Multi-agent state estimation and formation control method based on adaptive parameter reduction

Abstract

The present invention discloses a multi-agent state estimation and formation control method based on adaptive parameter reduction, which belongs to the field of intelligent agent formation control and includes the following steps: S1, constructing a dynamic model and a sensor model; S2, constructing a directed strongly connected communication topology; S3, designing a distributed formation controller for the multi-agent system; S4, designing a multi-agent output tracking estimator and a distributed state observer based on adaptive parameter reduction to complete the distributed adaptive state estimation of the multi-agent system; S5, when there is an intelligent agent sensor failure in the multi-agent system, redesigning the parameters described in step S3. The present invention adopts the above-mentioned multi-agent state estimation and formation control method based on adaptive parameter reduction, so that in a multi-agent system, when a certain sensor fails, the state estimation of the intelligent agent will not fail and diverge, thereby ensuring the realization of formation control of the multi-agent system.

Description

Technical Field

[0001] The present invention relates to the field of intelligent agent formation control, and in particular to a multi-agent state estimation and formation control method based on adaptive parameter reduction. Background Art

[0002] Multi-agent systems can complete many different types of collaborative tasks, among which consistency control is the basis of different tasks of multi-agent systems, and formation tasks are more valuable tasks of multi-agent systems in practical applications. The formation control of multi-agent systems can be divided into state feedback-based formation control algorithms and output feedback-based formation control algorithms according to the different physical quantities used. Among them, state feedback-based formation control is more common, but considering that the state of the agent is difficult to obtain directly, this method is usually difficult to use directly; in contrast, the output feedback-based formation control algorithm disclosed by Liu T and Jiang ZP in "Distributed output-feedback control of nonlinear multi-agent systems" uses the sensor output of each agent to design a suitable protocol to achieve formation control, which is easier to implement. However, when the output of the agent sensor of the multi-agent system is in heterogeneous form, the formation control algorithm based on output feedback is not applicable due to factors such as different output dimensions. Therefore, for multi-agent systems whose states are not directly available and whose output forms are heterogeneous, formation control becomes a more complex problem.

[0003] Although the state of the agent cannot be used directly for feedback control, Wang Y, Yuan Y, and Liu J published in "Finite-time leader-following output consensus for multi-agent systems via extended state observer" that the state of the agent is estimated by using the output of the agent's sensor, and the state estimate is used for feedback control of the system. When the state estimate converges asymptotically to the true state, its input is equivalent to the control using the system state feedback, so that the system can achieve the desired task. It can be seen that this method requires the design of a suitable state observer for the multi-agent system. Due to the large number of nodes in the system, a distributed approach is required for state estimation. When performing formation control tasks, the noise and external disturbances of the multi-agent system are not considered. The sensor output is used to design an easy-to-implement distributed state observer so that the agent can complete the state estimation, and the state estimation is further used to design the formation control protocol.

[0004] When using the output information of the sensor to estimate the state of the intelligent agent, once the sensor fails, it will cause a large error in the state estimation of the intelligent agent, making it impossible to complete the collaborative task of the system. Summary of the invention

[0005] To solve the above problems, the present invention provides a multi-agent state estimation and formation control method based on adaptive parameter reduction. Through the collaborative mutual perception of the multi-agent system, the output information of each agent is related to all agents in the system, so that the agent can estimate the state of other agents. When one or some of the sensors of the agents in the multi-agent system fail, other agent nodes can still estimate their states, so that the estimation error is too large to cause the failure of the collaborative task. The method has broad practical application value.

[0006] To achieve the above object, the present invention provides a multi-agent state estimation and formation control method based on adaptive parameter reduction, comprising the following steps:

[0007] S1. Based on the differential equation A multi-agent system consisting of 3 agents is used to build dynamics model and sensor model.

[0008] S2. Construct a directed strongly connected communication topology structure according to the requirements of the adaptive state estimation on the communication topology graph;

[0009] S3. Design a distributed formation controller for the multi-agent system and determine the parameters of the distributed formation controller;

[0010] S4. Under the directed strongly connected communication topology, design a multi-agent output tracking estimator and distributed state observer based on adaptive parameter reduction to complete the distributed adaptive state estimation of the multi-agent system;

[0011] S5. When there is an agent sensor failure in the multi-agent system, the parameters described in step S3 are redesigned.

[0012] Preferably, step S1 specifically includes the following steps:

[0013] S11. Construct the dynamic model of each agent in the multi-agent system:

[0014] (1)

[0015] In the formula, Indicates The derivative of the state of each agent; For the The state vector of each agent, and , The dimension is A vector collection of ; For the The control input of an agent, and , The dimension is A vector collection of ; is a known state matrix, and , The dimension is The matrix collection of ; is a known input matrix, and , The dimension is The matrix collection of ;

[0016] S12. Construct the sensor model of each agent in the multi-agent system:

[0017] (2)

[0018] In the formula, For the The sensors of each agent measure the output, and , The dimension is A vector collection of ; For the The output matrix of the agents, and , The dimension is The matrix collection of ; is the state of all agents in the multi-agent system, and , Respectively represent the The transpose of the agent state vector;

[0019] S13. Determine the requirements for the agent's dynamic parameters:

[0020] First, remember , For the system The sensor output of each agent, Respectively represent the The transpose of the sensor output of each agent, The dimension is A vector collection of ; , For the system The sensor output matrix of each agent is Respectively represent The transpose of the output matrix of the sensors of the agents; ;

[0021] Then determine the overall state equation and output equation of the multi-agent system:

[0022] (3)

[0023] In the formula, The dimension is The identity matrix of In multi-agent systems Control input for each agent; represents the Kronecker product;

[0024] And make the multi-agent system meet

[0025]

[0026] Where rank represents the rank of the matrix.

[0027] Preferably, in step S2, using a directed graph express The directed strongly connected communication topology of agents, where represents the set of agent nodes, and , They represent the agent’s nodes; represents the set of agent edges, and ; Among them, there is a directed path between any two nodes in a directed graph.

[0028] Preferably, step S3 specifically includes the following steps:

[0029] S31. Determine the formation position of each agent in the multi-agent system:

[0030] Setting the formation configuration of a multi-agent system ,in represents the overall formation configuration of the system, Respectively represent the The desired position of each agent; and set Representing an Agent and Agent The constant relative formation displacement between , , Indicates The desired position of each agent; Indicates The desired position of the agent; at the same time, the formation of the agent satisfies ;

[0031] S32. Design a distributed formation controller for multi-agent systems based on state estimation:

[0032] (4)

[0033] In the formula, represents constant gain; represents the feedback gain matrix; Indicates The agent's own state estimates; It is The agent is Agent state estimates; ,in, Indicates An agent estimates the state of all agents in a multi-agent system; Respectively represent The agent is State estimation of each agent;

[0034] S33. Determine the parameters of the distributed formation controller when it converges as the parameters of the distributed formation controller.

[0035] Preferably, in step S33, when the state estimation of the multi-agent system is achieved, formula (4) is transformed into:

[0036] (5)

[0037] Substituting into the system's dynamic equation (1), we get: When stable, the multi-agent system can achieve formation control, and the constant gain ; and the feedback gain matrix ,in Express satisfaction is a positive definite matrix.

[0038] Preferably, step S4 specifically includes the following steps:

[0039] S41, substituting the distributed formation control protocol into the dynamics model to obtain a closed-loop dynamics equation;

[0040] S42. Design an output tracking estimator based on adaptive parameter reduction;

[0041] S43. Design a distributed state observer based on the closed-loop dynamic equations of the multi-agent system;

[0042] S44. Analyze the convergence conditions of the distributed state estimator based on adaptive parameter reduction, and determine the parameters of the distributed state estimator.

[0043] Preferably, the closed-loop dynamic equation in step S41 is expressed as follows:

[0044] (6)

[0045] in, , , ;

[0046] In the formula, represents the state estimates of all agents in the system, and , Respectively represent State estimation of each agent; The dimension is All elements are A vector of Representation Matrix No. OK, Represents the Laplacian matrix corresponding to the fully connected graph;

[0047] The expression of the output tracking estimator based on adaptive parameter reduction in step S42 is as follows:

[0048] (7)

[0049] In the formula, Indicates The agent is Estimates of the outputs of the agents; Indicates The initial value of each agent is a positive adaptive parameter; represents the adaptive parameter auxiliary variable; The adjacency matrix corresponding to the communication topology is represented by Line Column elements; Indicates The agent is Estimates of the outputs of the agents; Represents the adjacency matrix Line Column elements; Indicates The sensor output of each agent; Indicates The sensor output matrix of each agent;

[0050] The distributed state observer expression in step S43 is as follows:

[0051] (8)

[0052] In the formula, Indicates The derivative vector of the agent state estimate; Indicates The output estimates of the agents, and , Respectively represent The agent is Estimates of the outputs of the agents; represents the gain matrix of the distributed state observer.

[0053] Preferably, step S44 specifically includes the following steps:

[0054] S441, Setting express The average of the state estimates of the agents, represents the error between the estimated mean and the true value of the agent state, represents the error between the estimated mean and the estimated state of each agent, represents the consistency error of the agent's output estimate;

[0055] When the state estimation error , and output estimation error When all converge to zero, the multi-agent system realizes state mutual estimation, and then realizes formation control, and obtains the gain matrix in the distributed observer ,in represents a positive definite gain matrix, which is determined by the positive definite solution of the following linear matrix inequality:

[0056] (9)

[0057] In the formula, and are positive definite matrices respectively.

[0058] Preferably, step S5 specifically includes the following steps:

[0059] S51. When a sensor of an agent in a multi-agent system fails, suppose the If a sensor of an intelligent agent fails, the output of the failed intelligent agent , so the output matrix of the faulty agent is , at this time, the overall output matrix of the multi-agent system is for:

[0060] (10)

[0061] In the formula, Respectively represent The output matrix of the agent, where The output matrices of all agents are set to zero;

[0062] S52, Verification Whether the observation conditions described in step S13 are met, if so, and when the intelligent body sensor fails, the linear matrix inequality in step S44 is re-solved to obtain the updated gain matrix of the distributed observer in step S43 , proving that the multi-agent system can detect sensor failures and reconstruct the distributed observer within 1s.

[0063] The present invention has the following beneficial effects:

[0064] 1. Each agent in the multi-agent system can estimate the output and state of all agents in the multi-agent system by using only the output information of itself and its neighboring nodes;

[0065] 2. Consider the situation of sensor failure. That is, when the sensor fails, the distributed state observer is recalculated to avoid the divergence of state estimation and the failure of collaborative tasks.

[0066] 3. The adopted formation control algorithm is based on state estimation. Compared with the existing formation control algorithm based on state feedback, it only uses the state estimation of the intelligent agent itself without the need for information interaction, which ensures the security of the intelligent agent state to a certain extent. It only requires fully distributed information and does not require any global information, which is convenient for collection.

[0067] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A flowchart of a multi-agent state estimation and formation control method based on adaptive parameter reduction of the present invention;

[0069] Figure 2 It is a schematic diagram of the communication topology of the multi-agent system in the simulation experiment of the present invention;

[0070] Figure 3 is a schematic diagram of the output estimation errors of all intelligent agents in the simulation experiment of the present invention;

[0071] Figure 4 is a schematic diagram of state estimation errors of all agents in the simulation experiment of the present invention;

[0072] Figure 5 is a schematic diagram of the adaptive gains of all intelligent agents in the simulation experiment of the present invention;

[0073] Figure 6 It is a schematic diagram of the displacement difference between other intelligent agents and the No. 1 intelligent agent in the simulation experiment of the present invention;

[0074] Figure 7 It is a schematic diagram of the speed difference between other intelligent agents and the No. 1 intelligent agent in the simulation experiment of the present invention;

[0075] Figure 8 It is a schematic diagram of the real state of all intelligent agents in the simulation experiment of the present invention;

[0076] Fig. 9 It is a schematic diagram of the actual output of all intelligent agents in the simulation experiment of the present invention. DETAILED DESCRIPTION

[0077] 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.

[0078] 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.

[0079] 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.

[0080] like Figure 1 As shown, a multi-agent state estimation and formation control method based on adaptive parameter reduction includes the following steps:

[0081] S1. Based on the differential equation A multi-agent system consisting of 3 agents is used to build dynamics model and sensor model.

[0082] Step S1 specifically includes the following steps:

[0083] S11. Construct the dynamic model of each agent in the multi-agent system:

[0084] (1)

[0085] In the formula, Indicates The derivative of the state of each agent; For the The state vector of each agent, and , The dimension is A vector collection of ; For the The control input of an agent, and , The dimension is A vector collection of ; is a known state matrix, and , The dimension is The matrix collection of ; is a known input matrix, and , The dimension is The matrix collection of ;

[0086] S12. Construct the sensor model of each agent in the multi-agent system:

[0087] (2)

[0088] In the formula, For the The sensors of each agent measure the output, and , The dimension is A vector collection of ; For the The output matrix of the agents, and , The dimension is The matrix collection of ; is the state of all agents in the multi-agent system, and , Respectively represent the The transpose of the agent state vector;

[0089] S13. Requirements for determining the dynamic parameters of the agent:

[0090] First, remember , For the system The sensor output of each agent, Respectively represent the The transpose of the sensor output of each agent, The dimension is A vector collection of ; , For the system The sensor output matrix of each agent is Respectively represent The transpose of the output matrix of the sensors of the agents; ;

[0091] Then determine the overall state equation and output equation of the multi-agent system:

[0092] (3)

[0093] In the formula, The dimension is The identity matrix of In multi-agent systems Control input for each agent; represents the Kronecker product;

[0094] And make the multi-agent system meet

[0095] ;

[0096] Where rank represents the rank of the matrix.

[0097] S2. Construct a directed strongly connected communication topology structure according to the requirements of the adaptive state estimation on the communication topology graph;

[0098] In step S2, using the directed graph express The directed strongly connected communication topology of agents, where represents the set of agent nodes, and , They represent the agent’s nodes; represents the set of agent edges, and ; Among them, there is a directed path between any two nodes in a directed graph.

[0099] In a directed graph, edges Represents an agent node Can obtain intelligent agent The information transmitted is called yes Neighbor nodes. For nodes in a directed graph and , if exists , , …, Such continuous edges are said to exist as directed paths between the two nodes.

[0100] S3. Design a distributed formation controller for the multi-agent system and determine the parameters of the distributed formation controller;

[0101] Step S3 specifically includes the following steps:

[0102] S31. Determine the formation position of each agent in the multi-agent system:

[0103] Setting the formation configuration of a multi-agent system ,in represents the overall formation configuration of the system, Respectively represent the The desired position of the agent; and set Representing an Agent and Agent The constant relative formation displacement between , , Indicates The desired position of each agent; Indicates The desired position of the agent; at the same time, the formation of the agent satisfies ;

[0104] S32. Design a distributed formation controller for multi-agent systems based on state estimation:

[0105] (4)

[0106] In the formula, represents constant gain; represents the feedback gain matrix; Indicates The agent's own state estimates; It is The agent is Agent state estimates; ,in, Indicates An agent estimates the state of all agents in a multi-agent system; Respectively represent The agent is State estimation of each agent;

[0107] S33. Determine the parameters of the distributed formation controller when it converges as the parameters of the distributed formation controller.

[0108] In step S33, when the state estimation of the multi-agent system is achieved, formula (4) is transformed into:

[0109] (5)

[0110] Substituting into the system's dynamic equation (1), we get: When stable, the multi-agent system can achieve formation control, and the constant gain ; and the feedback gain matrix ,in Express satisfaction is a positive definite matrix.

[0111] S4. Under the directed strongly connected communication topology, design a multi-agent output tracking estimator and distributed state observer based on adaptive parameter reduction to complete the distributed adaptive state estimation of the multi-agent system;

[0112] Step S4 specifically includes the following steps:

[0113] S41, substituting the distributed formation control protocol into the dynamics model to obtain a closed-loop dynamics equation;

[0114] The closed-loop dynamic equation in step S41 is expressed as follows:

[0115] (6)

[0116] in, , , ;

[0117] In the formula, represents the state estimates of all agents in the system, and , Respectively represent State estimation of each agent; The dimension is All elements are A vector of Representation Matrix No. OK, Represents the Laplacian matrix corresponding to the fully connected graph;

[0118] S42. Design an output tracking estimator based on adaptive parameter reduction;

[0119] The expression of the output tracking estimator based on adaptive parameter reduction in step S42 is as follows:

[0120] (7)

[0121] In the formula, Indicates The agent is Estimates of the outputs of the agents; Indicates The initial value of each agent is a positive adaptive parameter; represents the adaptive parameter auxiliary variable; The adjacency matrix corresponding to the communication topology is represented by Line Column elements; Indicates The agent is Estimates of the outputs of the agents; Represents the adjacency matrix Line Column elements; Indicates The sensor output of each agent; Indicates The sensor output matrix of each agent;

[0122] S43. Design a distributed state observer based on the closed-loop dynamic equations of the multi-agent system;

[0123] The distributed state observer expression in step S43 is as follows:

[0124] (8)

[0125] In the formula, Indicates The derivative vector of the agent state estimate; Indicates The output estimates of the agents, and , Respectively represent The agent is Estimates of the outputs of the agents; represents the gain matrix of the distributed state observer.

[0126] S44. Analyze the convergence conditions of the distributed state estimator based on adaptive parameter reduction, and determine the parameters of the distributed state estimator.

[0127] Step S44 specifically includes the following steps:

[0128] S441, Setting express The average of the state estimates of the agents, represents the error between the estimated mean and the true value of the agent state, represents the error between the estimated mean and the estimated state of each agent, represents the consistency error of the agent's output estimate;

[0129] When the state estimation error , and output estimation error When all converge to zero, the multi-agent system realizes state mutual estimation, and then realizes formation control, and obtains the gain matrix in the distributed observer ,in represents a positive definite gain matrix, which is determined by the positive definite solution of the following linear matrix inequality:

[0130] (9)

[0131] In the formula, and are positive definite matrices respectively.

[0132] S5. When there is an agent sensor failure in the multi-agent system, the parameters described in step S3 are redesigned to avoid the failure of the collaborative task of the multi-agent system.

[0133] Step S5 specifically includes the following steps:

[0134] S51. When a sensor of an agent in a multi-agent system fails, suppose the If a sensor of an intelligent agent fails, the output of the failed intelligent agent , so the output matrix of the faulty agent is , at this time, the overall output matrix of the multi-agent system is for:

[0135] (10)

[0136] In the formula, Respectively represent The output matrix of the agent, where The output matrices of all agents are set to zero;

[0137] S52, Verification Whether the observation conditions described in step S13 are met, if so, and when the intelligent body sensor fails, the linear matrix inequality in step S44 is re-solved to obtain the updated gain matrix of the distributed observer in step S43 , proving that the multi-agent system can detect sensor failures and reconstruct the distributed observer within 1s, that is, the state estimation of the multi-agent system will not diverge due to agent sensor failures, thereby ensuring the completion of the system collaborative tasks.

[0138] Simulation experiment

[0139] In this simulation experiment, a multi-agent system consisting of five agents is used as the research object. Its communication topology is as follows: Figure 2 As shown, the parameters in the agent's dynamic equation and sensor equation are:

[0140] ;

[0141] ;

[0142] The state of the first dimension of the agent is displacement, and the state of the second dimension is velocity; the initial states of the five agents are set as , , , , , the initial value of the adaptive gain is selected as , , set the formations of the five agents to be , , , , ; The controller gain matrix is ​​selected as , the gain matrix of the estimator is selected as:

[0143] ;

[0144] Setting up the fourth agent Five seconds into the simulation, the sensor failed and a simulation experiment was performed.

[0145] like Figure 3 As shown, at five seconds, the sensor malfunctioned, causing the fourth agent to The output estimate of produces a large error, but then the error converges asymptotically to zero.

[0146] like Figure 4 As shown in the figure, the error tends to diverge as the agent sensor fails, but as the agent builds a new distributed observer, the error converges again.

[0147] like Figure 5 As shown, the adaptive gain converges to a finite value.

[0148] Figure 6 is the displacement difference between agents 2, 3, 4, 5 and agent 1, Figure 7 is the speed difference between agents 2, 3, 4, 5 and agent 1, such as Figure 6 and Figure 7 As shown, the displacement of the intelligent body maintains the set distance and speed, and can run according to the set formation.

[0149] like Figure 8 and Fig. 9 As shown, it can be seen that the output of the fourth agent becomes zero at five seconds due to sensor failure.

[0150] Therefore, the present invention adopts the above-mentioned multi-agent state estimation and formation control method based on adaptive parameter reduction, which realizes that in a multi-agent system, when a sensor fails, the state estimation of the agent will not fail and diverge, thereby ensuring the realization of formation control of the multi-agent system.

[0151] 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. A multi-agent state estimation and formation control method based on adaptive parameter reduction, characterized in that: The following steps are involved: S1. Based on the differential equation A multi-agent system consisting of 3 agents is used to build dynamics model and sensor model. S2. Construct a directed strongly connected communication topology structure according to the requirements of the adaptive state estimation on the communication topology graph; S3. Design a distributed formation controller for the multi-agent system and determine the parameters of the distributed formation controller; Step S3 specifically includes the following steps: S31. Determine the formation position of each agent in the multi-agent system: Setting the formation configuration of a multi-agent system ,in represents the overall formation configuration of the system, Respectively represent the The desired position of the agent; and set Representing an Agent and Agent The constant relative formation displacement between , , Indicates The desired position of each agent; Indicates The desired position of the agent; at the same time, the formation of the agent satisfies ; S32. Design a distributed formation controller for multi-agent systems based on state estimation: （4） In the formula, represents constant gain; represents the feedback gain matrix; Indicates The agent's own state estimates; It is The agent is Agent state estimates; ,in, Indicates An agent estimates the state of all agents in a multi-agent system; Respectively represent The agent is State estimation of each agent; S33, determining that the parameters of the distributed formation controller when it converges are the parameters of the distributed formation controller; S4. Under the directed strongly connected communication topology, design a multi-agent output tracking estimator and distributed state observer based on adaptive parameter reduction to complete the distributed adaptive state estimation of the multi-agent system; S5. When there is an agent sensor failure in the multi-agent system, the parameters described in step S3 are redesigned.

2. The multi-agent state estimation and formation control method based on adaptive parameter reduction according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Construct the dynamic model of each agent in the multi-agent system: （1） In the formula, Indicates The derivative of the state of each agent; For the The state vector of each agent, and , The dimension is A vector collection of ; For the The control input of an agent, and , The dimension is A vector collection of ; is a known state matrix, and , The dimension is The matrix collection of ; is a known input matrix, and , The dimension is The matrix collection of ; S12. Construct the sensor model of each agent in the multi-agent system: （2） In the formula, For the The sensors of each agent measure the output, and , The dimension is A vector collection of ; For the The output matrix of the agents, and , The dimension is The matrix collection of ; is the state of all agents in the multi-agent system, and , Respectively represent the The transpose of the agent state vector; S13. Determine the requirements for the agent's dynamic parameters: First, remember , For the system The sensor output of each agent, Respectively represent the The transpose of the sensor output of each agent, The dimension is A vector collection of ; , For the system The sensor output matrix of each agent is Respectively represent The transpose of the sensor output matrix of the intelligent agent; ; Then determine the overall state equation and output equation of the multi-agent system: （3） In the formula, The dimension is The identity matrix of In multi-agent systems Control input for each agent; represents the Kronecker product; And make the multi-agent system meet Where rank represents the rank of the matrix.

3. The multi-agent state estimation and formation control method based on adaptive parameter reduction according to claim 2, characterized in that: In step S2, using the directed graph express The directed strongly connected communication topology of agents, where represents the set of agent nodes, and , They represent the agent’s nodes; represents the set of agent edges, and ; Among them, there is a directed path between any two nodes in a directed graph.

4. The multi-agent state estimation and formation control method based on adaptive parameter reduction according to claim 3, characterized in that: In step S33, when the state estimation of the multi-agent system is achieved, formula (4) is transformed into: （5） Substituting into the system's dynamic equation (1), we get: When stable, the multi-agent system can achieve formation control, and the constant gain ; and the feedback gain matrix ,in Express satisfaction is a positive definite matrix.

5. The multi-agent state estimation and formation control method based on adaptive parameter reduction according to claim 4, characterized in that: Step S4 The specific steps include: S41, substituting the distributed formation control protocol into the dynamics model to obtain a closed-loop dynamics equation; S42. Design an output tracking estimator based on adaptive parameter reduction; S43. Design a distributed state observer based on the closed-loop dynamic equations of the multi-agent system; S44. Analyze the convergence conditions of the distributed state estimator based on adaptive parameter reduction, and determine the parameters of the distributed state estimator.

6. The multi-agent state estimation and formation control method based on adaptive parameter reduction according to claim 5, characterized in that: The closed-loop dynamic equation in step S41 is expressed as follows: （6） in, , , In the formula, represents the state estimates of all agents in the system, and , Respectively represent State estimation of each agent; The dimension is All elements are A vector of Representation Matrix No. OK, Represents the Laplacian matrix corresponding to the fully connected graph; The expression of the output tracking estimator based on adaptive parameter reduction in step S42 is as follows: （7） In the formula, Indicates The agent is An estimate of the output of each agent; Indicates The initial value of each agent is a positive adaptive parameter; represents the adaptive parameter auxiliary variable; The adjacency matrix corresponding to the communication topology is represented by Line Column elements; Indicates The agent is An estimate of the output of each agent; Represents the adjacency matrix Line Column elements; Indicates The sensor output of each agent; Indicates The sensor output matrix of each agent; The distributed state observer expression in step S43 is as follows: （8） In the formula, Indicates The derivative vector of the agent state estimate; Indicates The output estimates of the agents, and , Respectively represent The agent is An estimate of the output of each agent; represents the gain matrix of the distributed state observer.

7. The multi-agent state estimation and formation control method based on adaptive parameter reduction according to claim 6, characterized in that: Step S44 specifically includes the following steps: S441, Setting express The average of the state estimates of the agents, represents the error between the estimated mean and the true value of the agent state, represents the error between the estimated mean and the estimated state of each agent, represents the consistency error of the agent's output estimate; When the state estimation error , and output estimation error When all converge to zero, the multi-agent system realizes state mutual estimation, and then realizes formation control, and obtains the gain matrix in the distributed observer ,in represents a positive definite gain matrix, which is determined by the positive definite solution of the following linear matrix inequality: （9） In the formula, and are positive definite matrices respectively.

8. The multi-agent state estimation and formation control method based on adaptive parameter reduction according to claim 7, characterized in that: Step S5 specifically includes the following steps: S51. When a sensor of an agent in a multi-agent system fails, suppose the If a sensor of an intelligent agent fails, the output of the failed intelligent agent , so the output matrix of the faulty agent is , at this time, the overall output matrix of the multi-agent system is for: （10） In the formula, Respectively represent The output matrix of the agent, where The output matrices of all agents are set to zero; S52, Verification Whether step S13 is satisfied, if so, and when the intelligent body sensor fails, the linear matrix inequality in step S44 is re-solved to obtain the updated gain matrix of the distributed observer in step S43 , proving that the multi-agent system can detect sensor failures and reconstruct the distributed observer within 1s.

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