Multi-agent cooperative formation control method based on unknown input state mutual estimation

Abstract

The invention discloses a multi-agent cooperative formation control method based on unknown input state mutual estimation, and belongs to the field of multi-agent control, and the method comprises the following steps: S1, building a state mutual estimation mechanism model of agents based on a multi-agent system; s2, constructing a communication topological structure of the multi-agent system according to graph theory knowledge; s3, determining a gain matrix in the distributed state mutual estimator; s4, constructing a formation control strategy based on a consistency theory for each agent according to the estimated values of each agent for all states; and S5, if the measurement of the agent sensor fails, returning to the step S3 to re-determine the gain matrix in the distributed state mutual estimator. By adopting the multi-agent cooperative formation control method based on unknown input state mutual estimation, the state mutual estimation can be accurately realized under the condition that the measurement output of the agent sensor fails, and a guarantee is provided for the completion of a multi-agent system formation task.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent control, and in particular to a multi-agent collaborative formation control method based on mutual estimation of unknown input states. Background Art

[0002] Multi-agent systems have the advantages of autonomy, fault tolerance, flexibility and scalability, and are widely used in space development and exploration, emergency search and rescue, satellite formations, multi-missile coordination and other fields. The multi-agent collaborative formation problem is a basic problem of collaborative control. When all the states of the agent and its neighboring agents are known, state feedback is a classic method for a multi-agent system to achieve formation control. However, in practical applications, it is unrealistic to obtain all the state information of the agent due to the limitations of the system itself or the sensor. One way to solve this problem is to use the limited information measured by the sensor to design a state observer to reconstruct the real state, and then use the reconstructed state to design a formation controller to ensure the realization of the formation task.

[0003] At present, the state estimation method of multi-agent system is mainly distributed state estimation method. For example, the classic distributed Kalman consensus filtering algorithm proposed in "Distributed Kalman Filtering for Sensor Networks" integrates multi-agent consistency theory and Kalman filtering. It only requires local measurement information of the node. As the number of iterations increases, the state estimation values ​​of all sensor nodes in the network can tend to be consistent.

[0004] Alternatively, Yuezu Lv, Zhongkui Li, and Zhisheng Duan proposed in "Minimal-OrderSpecified-Time Unknown Input Observers" to design a distributed observer based on observer technology to achieve consistency estimation while only using local measurement information.

[0005] It can be seen that the implementation of existing state estimation algorithms depends on the accuracy of local measurement information, which means that existing state estimation technology cannot be implemented when there is sensor measurement failure. Summary of the invention

[0006] To solve the above problems, the present invention provides a multi-agent collaborative formation control method based on mutual estimation of unknown input states. It considers using distributed state estimation technology to solve the problem that the complete state cannot be obtained in formation control, and further proposes a novel distributed state mutual estimation algorithm to solve the problem that the existing state estimation algorithm fails to estimate when the sensor measurement output fails, thereby ensuring the realization of the formation task when the sensor measurement output fails.

[0007] To achieve the above object, the present invention provides a multi-agent cooperative formation control method based on mutual estimation of unknown input states, comprising the following steps: S1. Construct a state mutual estimation mechanism model of intelligent agents based on multi-agent system; S2. Construct the communication topology of the multi-agent system based on graph theory knowledge; S3, combining the state mutual estimation mechanism model of the intelligent agent constructed in step S1 and the communication topology structure of the multi-agent system constructed in step S2, constructing a distributed state mutual estimator for each intelligent agent, and determining a gain matrix in the distributed state mutual estimator; S4. According to the estimated values ​​of all states of each agent, a formation control strategy based on consistency theory is constructed for each agent; S5. The intelligent agent sensor measurement fails, and the process returns to step S3 to redetermine the gain matrix in the distributed state mutual estimator.

[0008] Preferably, step S1 specifically includes the following steps: S11. Establish the state dynamics model of multi-agent system: (1) In the formula, For intelligent agents The derivative of the state, For intelligent agents of The actual state of the For intelligent agents of dimensional bounded control input, is the total number of agents in the multi-agent system, and are the state matrix and input matrix respectively; S12. Based on the state dynamics model, a state mutual estimation mechanism model is constructed in combination with the measurement output of the sensor.

[0009] Preferably, step S12 specifically includes the following steps: Remember all the states of the multi-agent system , Respectively represent The state of each agent, the measurement output of the sensor on each agent is used to measure its own state information, as well as the state information of other agents within the measurement range of the sensor. The state mutual estimation mechanism model expression of each agent is as follows: (2) In the formula, is the derivative of the state; for Dimensional sensor measurement output; is the state of all agents in the multi-agent system; Represented by the state matrix The matrix of evolution, , represents the Kronecker product operation, The dimension is The identity matrix of In multi-agent systems Control input for each agent; Represented by the input matrix The matrix of evolution, and ; for The output matrix of System Matrix The following rank conditions are satisfied: , (3) In the formula, represents the rank of the system matrix, The dimension is The identity matrix of is the complex frequency range of the multi-agent system, In a multi-agent system The sensor output matrix of each agent, and , Respectively represent The output matrix of the agent, represents the dimension of the control input, represents the total dimension of all agent measurement outputs, and .

[0010] Preferably, in step S2, a communication topology graph model is used to describe the communication relationship of the multi-agent system: Depend on The communication topology of a multi-agent system consisting of agents is shown in Figure Description, where represents the set of agent nodes, and , They represent the agent’s nodes; represents the set of agent edges, and ; represents the adjacency matrix, and ; Represents the adjacency matrix Line Column elements; If the agent Received Agent , then determine the agent For intelligent agents Neighbors of ,and ;otherwise , so the intelligent agent The neighbors of Representation; Agent The number of neighbors ;use represents the Laplacian matrix of the multi-agent system, represents the first Line Column elements; calculate: (4) In the formula, is the in-degree matrix, and , For the The elements of the in-degree matrix.

[0011] Preferably, the communication topology diagram of the multi-agent system constructed in step S2 meets the following requirements: The communication topology of a multi-agent system is a directed graph, and there is a directed communication path between any two agents: and Agent There are multiple agents Make the communication link .

[0012] Preferably, the distributed state mutual estimator described in step S3 includes a distributed output tracker and a distributed unknown input observer.

[0013] Preferably, step S3 specifically includes the following steps: S31. Design the following distributed output tracking estimator for each agent: (5) In the formula, For the Agent-to-agent system Agent output The estimate, , Respectively represent The output of an agent, The dimension is ,in , Indicates The dimension of the output measured by each agent; For the Agent pair All states of an agent The estimate, The dimension is ; represents an auxiliary matrix, and , Respectively represent the auxiliary matrix Diagonal elements; is the sliding mode nonlinear term; S32. Construct a distributed unknown input observer for each agent: (6) In the formula, for Auxiliary variables for unknown inputs; express The derivative of represents a diagonal positive definite matrix, and ; Represented by the system matrix and The matrix of evolution, and ; In order to make Hurwitz stable gain matrix; Representation and Matrix Identity matrices of the same dimensions; Represents the state of all agents The asymptotic convergence value of ; S33. Determine the gain constant The value range of is: is a positive constant gain that satisfies the following conditions: (7) In the formula, represents a constant calculated by formula (7); , Respectively represent the maximum eigenvalue of the gain matrix and the minimum eigenvalue of the gain matrix; represents the maximum singular value of the gain matrix; Representation Matrix The minimum eigenvalue of ; In order to make Positive definite diagonally positive definite matrices; represents a constant, and ; is a positive definite matrix, satisfying , is a positive definite matrix; The output of all agents The asymptotic convergence value of .

[0014] Preferably, the sliding mode nonlinear term described in step S31 The calculation formula is as follows: (8) In the formula, is a positive constant that satisfies , is the upper bound of the control input; express dimensional identity matrix; represents a vector, and , , Respectively represent The auxiliary matrix of the evolution of the identity matrix related to the communication relationship of the agents and the measurement output dimension, In order to make Positive definite diagonally positive definite matrices; for The minimum eigenvalue of ; is the Euclidean norm of the matrix or vector.

[0015] Preferably, step S4 specifically includes the following steps: S41, the overall state reconstructed by the state mutual estimator of each agent , design the following local formation control strategy for each agent : (9) In the formula, Indicates The agent's own state estimates; Indicates The agent's own state estimates; represents constant gain; represents the feedback gain matrix; Indicates The desired position of each agent; Indicates The desired position of the agent, and the formation of the agent satisfies ; S42. Determine the constant gain in the formation control strategy and the feedback gain matrix The value of: Take constant gain , the feedback gain matrix ,in In order to make A positive definite matrix is ​​formed and maintained to form a constant formation configuration.

[0016] Preferably, step S5 specifically includes the following sub-steps: S51, assuming When the output measurement of an intelligent sensor fails, the output matrix after failure is recorded. The expression is as follows: (10) In the formula, Respectively represent The output matrix of the agent, where The output matrices of all agents are set to zero; If the system matrix after failure The following rank conditions are satisfied: , (11) Then execute step S52; S52. After detecting that the measurement output of an agent has failed, keep the form of the distributed state mutual estimator unchanged, redetermine the constant gains and gain matrices in the distributed output tracker and the distributed unknown input observer according to steps S31-S33, and estimate the states of all agents based on the redetermined constant gains and gain matrices.

[0017] The present invention has the following beneficial effects: 1. Construct a state mutual estimator based on an unknown input observer for each agent to ensure that each agent can estimate all states of the agent system, thereby solving the problem of estimation failure of existing state estimation algorithms when the measurement output of the agent sensor fails; 2. The formation control algorithm constructed for each agent is designed only based on its own mutual state estimation value, which effectively avoids the information interaction between multiple agents in formation control and increases the robustness of the formation control algorithm to a certain extent.

[0018] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a flow chart of a multi-agent cooperative formation control method based on mutual estimation of unknown input states of the present invention; Figure 2 is a communication topology diagram of an embodiment of the present invention; Figure 3is a difference diagram of the position states of the remaining agents in the embodiment of the present invention relative to the first dimension of agent 1; Figure 4 is a difference diagram of the second dimension position states of the remaining agents relative to the No. 1 agent in the embodiment of the present invention; Figure 5 1 is a measurement output diagram of the intelligent agent sensor of an embodiment of the present invention, wherein (a) is the measurement output diagram of the intelligent agent 1 sensor; (b) is the measurement output diagram of the intelligent agent 2 sensor; (c) is the measurement output diagram of the intelligent agent 3 sensor; (d) is the measurement output diagram of the intelligent agent 4 sensor; (e) is the measurement output diagram of the intelligent agent 5 sensor; and (f) is the measurement output diagram of the intelligent agent 6 sensor. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical scheme and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention are further described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions.

[0021] It should be noted that the terms "include", "have" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or server comprising a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products or devices.

[0022] Like reference numerals and letters denote similar items in the following drawings, and thus, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0023] like Figure 1 As shown, the multi-agent cooperative formation control method based on mutual estimation of unknown input states includes the following steps: S1. Construct a state mutual estimation mechanism model of intelligent agents based on multi-agent system; Step S1 specifically includes the following steps: S11. Establish the state dynamics model of multi-agent system: (1) In the formula, For intelligent agents The derivative of the state, For intelligent agents of The actual state of the dimension, For intelligent agents of dimensional bounded control input, is the total number of agents in the multi-agent system, and are the state matrix and input matrix respectively; S12. Based on the state dynamics model, a state mutual estimation mechanism model is constructed in combination with the measurement output of the sensor; Step S12 specifically includes the following steps: Remember all the states of the multi-agent system , Respectively represent The state of each agent, the measurement output of the sensor on each agent is used to measure its own state information, as well as the state information of other agents within the measurement range of the sensor. The state mutual estimation mechanism model expression of each agent is as follows: (2) In the formula, is the derivative of the state; for Dimensional sensor measurement output; is the state of all agents in the multi-agent system; Represented by the state matrix The matrix of evolution, , represents the Kronecker product operation, The dimension is The identity matrix of In multi-agent systems Control input for each agent; Represented by the input matrix The matrix of evolution, and ; for The output matrix of System Matrix The following rank conditions are satisfied: , (3) In the formula, represents the rank of the system matrix, The dimension is The identity matrix of is the complex frequency range of the multi-agent system, In a multi-agent system The sensor output matrix of each agent, and , Respectively represent The output matrix of the agent, represents the dimension of the control input, represents the total dimension of all agent measurement outputs, and .

[0024] S2. Construct the communication topology of the multi-agent system based on graph theory knowledge; In step S2, the communication relationship of the multi-agent system is described using the communication topology graph model: Depend on The communication topology of a multi-agent system consisting of agents is shown in Figure Description, where represents the set of agent nodes, and , They represent the agent’s nodes; represents the set of agent edges, and ; represents the adjacency matrix, and ; Represents the adjacency matrix Line Column elements; If the agent Received Agent , then determine the agent For intelligent agents Neighbors of ,and ;otherwise , so the intelligent agent The neighbors of Representation; Agent The number of neighbors ;use represents the Laplacian matrix of the multi-agent system, represents the first Line Column elements; calculate: (4) In the formula, is the in-degree matrix, and , For the The elements of the in-degree matrix.

[0025] The communication topology of the multi-agent system constructed in step S2 meets the following requirements: The communication topology of a multi-agent system is a directed graph, and there is a directed communication path between any two agents: and Agent There are multiple agents Make the communication link That is, the communication topology constructed is a directed strongly connected graph (there is a directed communication path between any two intelligent agents, that is, the intelligent agents and Agent There are some intelligent agents Make the communication link ).

[0026] S3, combining the state mutual estimation mechanism model of the intelligent agent constructed in step S1 and the communication topology structure of the multi-agent system constructed in step S2, constructing a distributed state mutual estimator for each intelligent agent, and determining a gain matrix in the distributed state mutual estimator; The distributed state mutual estimator described in step S3 includes a distributed output tracker and a distributed unknown input observer.

[0027] Step S3 specifically includes the following steps: S31. Design the following distributed output tracking estimator for each agent: (5) In the formula, For the Agent-to-agent system Agent output The estimate, , Respectively represent The output of an agent, The dimension is ,in , Indicates The dimension of the output measured by each agent; For the Agent pair All states of an agent The estimate, The dimension is ; represents an auxiliary matrix, and , Respectively represent the auxiliary matrix Diagonal elements; is the sliding mode nonlinear term; The sliding mode nonlinear term described in step S31 The calculation formula is as follows: (8) In the formula, is a positive constant that satisfies , is the upper bound of the control input, express dimensional identity matrix; represents a vector, and , , Respectively represent The auxiliary matrix of the evolution of the identity matrix related to the communication relationship of the agents and the measurement output dimension, In order to make Positive definite diagonally positive definite matrices; for The minimum eigenvalue of ; is the Euclidean norm of the matrix or vector.

[0028] S32. Construct a distributed unknown input observer for each agent: (6) In the formula, for Auxiliary variables for unknown inputs; express The derivative of represents a diagonal positive definite matrix, and ; Represented by the system matrix and The matrix of evolution, and ; In order to make Hurwitz stable gain matrix; Representation and Matrix Identity matrices of the same dimensions; Represents the state of all agents The asymptotic convergence value of ; S33. Determine the gain constant The value range of is: is a positive constant gain that satisfies the following conditions: (7) In the formula, represents a constant calculated by formula (7); , Respectively represent the maximum eigenvalue of the gain matrix and the minimum eigenvalue of the gain matrix; represents the maximum singular value of the gain matrix; Representation Matrix The minimum eigenvalue of ; In order to make Positive definite diagonally positive definite matrices; represents a constant, and ; is a positive definite matrix, satisfying , is a positive definite matrix; The output of all agents The asymptotic convergence value of .

[0029] S4. According to the estimated values ​​of all states of each agent, a formation control strategy based on consistency theory is constructed for each agent; Step S4 specifically includes the following steps: S41, the overall state reconstructed by the state mutual estimator of each agent , design the following local formation control strategy for each agent : (9) In the formula, Indicates The agent's own state estimates; Indicates The agent's own state estimates; represents constant gain; represents the feedback gain matrix; Indicates The desired position of each agent; Indicates The desired position of the agent, and the formation of the agent satisfies ; S42. Determine the constant gain in the formation control strategy and the feedback gain matrix The value of: Take constant gain , the feedback gain matrix ,in In order to make A positive definite matrix is ​​formed and maintained to form a constant formation configuration.

[0030] S5. The intelligent agent sensor measurement fails, and the process returns to step S3 to redetermine the gain matrix in the distributed state mutual estimator.

[0031] Step S5 specifically includes the following sub-steps: S51, assuming When the output measurement of an intelligent sensor fails, the output matrix after failure is recorded. The expression is as follows: (10) In the formula, Respectively represent The output matrix of the agent, where The output matrices of all agents are set to zero; If the system matrix after failure The following rank conditions are satisfied: , (11) Then execute step S52; otherwise, too many sensors fail, and the effective measurement output information is too little, and the state of the intelligent body cannot be estimated using the limited information; S52. After detecting that the measurement output of an agent has failed, keep the form of the distributed state mutual estimator unchanged, redetermine the constant gains and gain matrices in the distributed output tracker and the distributed unknown input observer according to steps S31-S33, and estimate the states of all agents based on the redetermined constant gains and gain matrices.

[0032] Example: This embodiment is a multi-agent system composed of 6 agents.

[0033] Step 1: A multi-agent system consisting of 6 agents, the state dynamics of each agent is as follows: ;

[0034] The sensor measurement output equations of each agent are as follows: ; ; ; ; ; ;

[0035] In this embodiment, the first-dimensional state of each agent represents 1-dimensional position information, and the second-dimensional state represents 1-dimensional speed information; the formation configuration of the multi-agent system is set as: , , , , , ; Select the measurement output of the fifth agent in When it fails, When the system detects a failure, the measured output of the fifth agent is When is 0; Step 2: Build Figure 2 The communication topology diagram of the multi-agent system composed of 6 agents is shown; Step 3: The relevant parameters of the distributed state mutual estimator are selected as follows: , ; ;

[0036] Step 4: The relevant parameters in the formation control strategy are selected as follows: , ; Step 5: When the sensor measurement output of the fifth agent fails, the parameters are redesigned according to step 3. The parameters of the distributed state mutual estimation after failure are selected as follows: , ; ;

[0037] In this embodiment, there are 48 trajectories of the output tracking error of the intelligent agent, and the output tracking error converges to zero asymptotically when the sensor measurement output fails; there are 72 intelligent agent distributed state mutual estimation errors, and the state mutual estimation error converges to zero when the sensor fails ( ) error increases, but after parameter redesign ( ) The estimation error converges to zero quickly, realizing distributed state mutual estimation; like Figure 3-Figure 5 As shown, the fifth agent measures the output in After that, it is 0, and the formation configuration is formed and maintained. The above verifies the effectiveness of the multi-agent collaborative formation control method based on mutual estimation of unknown input states given in the present invention.

[0038] Therefore, the present invention adopts the above-mentioned multi-agent collaborative formation control method based on mutual estimation of unknown input states, which can accurately realize mutual estimation of states in the event of failure of measurement output of intelligent body sensors, thereby providing guarantee for the completion of the multi-agent system formation task.

[0039] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. Multi-agent collaborative formation control method based on mutual estimation of unknown input states, Features: The following steps are involved: S1. Construct a state mutual estimation mechanism model of intelligent agents based on multi-agent system; S2. Construct the communication topology of the multi-agent system based on graph theory knowledge; S3, combining the state mutual estimation mechanism model of the intelligent agent constructed in step S1 and the communication topology structure of the multi-agent system constructed in step S2, constructing a distributed state mutual estimator for each intelligent agent, and determining a gain matrix in the distributed state mutual estimator; S4. According to the estimated values ​​of all states of each agent, a formation control strategy based on consistency theory is constructed for each agent; S5. The intelligent agent sensor measurement fails, and the process returns to step S3 to redetermine the gain matrix in the distributed state mutual estimator.

2. According to the multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 1, Features: Step S1 specifically includes the following steps: S11. Establish the state dynamics model of multi-agent system: （1） In the formula, For intelligent agents The derivative of the state, For intelligent agents of The actual state of the dimension, For intelligent agents of dimensional bounded control input, is the total number of agents in the multi-agent system, and are the state matrix and input matrix respectively; S12. Based on the state dynamics model, a state mutual estimation mechanism model is constructed in combination with the measurement output of the sensor.

3. The multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 2, Features: Step S12 specifically includes the following steps: Remember all the states of the multi-agent system , Respectively represent The state of each agent, the measurement output of the sensor on each agent is used to measure its own state information, as well as the state information of other agents within the measurement range of the sensor. The state mutual estimation mechanism model expression of each agent is as follows: （2） In the formula, is the derivative of the state; for Dimensional sensor measurement output; is the state of all agents in the multi-agent system; Represented by the state matrix The matrix of evolution, , represents the Kronecker product operation, The dimension is The identity matrix of In multi-agent systems Control input for each agent; Represented by the input matrix The matrix of evolution, and ; for The output matrix of System Matrix The following rank conditions are satisfied: ， （3） In the formula, represents the rank of the system matrix, The dimension is The identity matrix of is the complex frequency range of the multi-agent system, In a multi-agent system The sensor output matrix of each agent is , Respectively represent The output matrix of the agent, represents the dimension of the control input, represents the total dimension of all agent measurement outputs, and .

4. The multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 3, Features: In step S2, the communication relationship of the multi-agent system is described using the communication topology graph model: Depend on The communication topology of a multi-agent system consisting of agents is shown in Figure Description, where represents the set of agent nodes, and , They represent the agent’s nodes; represents the set of agent edges, and ; represents the adjacency matrix, and ; Represents the adjacency matrix Line Column elements; If the agent Received Agent , then determine the agent For intelligent agents 's neighbors, then there are ,and ;otherwise , so the intelligent agent The neighbors of Representation; Agent The number of neighbors ;use represents the Laplacian matrix of the multi-agent system, represents the first Line Column elements; calculate: （4） In the formula, is the in-degree matrix, and , For the The elements of the in-degree matrix.

5. The multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 4, Features: The communication topology of the multi-agent system constructed in step S2 meets the following requirements: The communication topology of a multi-agent system is a directed graph, and there is a directed communication path between any two agents: and Agent There are multiple agents Make the communication link .

6. The multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 5, Features: The distributed state mutual estimator described in step S3 includes a distributed output tracker and a distributed unknown input observer.

7. The multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 6, Features: Step S3 specifically includes the following steps: S31. Design the following distributed output tracking estimator for each agent: （5） In the formula, For the Agent-to-agent system Agent output The estimate, , Respectively represent The output of an agent, The dimension is ,in , Indicates The dimension of the output measured by each agent; For the Agent pair All states of an agent The estimate, The dimension is ; represents an auxiliary matrix, and , Respectively represent the auxiliary matrix Diagonal elements; is the sliding mode nonlinear term; S32. Construct a distributed unknown input observer for each agent: （6） In the formula, for Auxiliary variables for unknown inputs; express The derivative of represents a diagonal positive definite matrix, and ; Represented by the system matrix and The matrix of evolution, and ; In order to make Hurwitz stable gain matrix; Representation and Matrix Identity matrices of the same dimensions; Represents the state of all agents The asymptotic convergence value of ; S33. Determine the gain constant The value range of is: is a positive constant gain that satisfies the following conditions: （7） In the formula, represents a constant calculated by formula (7); , Respectively represent the maximum eigenvalue of the gain matrix and the minimum eigenvalue of the gain matrix; represents the maximum singular value of the gain matrix; Representation Matrix The minimum eigenvalue of ; In order to make Positive definite diagonally positive definite matrices; represents a constant, and ; is a positive definite matrix, satisfying , is a positive definite matrix; The output of all agents The asymptotic convergence value of .

8. The multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 7, Features: The sliding mode nonlinear term described in step S31 The calculation formula is as follows: （8） In the formula, is a positive constant that satisfies , is the upper bound of the control input; express dimensional identity matrix; represents a vector, and , , Respectively represent The auxiliary matrix of the communication relationship between the agents and the evolution of the identity matrix, In order to make Positive definite diagonally positive definite matrices; for The minimum eigenvalue of ; is the Euclidean norm of the matrix or vector.

9. The multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 8, Features: Step S4 The specific steps include: S41, the overall state reconstructed by the state mutual estimator of each agent , design the following local formation control strategy for each agent : （9） In the formula, Indicates The agent's own state estimates; Indicates The agent's own state estimates; represents constant gain; represents the feedback gain matrix; Indicates The desired position of each agent; Indicates The desired position of the agent, and the formation of the agent satisfies ; S42. Determine the constant gain in the formation control strategy and the feedback gain matrix The value of: Take constant gain , the feedback gain matrix ,in In order to make A positive definite matrix is ​​formed and maintained to form a constant formation configuration.

10. The multi-agent cooperative formation control method based on mutual estimation of unknown input states according to claim 9, Features: Step S5 specifically includes the following sub-steps: S51, assuming When the output measurement of an intelligent sensor fails, the output matrix after failure is recorded. The expression is as follows: （10） In the formula, Respectively represent The output matrix of the agent, where The output matrices of all agents are set to zero; If the system matrix after failure The following rank conditions are satisfied: ， （11） Then execute step S52; S52. After detecting that the measurement output of an agent has failed, keep the form of the distributed state mutual estimator unchanged, redetermine the constant gains and gain matrices in the distributed output tracker and the distributed unknown input observer according to steps S31-S33, and estimate the states of all agents based on the redetermined constant gains and gain matrices.

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