CN116627042B - Distributed collaborative tracking method for asymmetrically saturated multi-agent systems with actuators - Google Patents

Abstract

The invention belongs to the field of adaptive controllers and discloses a distributed collaborative tracking method for a asymmetrically saturated actuator multi-agent system, which includes: using a radial basis function neural network to estimate the oversaturation and external disturbance parts of the system, and modifying the original The multi-agent system model is converted. According to the converted system model, a dimensionality reduction observer is designed to estimate the unmeasurable state trajectory of each agent in the multi-agent system. Based on the output information and the dimensionality reduction observer information, the dimensionality reduction observer is constructed The adaptive protocol based on the reduced-order observer for the multi-agent system, and then based on the designed adaptive control algorithm, provide sufficient conditions to drive the asymmetric saturated multi-agent system of this type of actuator to achieve semi-global robust cooperative tracking. This method extends the adaptive neural network controller from a single system to a multi-agent system and solves the problem of dimensionality reduction observer design and robust distributed collaborative tracking of networked multi-agent systems with asymmetric saturated actuators.

Description

Distributed cooperative tracking method for multi-agent systems with asymmetric actuator saturation

Technical Field

The present invention belongs to the field of adaptive controllers, and more specifically relates to a distributed collaborative tracking method for an actuator asymmetric saturated multi-agent system.

Background Art

In recent years, with the rapid development of distributed networks and multi-agent systems, distributed cooperative control has become a hot topic in the field of control research. The main purpose of studying multi-agent systems is to replace expensive single systems with large-scale cooperation between intelligent agents to complete complex tasks. As the basis for cooperation between intelligent agents, the consistency problem has attracted the attention of researchers from various fields and has become an important research topic in the field of systems and control.

In practical applications, due to the physical condition limitations of the actuator and the consideration of system operation safety, multi-agent systems will inevitably experience actuator saturation. For example, the amplitude and frequency of the controller output current and voltage are limited, the valve opening is limited to a certain range, and the water level in the water tank has a fixed maximum value. Seeking a saturation compensation strategy to enable the actuator to quickly exit saturation after entering saturation or to avoid the actuator from entering saturation has become the key to achieving high-precision control of saturated systems, and very impressive research results have been achieved in this regard. It should be pointed out that these studies are all dedicated to the control method of symmetrical saturation of actuators. However, in practical applications, asymmetrical saturation of actuators often occurs. For example, when the actuator is partially damaged, asymmetrical saturation is very likely to occur. The study of robust consistency of multi-agent systems with asymmetric saturated actuators is very challenging.

Summary of the invention

In order to solve the problems existing in the prior art, the present invention provides a distributed collaborative tracking method for a multi-agent system with asymmetric saturated actuators. The method extends the adaptive neural network controller from a single system to a multi-agent system, and solves the dimensionality reduction observer design and robust distributed collaborative tracking consistency problems of the network multi-agent system with asymmetric saturated actuators.

In order to achieve the above object, the present invention is achieved through the following technical solutions:

The present invention is a distributed collaborative tracking method for an actuator asymmetric saturated multi-agent system, the method comprising the following steps:

Step 1: Construct a multi-agent system subject to actuator asymmetric saturation and external disturbances;

Step 2: Multi-agent system status Decompose the special coordinate basis to obtain the corresponding dynamic equations of the corresponding sub-states;

Step 3: Design a dimension reduction observer to estimate the value of the unmeasurable state;

Step 4: Use radial basis function neural network to estimate the oversaturation and external disturbance parts;

Step 5: Design an adaptive control algorithm based on the reduced-dimensional observer and give the conditions for achieving robust consistency tracking of the asymmetric saturated system.

A further improvement of the present invention is that the implementation process of step 1 is as follows:

For asymmetric input saturation and external disturbance A continuous-time system of follower agents and an autonomous system of a leader agent, specifically:

,

,

in: Expressed as The derivatives of the agent's state variables, Expressed as measurable output variables following the agent, It is represented by the number of following agents, Expressed as state variables of the following agent, Represented as the state variable of the leader agent, It is represented as the input of the multi-agent system and the output value of the asymmetric saturated actuator, Expressed as external disturbances following the agent, Expressed as a measurable output variable of the leader agent,

Followers are marked as , the leader's index is 0, is the state variable of the agent, is the measurable output variable, is the derivative of the state variable, , n represents the dimension of each agent's state variable, p represents the dimension of each agent's measurable output variable, Indicates external disturbances of the agents, and there exists a bounded disturbance function Make The relationship is established, is the input of the system and the output value of the asymmetric saturated actuator, specifically:

in , and They are Unknown upper and lower bounds, is the control input variable without considering input saturation, is a matrix with matching dimensions, The dimension of the Euclidean space is The matrix of express dimensional identity matrix, represents the zero matrix of the corresponding dimension or the constant zero;

In order to facilitate the design of the controller, a new function is defined as and ,therefore The transition dynamics model of the following agent is:

,

in For the part exceeding saturation, represents the sum of supersaturation and external disturbance, Represents the control input variable without considering input saturation.

A further improvement of the present invention is that step 2 specifically comprises the following steps:

Step 21: Matrix pair in the actuator asymmetric saturated multi-agent system Under the premise that the conditions of stabilization, detectability, left reversibility and minimum phase are met, and all elements in the left reversible and infinite zero-point structure in the system are 1, that is, the order is 1, the conversion dynamics model of the following agent is decomposed by using the special coordinate basis decomposition technology, and the non-singular state transition matrix is obtained. And the output transformation matrix , where the inverse matrix of the state transition matrix is ,and The states and outputs of each follower agent and leader agent are decomposed into matrices with corresponding dimensions. and ,in , and They are the converted state vector and output vector, and the three sub-states , and ,in Represents subsystems without direct inputs and outputs, showing the finite zero-point structure of a given system; Represents a subsystem with no direct input, showing the left-reversible structure of a given system; represents a subsystem with direct inputs and outputs, showing the infinite zero structure of a given system, and , , , , is a specific decomposition vector, and its specific representation is:

,

in All represent real numbers;

Step 22: Give the corresponding dynamic equations of the corresponding sub-states. ,have

,

Due to the asymmetric saturation of the actuator, the matrix pair in the multi-agent system is the minimum phase assumption, so It's Hurwitz's. and is a matrix with the corresponding dimension;

For sub-state Each element in ,have

,

For sub-state Each element in ,have

,

in, is the subsystem parameter matrix with corresponding matching dimensions obtained by solving the Linear System Toolkit in MATLAB, represents the control input variable without considering input saturation, represents the sum of supersaturation and external disturbance,

From the above formula, we can know that the substate and By measuring the output as the measurable part, the sub-state It is an unmeasurable part and is not affected by unknown input signals.

A further improvement of the present invention is that: the value of the unmeasurable state estimated by designing a dimension reduction observer in step 3 is specifically:

According to step 21, the special coordinate basis method divides the state into three sub-states , and , for step 22 substate Design an observer that is not affected by unknown input signals to observe the state of the unmeasurable part, where: , and design an observer for the actuator asymmetric saturation multi-agent system to estimate the state trajectory of the agent, specifically:

,

in, and They are and The observer, is the dimension-reduced observer of the system following the state of the agent, The output transformation matrix The inverse matrix of represents the output vector after transformation, Indicates A measurable output variable that follows the agent.

A further improvement of the present invention is that: the sum of supersaturation and external disturbance in step 4 is The estimates are as follows:

is an unknown function of oversaturation and external disturbance, and this part needs to be estimated. The radial basis function neural network can approximate the compact set Any continuous function on the Continuous function of an agent , the specific form is:

,

Among them: The number of nodes in the neural network is , the more nodes there are, the more accurate the approximation is, is the ideal weight vector, is the transpose of the ideal weight vector, For The approximation error is bounded on is the radial basis function vector, represents the input vector, The expression using the general Gaussian function is: , the number of nodes in the neural network is , the more nodes there are, the more accurate the approximation is, is the Euclidean norm, and are the center and variance of the Gaussian function respectively, and the ideal weight vector is the artificial value required for theoretical analysis: ,in and is the estimate of the ideal weight vector and its transpose, so It needs to be estimated through function approximation.

A further improvement of the present invention is that the step 5 comprises the following steps:

Step 51, use a A connected directed graph with 1 follower agent and 1 leader agent To describe the topological relationship of information interaction between agents, the leader agent is the root node of the directed spanning tree, and all follower agents can obtain the directed information of the leader agent. The adjacency matrix and Laplace matrix are defined as and ,in, Represents the specific element value in the adjacency matrix, which is 0 or 1. represents the specific element value in the Laplacian matrix, represents the topological relationship between the leader agent and the follower agent, Satisfy non-singularity The definition of a matrix, its eigenvalues are have positive real parts, and there exists a positive definite diagonal matrix , so that Established, of which ,definition The minimum eigenvalue of ;

Step 52: Solve the algebraic Riccati equation to obtain :

;

Step 53: Based on the obtained and ,definition and ,have ,in , combined with , and ,definition for , , Related variables, design adaptive control algorithm:

,

in: For and The time-varying coupling weights associated with the following agents, and their initial values satisfy , is a time-varying function, and each value is a positive number, for The estimated value of represents a small positive constant, and defines , , , , , , , the adaptive control algorithm based on the reduced-order observer for each follower agent can be written in a compact form as:

,

Among them, the adaptive law of the neural network is

,

and is the adaptive gain matrix, and is a positive constant;

In the semi-global collaborative consensus result, the initial state values of all agents are selected from an arbitrarily large bounded set , so according to the Lasalle invariant set principle, the coupling state , kinetic parameters and are all bounded, according to the neural network adaptive system with bounded input and bounded output and is bounded, and because the Gaussian function and function is bounded, and thus Each term in is bounded, so the control input is bounded, combined with step 2, we know is bounded, and because and are bounded, respectively , and So, we define The specific form is ;

Then, for a given compact set Any initial value on can construct a ratio Large tight set , so the radial basis function neural network approximates is effective when the appropriate , , , and , and the parameters satisfy , When , the system achieves semi-global robust consistent tracking, and Converges to the residual set

,

in: The expression is , , is the transpose of the subsystem parameter matrix with corresponding matching dimensions solved by the Linear System Toolkit in MATLAB, express The transpose of

, ,and It is the equation The solution.

The beneficial effects of the present invention are as follows: the distributed cooperative tracking method of the present invention is mainly aimed at a multi-agent system affected by an asymmetric saturated actuator and external disturbances. Under the premise that the system input and external disturbances are bounded and the state is unmeasurable, the method uses a radial basis function neural network to estimate the oversaturated and externally disturbed parts, and transforms the original multi-agent system model; according to the transformed system model, a reduced-dimensionality observer is designed to estimate the unmeasurable state trajectory of each intelligent agent in the multi-agent system; according to the output information and the reduced-dimensionality observer information, an adaptive protocol based on a reduced-order observer is constructed for the multi-agent system; and then, according to the designed adaptive control algorithm, sufficient conditions are given to drive this type of actuator asymmetric saturated multi-agent system to achieve semi-global robust cooperative tracking.

This method expands the adaptive neural network controller from a single system to a multi-agent system, and from an undirected topology to a directed topology, achieving the goal of distributed characteristics in algorithm design, parameter selection, and sufficient conditions, improving the variability and flexibility of centralized characteristics, and can be used in large and complex networks, with greater fault tolerance for system intelligent agents.

This scheme simultaneously overcomes the complex challenges of nonlinearity caused by asymmetric saturation and interference of actuators, and coupling caused by information exchange between intelligent agents.

At the same time, this method solves the problem of dimensionality reduction observer design and robust distributed cooperative tracking for networked multi-agent systems with asymmetric saturated actuators.

The robust distributed cooperative tracking method for a multi-autonomous system with asymmetric saturated actuators proposed in the present invention takes into account asymmetric saturation and external disturbance factors based on output feedback in the study of cooperative tracking control of the multi-autonomous system. It does not require prior knowledge of external disturbance functions and upper and lower bounds of asymmetric saturated actuators, and gets rid of the dependence on system state information, thus providing sufficient conditions for the system to achieve robust cooperative tracking.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow diagram of the method of the present invention.

FIG. 2 is a state trajectory of the leading intelligent agent and the following intelligent agent of the multi-autonomous agent system of the present invention.

Figure 3 shows the trajectory of the adaptive control algorithm based on the reduced-dimensionality observer.

Figure 4 shows the overall change trajectory of the adaptive gain in the control algorithm.

Figure 5 shows the estimated trajectory process with external disturbances and oversaturation.

DETAILED DESCRIPTION

The following will disclose the embodiments of the present invention with drawings. For the purpose of clear description, many practical details will be described together in the following description. However, it should be understood that these practical details should not be used to limit the present invention. That is to say, in some embodiments of the present invention, these practical details are not necessary.

As shown in FIG1 , the present invention is a distributed cooperative tracking method for a multi-agent system with asymmetric saturated actuators. By using this method, the adaptive neural network controller is expanded from a single system to a multi-agent system, and the dimension reduction observer design and robust distributed cooperative tracking problems of a network multi-agent system with asymmetric saturated actuators are solved. The method comprises the following steps:

Step 1: Construct a multi-agent system affected by actuator asymmetric saturation and external disturbance. The specific implementation process is as follows:

For asymmetric input saturation and external disturbance A continuous-time system of follower agents and an autonomous system of a leader agent, specifically:

,

,

in: Expressed as The derivatives of the agent's state variables, Expressed as measurable output variables following the agent, It is represented by the number of following agents, Expressed as state variables of the following agent, Represented as the state variable of the leader agent, It is represented as the input of the multi-agent system and the output value of the asymmetric saturated actuator, Expressed as external disturbances following the agent, Expressed as a measurable output variable of the leader agent,

Followers are marked as , the leader's index is 0, is the state variable of the agent, is the measurable output variable, is the derivative of the state variable, , n represents the dimension of each agent's state variable, p represents the dimension of each agent's measurable output variable, Indicates external disturbances of the agents, and there exists a bounded disturbance function Make The relationship is established, is the input of the system and the output value of the asymmetric saturated actuator, specifically:

in , and They are Unknown upper and lower bounds, is the control input variable without considering input saturation, is a matrix with matching dimensions, The dimension of the Euclidean space is The matrix of express dimensional identity matrix, represents the zero matrix of the corresponding dimension or the constant zero;

In order to facilitate the design of the controller, a new function is defined as and ,therefore The transition dynamics model of the following agent is:

,

in For the part exceeding saturation, represents the sum of supersaturation and external disturbance, Represents the control input variable without considering input saturation.

Step 2: Multi-agent system status By performing special coordinate basis decomposition, the corresponding dynamic equations of the corresponding sub-states are obtained.

The specific steps include:

Step 21: Matrix pair in the actuator asymmetric saturated multi-agent system Under the premise that the conditions of stabilization, detectability, left reversibility and minimum phase are met, and all elements in the left reversible and infinite zero-point structure in the system are 1, that is, the order is 1, the conversion dynamics model of the following agent is decomposed by using the special coordinate basis decomposition technology, and the non-singular state transition matrix is obtained. And the output transformation matrix , where the inverse matrix of the state transition matrix is ,and The states and outputs of each follower agent and leader agent are decomposed into matrices with corresponding dimensions. and ,in , and They are the converted state vector and output vector, and the three sub-states , and ,in Represents subsystems without direct inputs and outputs, showing the finite zero-point structure of a given system; Represents a subsystem with no direct input, showing the left-reversible structure of a given system; represents a subsystem with direct inputs and outputs, showing the infinite zero structure of a given system, and , , , , is a specific decomposition vector, and its specific representation is:

,

in All represent real numbers;

Step 22: Give the corresponding dynamic equations of the corresponding sub-states. ,have

,

Due to the asymmetric saturation of the actuator, the matrix pair in the multi-agent system is the minimum phase assumption, so It's Hurwitz's. and is a matrix with the corresponding dimension;

For sub-state Each element in ,have

,

For sub-state Each element in ,have

,

in, is the subsystem parameter matrix with corresponding matching dimensions obtained by solving the Linear System Toolkit in MATLAB, represents the control input variable without considering input saturation, represents the sum of supersaturation and external disturbance,

From the above formula, we can know that the substate and By measuring the output as the measurable part, the sub-state It is an unmeasurable part and is not affected by unknown input signals.

Step 3: Design a dimension reduction observer to estimate the value of the unmeasurable state.

According to step 21, the special coordinate basis method divides the state into three sub-states , and , for step 22 substate Design an observer that is not affected by unknown input signals to observe the state of the unmeasurable part, where: , and design an observer for the actuator asymmetric saturation multi-agent system to estimate the state trajectory of the agent, specifically:

,

in, and They are and The observer, is the dimension-reduced observer of the system following the state of the agent, The output transformation matrix The inverse matrix of represents the output vector after transformation, Indicates A measurable output variable that follows the agent.

Step 4: Use radial basis function neural network to estimate the oversaturation and external disturbance parts, specifically:

According to step 2, is an unknown function of oversaturation and external disturbance, and this part needs to be estimated. The radial basis function neural network can approximate the compact set Any continuous function on the Continuous function of an agent , the specific form is:

,

Among them: The number of nodes in the neural network is , the more nodes there are, the more accurate the approximation is, is the ideal weight vector, is the transpose of the ideal weight vector, For The approximation error is bounded on is the radial basis function vector, represents the input vector, The expression using the general Gaussian function is: , the number of nodes in the neural network is , the more nodes there are, the more accurate the approximation is, is the Euclidean norm, and are the center and variance of the Gaussian function respectively, and the ideal weight vector is the artificial value required for theoretical analysis: ,in and is the estimate of the ideal weight vector and its transpose, so It needs to be estimated through function approximation.

Step 5: Design an adaptive control algorithm based on a reduced-dimensional observer and give the conditions for robust consistency tracking of an asymmetric saturated system, including the following steps:

Step 51, use a A connected directed graph with 1 follower agent and 1 leader agent To describe the topological relationship of information interaction between agents, the leader agent is the root node of the directed spanning tree, and all follower agents can obtain the directed information of the leader agent. The adjacency matrix and Laplace matrix are defined as and ,in, Represents the specific element value in the adjacency matrix, which is 0 or 1. represents the specific element value in the Laplacian matrix, represents the topological relationship between the leader agent and the follower agent, Satisfy non-singularity The definition of a matrix, its eigenvalues are have positive real parts, and there exists a positive definite diagonal matrix , so that Established, of which ,definition The minimum eigenvalue of ;

Step 52: Solve the algebraic Riccati equation to obtain :

;

Step 53: Based on the obtained and ,definition and ,have ,in , combined with , and ,definition for , , Related variables, design adaptive control algorithm:

,

in: For and The time-varying coupling weights associated with the following agents, and their initial values satisfy , is a time-varying function, and each value is a positive number, for The estimated value of represents a small positive constant, and defines , , , , , , , the adaptive control algorithm based on the reduced-order observer for each follower agent can be written in a compact form as:

,

Among them, the adaptive law of the neural network is

,

and is the adaptive gain matrix, and is a positive constant;

In the semi-global collaborative consensus result, the initial state values of all agents are selected from an arbitrarily large bounded set , so according to the Lasalle invariant set principle, the coupling state , kinetic parameters and are all bounded, according to the neural network adaptive system with bounded input and bounded output and is bounded, and because the Gaussian function and function is bounded, and thus Each term in is bounded, so the control input is bounded, combined with step 2, we know is bounded, and because and are bounded, respectively , and So, we define The specific form is ;

Then, for a given compact set Any initial value on can construct a ratio Large tight set , so the radial basis function neural network approximates is effective when the appropriate , , , and , and the parameters satisfy , When , the system achieves semi-global robust consistent tracking, and Converges to the residual set

,

in: The expression is , , is the transpose of the subsystem parameter matrix with corresponding matching dimensions solved by the Linear System Toolkit in MATLAB, express The transpose of

, ,and It is the equation The solution.

The following is a detailed explanation with reference to specific examples.

Consider a multi-agent system consisting of 6 follower agents and 1 leader agent, where the directed communication topology of the 6 follower agents is represented by the adjacency matrix as And only the first follower agent can directly obtain the directed information of the leader agent.

In this example, the specific form of the reduced-dimensionality observer is given by using special coordinate basis decomposition, and combined with the radial basis function neural network, a corresponding adaptive control algorithm based on the reduced-dimensionality observer is designed to drive the state trajectory of each intelligent agent to achieve consistency.

The system matrix that satisfies the conditions is given as , it is clear that the matrix of the actuator asymmetric saturation multi-agent system is The form of special coordinate basis decomposition is satisfied, where , for unmeasurable substates The observer is designed as , so the dimension reduction observer of the system state is designed as The initial state of the leader agent Randomly selected , following the agent Initial state Randomly selected The lower and upper limits of the asymmetric saturated actuator are For simplicity, the external perturbation function of each follower agent is selected as .

In this example, solving the algebraic Riccati equation yields , and select Choose the appropriate , , , , , .

Figure 2 depicts the leader agent and the follower agent. movement trajectory.

Figure 3 expresses the motion trajectory of the control input, indicating that the designed adaptive control algorithm based on dimensionality reduction observer can enable the multi-agent system with asymmetric saturated actuators to achieve robust consistency tracking, and the control input is maintained within the upper and lower bounds of the asymmetric saturated actuator, ensuring the performance of the multi-agent system.

Figure 4 depicts the adaptive gain The overall change process of , which shows that it is bounded and gradually tends to 0.

Figure 5 depicts the estimation function The trajectory shows that the radial basis function neural network can better estimate the unknown external disturbance and the oversaturated part of the control input.

This method extends the adaptive neural network controller from a single system to a multi-agent system, and simultaneously solves the problem of dimensionality reduction observer design and robust distributed cooperative tracking for networked multi-agent systems with asymmetric saturated actuators.

The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (5)

1. A distributed collaborative tracking method for an actuator asymmetric saturation multi-agent system, characterized in that the method comprises the following steps: Step 1: Construct a multi-agent system subject to actuator asymmetric saturation and external disturbances; Step 2: Decompose the multi-agent system state _xi in a special coordinate basis to obtain the corresponding dynamic equations of the corresponding sub-states; Step 3: Design a dimension reduction observer to estimate the value of the unmeasurable state; Step 4: Use radial basis function neural network to estimate the oversaturation and external disturbance parts; Step 5: Design an adaptive control algorithm based on the reduced-dimensional observer and give the conditions for robust consistency tracking of the asymmetric saturated system. The implementation process of step 1 is as follows: For a continuous-time system of N follower agents and an autonomous system of 1 leader agent with asymmetric input saturation and external disturbances, it is: in: is represented by the derivative of the state variable of the ith follower agent, _yi is represented by the measurable output variable of the ith follower agent, i is the number of follower agents, _xi is represented by the state variable of the ith follower agent, _x0 is represented by the state variable of the leader agent, _ui ( _vi ) is represented by the input of the multi-agent system and the output value of the asymmetric saturated actuator, is represented as the external disturbance of the ith follower agent, _y0 is expressed as the measurable output variable of the leader agent, followers are labeled 1-N, and the leader is labeled 0. is the state variable of the agent, is the measurable output variable, is the derivative of the state variable, s = 0, 1, ..., N, n represents the dimension of each agent's state variable, p represents the dimension of each agent's measurable output variable, represents the external disturbance of the ith agent, and there exists a bounded disturbance function _wi such that The relationship is established, is the input of the system and the output value of the asymmetric saturated actuator, specifically: where k = 1, 2, ..., m, and are the unknown upper and lower bounds of _uik , respectively; _vik is the control input variable without considering input saturation; A, B, C are matrices with matching dimensions. represents a matrix of dimension m×n in Euclidean space, I _n represents the n-dimensional identity matrix, and 0 represents the zero matrix of the corresponding dimension or the constant zero; Define new functions as σ _i (v _i ) = _ui (v _i ) - v _i and σ _i (v _i ) + w _i = δ _i , so the transition dynamics model of N follower agents is: Where σ _i ( _vi ) is the part exceeding saturation, δ _i represents the sum of oversaturation and external disturbance, and _vi represents the control input variable without considering input saturation. 2. The distributed collaborative tracking method for an actuator asymmetric saturation multi-agent system according to claim 1 is characterized in that: the step 2 specifically includes the following steps: Step 21. The matrix pair (A, B, C) in the actuator asymmetric saturated multi-agent system satisfies the conditions of stabilization, detectability, left reversibility and minimum phase, and all elements in the left reversible and infinite zero point structure of the system are 1, that is, under the premise that the order is 1, the conversion dynamics model of the follower agent is decomposed using the special coordinate basis decomposition technology, through the non-singular state transition matrix Γ _s =[Γ _sa Γ _sb Γ _sd ] and the output transition matrix Γ _o , where the inverse matrix of the state transition matrix is and The states and outputs of each follower agent and leader agent are decomposed into matrices with corresponding dimensions. and where i = 0, 1, ..., N, and They are the converted state vector and output vector, and the three sub-states and in Represents subsystems without direct inputs and outputs, showing the finite zero-point structure of a given system; Represents a subsystem with no direct input, showing the left-reversible structure of a given system; represents a subsystem with direct inputs and outputs, showing the infinite zero structure of a given system, and is a specific decomposition vector, and its specific representation is: in All represent real numbers; Step 22: Give the corresponding dynamic equations of the corresponding sub-states. have Since the matrix pair (A, B, C) in the actuator asymmetric saturated multi-agent system is the minimum phase assumption, is Hurwitz's, _Lab and L _ad are matrices with corresponding dimensions; For sub-state Each element in have For sub-state Each element in have Wherein, L _bbk , L _dbk , L _ddk , E _ka , E _kb , E _kd are subsystem parameter matrices with corresponding matching dimensions obtained by solving the linear system toolkit in MATLAB, _vik represents the control input variable without considering input saturation, δ _ik represents the sum of oversaturation and external disturbance, From the above formula, we can know that the substate and By measuring the output as the measurable part, the sub-state It is an unmeasurable part and is not affected by unknown input signals. 3. The distributed collaborative tracking method for an actuator asymmetric saturation multi-agent system according to claim 2 is characterized in that: the value of the unmeasurable state estimated by the dimension reduction observer in step 3 is specifically: For step 22 substate Design an observer that is not affected by unknown input signals to observe the state of the unmeasurable part, where i = 0, 1, ..., N, and design an observer for the actuator asymmetric saturation multi-agent system to estimate the state trajectory of the agent, specifically: in, and They are and x _ia 's observer, is the dimension-reduced observer of the system following the state of the agent, is the inverse matrix of the output conversion matrix Γ _o , represents the transformed output vector, and _yi represents the measurable output variable of the i-th following agent. 4. The distributed collaborative tracking method for an actuator asymmetric saturation multi-agent system according to claim 3 is characterized in that: the step 4 estimates the sum of the oversaturation and the external disturbance δ _i as follows: A radial basis function neural network is used to estimate the continuous function δ _i of the i-th agent, i=1,…,N, and the specific form is: in: is the ideal weight vector, is the transpose of the ideal weight vector, ∈ _i is the approximation error bounded on Π, is the radial basis function vector, represents the input vector, The expression using the general Gaussian function is: The number of nodes in a neural network is l ≥ 1. The more nodes there are, the more accurate the approximation is. is the Euclidean norm, μ _it and k _it are the center and variance of the Gaussian function respectively, and the ideal weight vector is the artificial value required for theoretical analysis: in and is the estimate of the ideal weight vector and its transpose, so It needs to be estimated through function approximation. 5. The distributed collaborative tracking method for an actuator asymmetric saturation multi-agent system according to claim 4 is characterized in that: step 5 comprises the following steps: Step 51: Use a connected directed graph g containing N follower agents and one leader agent to characterize the information interaction topological relationship between agents, where the leader agent is the root node of the directed spanning tree, and all follower agents can obtain the directed information of the leader agent. Define their adjacency matrix and Laplace matrix as and Among them, a _ij represents the specific element value in the adjacency matrix, and its value is 0 or 1, l _ij l _ij represents the specific element value in the Laplace matrix, L ₀ represents the topological relationship _between the leader agent and the follower agent, L ₁ satisfies the definition of a non-singular M matrix, its eigenvalue is 0 = λ ₁ ≤λ ₂ ≤...≤λ _N all have positive real parts, and there exists a positive definite diagonal matrix G = diag{g ₁ ,...,g _N }∈R ^N×N , such that Established, of which definition The minimum eigenvalue of is λ ₀ ; Step 52, solve the algebraic Riccati equation to obtain Q＞0: A ^T Q + QA - 2QBB ^T Q + I = 0; Step 53: Based on the obtained and definition and have in Combining σ _i (v _i ), w _i and ∈ _i , defining η _i as a variable related to σ _i (v _i ), w _i , ∈ _i , and designing an adaptive control algorithm: Where: d _i is the time-varying coupling weight associated with the ith follower agent, and its initial value satisfies d _i (0) > 1, ρ _i is a time-varying function, and each value is a positive number, is the estimated value of _ηi , represents a small positive constant, and defines The adaptive control algorithm based on the reduced-order observer for each follower agent can be written in a compact form as: Among them, the adaptive law of the neural network is Γ＝Γ ^T ＞0 and Ξ＝Ξ ^T ＞0 are adaptive gain matrices, k _w and k _η are positive constants; In the semi-global collaborative consensus result, the initial state values of all agents are selected from an arbitrarily large bounded set Therefore, according to the Lasalle invariant set principle, the coupling state ξ _i (t), the dynamic parameters d _i (t) and ρ _i (t) are all bounded. According to the bounded input and bounded output neural network adaptive system, we can get and is bounded, and because the Gaussian function and tanh function is bounded, and thus each item in _vi is bounded, so the control input _vi is bounded, σ _i ( _vi ) is bounded, and because w _i and ∈ _i are both bounded, we use and Therefore, the specific form of defining η _i is Then, for any initial value on a given compact set Π _v , a compact set Π larger than Π _v can be constructed, so that the radial basis function neural network approximate estimation of δ _i is effective. When appropriate Γ, Ξ, k _w , k _η and And the parameters satisfy When , the system achieves semi-global robust consistent tracking, and ξ converges to the residual set Among them: The expression of E _a is is the transpose of the subsystem parameter matrix with corresponding matching dimensions solved by the Linear System Toolkit in MATLAB, represents the transpose of E _a , And P _aa ＞0 is the equation The solution.