-time consensus control protocol for leader-led multi-agent second-order systems. This protocol addresses consensus problems arising from unknown system models and mismatched disturbances. The strategy introduces dynamic high-gain scaling technology into uncertain nonlinear systems, achieving specified-time system stability and resolving the "algebraic loop problem" inherent in traditional strict feedback control methods. However, the complexity of calculating the derivative of the scaling function (i.e., the time scale function) increases due to the introduction of a time-varying function to scale the state. Therefore, the time scale function designed in this invention maintains simplicity while ensuring controller performance, which helps reduce resource consumption. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0053] Figure 2 This is a communication diagram of a multi-agent system in an embodiment of the present invention. Detailed Implementation

[0054] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0055] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual images. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0056] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0057] Please see Figure 1 This invention provides a multi-agent consensus cooperative control method with an unknown model, comprising:

[0058] S1: Construct a communication topology by treating each agent in a multi-agent system as a communication node;

[0059] S2: Construct a dynamic model of the agent in a second-order system based on algebraic graph theory and cybernetics, and initialize the system;

[0060] S3: Use fuzzy logic control algorithms to estimate the unknown parts and external disturbances in a multi-agent system;

[0061] S4: Constrain the convergence time of the multi-agent system by setting a time scale function;

[0062] S5: Based on the time scale function, the unknown parts of the multi-agent system and external disturbances, set a second-order consensus control protocol to update the position and velocity information of each agent in the system within a specified time.

[0063] S6: Construct an error system based on the state information of each agent and its neighboring agents. When the error system is stable, all agents achieve second-order consistency.

[0064] Preferably, the process of constructing the communication topology includes:

[0065] Let G = (V, E, A) be an N-order directed graph. Let V = {1, 2, ..., N} represent the set of nodes, where N is the total number of nodes in the multi-agent system. The directed graph has a weighted adjacency matrix A = (a...). ij ) N×N a ij Let a be the weight of the ordered edges from node i to node j, and let a be the weight of the edges if and only if there are no edges between nodes i and j. ij =0; Based on the degree matrix D and the adjacency matrix B of the leader node in the directed graph, B = diag{b1,...,b...} i ,...,b n}; `deg(.)` represents the diagonalization operation; if follower node i has obtained information from the leader node, then `b`... i =1, otherwise b i =0.

[0066] Please see Figure 2 , Figure 2 It includes the leader agent node L0 and the follower agent nodes F1 to F4. The adjacency matrix A, degree matrix D, and leader adjacency matrix B have the following values:

[0067]

[0068] Preferably, the dynamic model representation of the agent in the second-order system includes:

[0069]

[0070] Where, x i (t) represents the position of the i-th agent, v i (t) represents the velocity of the i-th agent; f i (x i (t),v i (t)) and g i (x i (t),v i (t) represents the unknown part of the i-th agent in a multi-agent system, d i1 (t) and d i2 (t) represents the external disturbance experienced by the i-th agent in a multi-agent system, u i(t) represents the control input of the multi-agent system.

[0071] Preferably, the estimation of unknown components and external disturbances in a multi-agent system using a fuzzy logic control algorithm includes:

[0072] The fuzzy logic control system is defined as follows:

[0073]

[0074] make The fuzzy logic control system is then represented as:

[0075]

[0076] in,

[0077] Define any continuous function on the compact set Ω W * Let f be the ideal value of W. * (x) represents h(m) i The ideal value of ); let F i2 =g i +d i2 Then the unknown parts and external disturbances in a multi-agent system are represented as:

[0078]

[0079]

[0080]

[0081]

[0082] in, Let ε represent the set of neighboring agents of the i-th agent. i1 With ε i2 x is an unknown constant greater than 0. j Let m represent the location information of the j-th neighboring agent of the i-th agent. i h(m) represents the input of the fuzzy logic control system. i ) represents the output of a fuzzy logic control system; The output h(m) of the fuzzy logic control system i The fuzzy membership function of ) reaches its maximum value h(m) under certain rules. i The value of ); G l These are fuzzy sets of linguistic variables; represents the membership function with respect to the input in a fuzzy logic control system; n represents the total number of agents in a multi-agent system; M represents the total number of rules in the fuzzy rule base; z i1 (t) represents the positional error between the i-th agent and the leader agent, z i2 (t) represents the indirect velocity error of the i-th agent, x d (t) represents the location information of the leading agent, d i1 (t), d i2 (t) represents the external disturbance received by the i-th agent. In this example, f i =2*x i +cos(x i ), g i =x i 2 +0.5*x i The fuzzy rule base is defined by experts in this field and will not be elaborated upon in this article.

[0083] Preferably, the time scale function is expressed as:

[0084]

[0085]

[0086]

[0087] Where ξ(t) represents the time gain function, t0 represents the initial time of the multi-agent system, T represents the convergence time of the multi-agent system, m is a variable factor parameter, h is a constant parameter, and ψ(t) is the time scale function.

[0088] Preferably, the second-order consistency control protocol is expressed as:

[0089]

[0090]

[0091] in, Let u represent the set of neighbor nodes of the i-th agent. i (t) represents the control input of the multi-agent system. and Indicates W i1 and W i2 The estimated value, ρ i1 With ρ i2 z is a constant parameter greater than 1. i1 This represents the state error between the i-th agent and the leader agent. z represents the rate of change of the intermediate control law of the i-th agent.i2 Let α represent the indirect velocity error of the i-th agent. i Φ(X) represents the intermediate control law of a multi-agent system, where k is a constant parameter greater than 0. i1 (t) represents the intermediate parameter about position in the fuzzy logic system, Φ(X i2 (t) represents the intermediate parameter of velocity in the fuzzy logic system, expressed as:

[0092]

[0093]

[0094] Where tanh(.) is the hyperbolic tangent function, with a range of [-1, 1]. and They represent ε respectively i1 and ε i2 In the ideal state, θ represents a constant parameter. This indicates the rate of change of the leader agent's position.

[0095] Preferably, the W i1 and W i2 The estimated values ​​include: real-time estimation of W by designing an adaptive control law. i1 and W i2 The estimated adaptive control law is as follows:

[0096]

[0097]

[0098] in, and express and Adaptive control law, Indicates W i1 The estimation error, Indicates W i2 The estimation error, γ i1 η i1 γ i2 and η i2 This represents a constant parameter.

[0099] Preferably, the error system is represented as:

[0100] z i1 (t)=b i (x i (t)-x d (t))

[0101]

[0102] Where, x i (t) represents the position of the i-th agent, x d (t) represents the position of the leader agent, b i z represents the weight between followers and leaders. i1 Let a represent the positional error between the i-th agent and the leader. ij z represents the weights between the various agents. i2 This represents the indirect velocity error of the i-th agent.

[0103] The stability proof of a multi-agent system mainly utilizes this error system. When multiple agents in the system reach consensus within a specified time, z i1 , z i2 All will tend towards 0. At this point, each agent will reach the following state within a specified time:

[0104]

[0105]

[0106] Stability verification primarily utilizes Lyapunov's stability theorem. The verification process is divided into two parts: one within a specified time period (t ∈ [t0, t0+T)), during which all agents achieve second-order consistency; the other after a specified time period (t ∈ [t0+T, +∞)), during which each agent maintains its position and velocity, remaining consistent with the leader. When second-order consistency is achieved, the controller will also tend to zero, and each agent will save its latest state information.

[0107] ① When t∈[t0,t0+T):

[0108] Let the Lyapunov function be:

[0109]

[0110] Where V1 and V2 represent the local indirect Lyapunov functions, corresponding to the position and velocity information of each agent, respectively. They are represented as follows:

[0111]

[0112]

[0113] Where, λ min (B -1 ) and λ min (D -1Let λ and B represent the minimum eigenvalues ​​of the inverse matrices of the degree matrix D and the leader adjacency matrix B of the multi-agent network used in the communication topology, respectively. To minimize the convergence error of each agent, the two matrices should satisfy: λ min (B -1 )≥0,λ min (D -1 If λ ≥ 0, in this instance, λ min (B -1 ), λ min (D -1 All values ​​are 1. Because so,

[0114]

[0115] in, Indicates W i1 The rate of change of the estimation error Indicates W i2 The rate of change of the estimation error can be determined by the inequality theorem:

[0116]

[0117]

[0118] Furthermore, it can be obtained that,

[0119]

[0120] set up Calculations show that:

[0121]

[0122] Where, ρ i1 ,ρ i2 ,η i1 ,η i2 ,γ i1 ,γ i2 It is a positive constant and satisfies the condition: ρ i1 ≥1,ρ i2 ≥1, And parameter b satisfies:

[0123] In this example, v i1 =2,ρ i2 =4,η i1 =10,η i2 =10,γ i1 =5,γ i2 =5,

[0124] k=1, h=3, m=0.000001. m is a variable factor that can be adjusted based on the convergence performance of the agent. It is then easy to obtain: Based on this inequality, using the time scale function and further differentiation, we can easily obtain:

[0125] Therefore, as t→t0+T, we can conclude that V→0, thus obtaining V1→0, V2→0, and u→0. Final implementation:

[0126] In this example, let the leader's trajectory be: x d = 1 + 2*sin(t), the initial states of the four agents are: x1 = -0.1, v1 = 0; x2 = -0.2, v2 = 0.1; x3 = 0.2, v3 = 0; x4 = 0.15, v3 = 0.3. When the system reaches second-order consistency, the trajectories of the four agents will be aligned with the leader x. d Their trajectories almost overlapped.

[0127] ② When t∈[t0+T,+∞): At this time, the position and velocity states of the four agents are asymptotically and dynamically consistent with the leader's state. The controller u≡0, and each agent will save the latest state information. From the above, we can see that:

[0128]

[0129] Therefore, 0 ≤ V ≤ V(t0+T) = 0, thus we obtain the following equation holds in the interval [t0+T, +∞):

[0130]

[0131] As can be seen from the above, both time periods demonstrate that the error system is asymptotically stable. Therefore, the multi-agent system can achieve second-order time-bound consensus, meaning that all agents reach consensus within a specified time. After the agents reach consensus within the specified time, the agent system saves the latest state information, and all agents can execute corresponding operations based on the latest control input, achieving the purpose of coordinated control of the agent system.

[0132] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-agent consensus cooperative control method with an unknown model, characterized in that, include: S1: Construct a communication topology by treating each agent in a multi-agent system as a communication node; S2: Construct a dynamic model of the agent in a second-order system based on algebraic graph theory and cybernetics, and initialize the system; The dynamic model representation of the agent in the second-order system includes: in, Indicates the first The location of each agent. Indicates the first The speed of each intelligent agent; and In a multi-agent system, the first The unknown aspects of an intelligent agent. and In a multi-agent system, the first External disturbances experienced by an intelligent agent This represents the control input of a multi-agent system; S3: Use fuzzy logic control algorithms to estimate the unknown parts and external disturbances in a multi-agent system; The estimation of unknown components and external disturbances in a multi-agent system using fuzzy logic control algorithms includes: The fuzzy logic control system is defined as follows: make , Then the fuzzy logic control system is represented as: in, Define compact set any continuous function on , Represented as The ideal value, express The ideal value; let , Then the unknown parts and external disturbances in a multi-agent system are represented as: in, Indicates the first The set of neighboring intelligent agents of an intelligent agent, and For unknown constants greater than 0, Indicates the first A smart agent The Location information of each neighboring intelligent agent. This represents the input to a fuzzy logic control system. This represents the output of a fuzzy logic control system. , Represents the output of a fuzzy logic control system The maximum value of the fuzzy membership function under certain rules The value of ; These are fuzzy sets of linguistic variables; represents the membership function with respect to the input in a fuzzy logic control system; n represents the total number of agents in a multi-agent system; and M represents the total number of rules in the fuzzy rule base. Indicates the first The positional error between the individual agent and the leader agent This indicates the location information of the leading intelligent agent. and Indicates the first External disturbances experienced by an intelligent agent; S4: Constrain the convergence time of the multi-agent system by setting a time scale function; S5: Based on the time scale function, the unknown parts of the multi-agent system and external disturbances, set a second-order consensus control protocol to update the position and velocity information of each agent in the system within a specified time. S6: Construct an error system based on the state information of each agent and its neighboring agents. When the error system is stable, all agents achieve second-order consistency.

2. The multi-agent consensus cooperative control method with an unknown model according to claim 1, characterized in that, The process of constructing a communication topology includes: set up yes Ordered directed graph, It is an edge set. Represents a set of nodes. Let be the total number of nodes in a multi-agent system, and let be the weighted adjacency matrix of the directed graph with non-negative elements. , For nodes To the node The weight of the ordered edges is given if and only if the node and nodes When there is no boundary between them, Determine the degree matrix based on the directed graph. Adjacency matrix of the leader node , ; , This indicates a diagonalization operation; if the follower node... If the information about the leader node is obtained, then ,on the contrary .

3. The multi-agent consensus cooperative control method for an unknown model according to claim 1, characterized in that, The time scale function is expressed as: in, Represents the time gain function. Indicates the initial time of operation of the multi-agent system. Indicates the convergence time of a multi-agent system; It is a variable factor parameter. It is a constant parameter; This is a time-scale function.

4. The multi-agent consensus cooperative control method with an unknown model according to claim 3, characterized in that, The second-order consensus control protocol is represented as follows: in, This represents the control input of a multi-agent system. and Indicates to and The estimated value, and For constant parameters greater than 1, Indicates the first The positional error between the individual agent and the leader agent Indicates the first Indirect velocity error of each agent Indicates the first Intermediate control rate of an agent, Indicates the first Rate of change of intermediate control rate of each agent For constant parameters that are greater than 0, This represents intermediate parameters related to position in a fuzzy logic system. The intermediate parameter for velocity in a fuzzy logic system is represented as: in, Let be the hyperbolic tangent function, with a range of . , and They represent and The ideal state Represents a constant parameter. This indicates the rate of change of the leader agent's position.

5. The multi-agent consensus cooperative control method with an unknown model as described in claim 4 is characterized in that, The and The estimated values ​​include: real-time adjustments made by designing an adaptive control law. and The estimated adaptive control law is as follows: in, and express and Adaptive control law, Indicates to The estimation error, Indicates to The estimation error, , , and This represents a constant parameter.

6. The multi-agent consensus cooperative control method with an unknown model according to claim 5, characterized in that, The error system is represented as follows: in, Indicates the first The location of each agent. Indicates the position of the leader agent. This indicates the weight between followers and leaders. Indicates the first The positional error between the agent and the leader This represents the weights between the various agents. Indicates the first Indirect velocity error of each agent.

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