Heterogeneous multi-agent tracking control method coupled with neural network output regulator

Abstract

The application discloses a heterogeneous multi-agent tracking control method of a neural network coupled output regulator, first establishes a dynamic model of a leader agent and a follower agent, estimates the uncertainty in the follower model and solves the model mismatch problem between the followers and the leaders in the heterogeneous multi-agent system by designing a framework combining a neural network and an output regulator, further designs a robust two-part output consensus tracking control protocol, redesigns a parameter adaptive update rate, completes the design of a neural network adaptive parameter, and applies the control protocol to the dynamic model of the heterogeneous multi-agent system. The method designs a robust controller combining a neural network and an output regulator, solves the two-part output consensus tracking problem of the heterogeneous multi-agent system, improves the robustness of system control, introduces a signed network, extends the behavior of the heterogeneous multi-agent system to two-part consensus tracking, and expands the application scene of the algorithm.

Description

Technical Field

[0001] This invention belongs to the field of cooperative control technology for multi-agent systems, and specifically relates to a heterogeneous multi-agent tracking control method with a neural network coupled output regulator. Background Technology

[0002] The swarm intelligence of multi-agent systems (MAS) is typically manifested in cluster behavior, which takes many forms. Convergence is common in cooperation, but dispersion is equally prevalent in nature, such as fish scattering when encountering obstacles or ant colonies separating on their way to food. Similarly, for multi-agent systems, behaviors like covering, formation, and encirclement play a crucial role in agent dispersion, and related research has significant application value in the civilian field. Bipartite partitioning of agent networks is an effective method for addressing agent dispersion. Bipartite consensus is a multi-agent behavior based on structurally balanced symbolic networks. In bipartite consensus problems, current research extends the order of agents from first to second or even higher, and its dynamics model gradually expands from linear to nonlinear. Furthermore, leader-follower cooperative structures have also been extended to symmetric divergent behavior, i.e., the bipartite tracking problem, which is currently attracting widespread attention for its potential applications in moving target capture and swarm adversarial problems.

[0003] On the other hand, swarm intelligence occurs not only among homogeneous agents but also among heterogeneous agents. In many practical applications, due to specific needs and physical constraints, different agents often exhibit different dynamics. For example, in air-ground collaborative scenarios, drones and ground vehicles display different dynamic characteristics; the former's state variables are represented by a third-order model, while the latter's are represented by a second-order model. Accurately modeling moving objects is difficult, and agents are always subject to environmental disturbances in real-world tasks. This unavoidable uncertainty leads to the heterogeneity of the swarm, and these factors can potentially affect the system's stability.

[0004] Many existing studies have attempted to solve the robust bipartite tracking control problem and have innovatively proposed various methods to reduce or mitigate the impact of uncertainties on system stability and control accuracy. However, previous studies have not fully considered robust bipartite output-consistent tracking control of heterogeneous multi-agent systems, while such research has important application value in moving target acquisition. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a heterogeneous multi-agent tracking control method for a neural network coupled output regulator, which can improve the robustness of system control and expand the application scenarios of the algorithm.

[0006] The technical solution of this invention is: a heterogeneous multi-agent tracking control method for a neural network coupled output regulator, the specific steps of which are as follows:

[0007] S1. Establish a third-order model of the leader agent and a dynamic model of the follower agent in a multi-agent system to form a heterogeneous multi-agent system;

[0008] S2. For multi-agent systems, a fusion framework with a neural network coupled output regulator is designed to estimate the uncertainty in the follower model and solve the model mismatch problem between the follower and the leader in heterogeneous multi-agent systems.

[0009] S3. The estimated value obtained in step S2 is compensated to the controller, and then a robust two-part tracking control protocol is designed.

[0010] S4. Design the adaptive law of the control protocol established in step S3 to complete the design of the neural network adaptive parameters.

[0011] S5. Apply the control protocol to the dynamic model of the follower agent to complete the bipartition of the multi-agent system under the symbolic network. One group of agents tracks the trajectory of the leader, while the other group tracks the trajectory away from the leader, thus completing the bipartition of the followers and the bipartition of the leader's output consistency tracking.

[0012] Furthermore, step S1 is specifically as follows:

[0013] S11. In a heterogeneous multi-agent system, there exists one leader and n followers, connected by a symbolic network G. Let... , Let the set of all followers be represented. The model of the leader in a multi-agent system is as follows:

[0014] (1)

[0015] in, Indicates time, and These represent the leader's state and output, respectively. The derivative representing the leader's state, This represents the state matrix.

[0016] S12, the integer-order model of n follower agents is as follows:

[0017] (2)

[0018] in, and They represent the first The state and output of each follower. The derivative of the follower state, Indicates control input, It is a smooth and continuous unknown function, related to the state and time of the follower, representing the model uncertainty of the follower, and the state matrix is... and The dimensions are compatible.

[0019] S13. To achieve two-part output consistency tracking control in a heterogeneous multi-agent system, the following definition is given:

[0020] (3)

[0021] in, This means that if the output states of the i-th agent and the leader eventually converge, then... ,otherwise When the above conditions are met, it means that the two-part output consistency tracking control is completed.

[0022] Furthermore, step S2 is specifically as follows:

[0023] S21. Using the linear parameterization method in adaptive control theory, in equation (2) It can be parameterized in the following form:

[0024] (4)

[0025] in, Denotes the basis functions. Represents an unknown parameter vector; each agent For parameter vectors The estimated value is denoted as ; This represents the estimation error of the neural network, assuming... There exists a bound for an unknown constant. ,Right now , The estimated value is written as , The estimated value is denoted as Assuming It has the following forms:

[0026] (5)

[0027] S22. Introduce the following output regulation equation:

[0028] (6)

[0029] Among them, for The above equation has a solution. The state matrix is ​​obtained. and The goal is to ensure consistent two-part output tracking control in heterogeneous multi-agent systems.

[0030] Furthermore, step S3 is specifically as follows:

[0031] S31. The robust adaptive state feedback protocol composed of dynamic compensators is as follows:

[0032] (7)

[0033] in, Let T denote the coupling gain, and let T denote the transpose of the matrix. , Indicates the first The follower's state of mind towards the leader The estimated quantity, Indicates the first Follower-leader status The estimated quantity, The derivative of the leader's state estimator, It is a matrix with a value greater than zero. Indicates the first A follower-leader state matrix The estimated quantity, Indicates the first An estimate of the leader's state matrix by each follower. The derivative of the leader state matrix estimator is given by... Represents a constant greater than zero. and This indicates the control parameters that need to be determined. It represents the set of all followers. Represent the adjacency matrix, if the agent Acquire intelligent agent The information, ,on the contrary, . and Representing intelligent agents respectively and intelligent agents The relationship of cooperation and confrontation between them, defined Represent a diagonal matrix, if the follower Upon receiving a message from the leader, ;otherwise .

[0034] S32. To achieve convergence of the two-part tracking error in step S13, the robust adaptive control algorithm, i.e., equation (7), needs to satisfy the following two conditions. Then, the algorithm equation (7) will solve the two-part output consistency tracking problem of system equations (1) and (2):

[0035] Condition 1: For , Represent the Herwitz matrix, and at the same time , The output regulation equation (6) is satisfied.

[0036] Condition 2: The following inequalities have a solution. :

[0037] (8)

[0038] Furthermore, step S4 is specifically as follows:

[0039] S41. To achieve adaptive estimation in a neural network, the following adaptive law is designed:

[0040] (9)

[0041] in, , Let represent a positive definite matrix, and the Laplace matrix is ​​defined as follows: , The degree matrix is ​​defined as follows: , , , With the state matrix Consistent, ( (representing a block diagonal matrix) express 3D identity matrix Indicates the parameter The adaptive law, Indicates the parameter The update rate.

[0042] S42. Using the control protocol designed in step S41, complete the adaptive parameter... and The updated values ​​of both are then substituted into the control protocol in step S31.

[0043] The beneficial effects of this invention are as follows: First, the method of this invention establishes dynamic models of the leader and follower agents. By designing a framework combining neural networks and output regulators, it estimates the uncertainties in the follower model and solves the model mismatch problem between followers and the leader in heterogeneous multi-agent systems. Then, it designs a robust two-part output consistency tracking control protocol, followed by an adaptive parameter update rate, completing the design of the neural network's adaptive parameters. Finally, it applies the control protocol to the dynamic model of the heterogeneous multi-agent system. This invention designs a robust controller combining a neural network and an output regulator to solve the two-part output consistency tracking problem in heterogeneous multi-agent systems, improving the robustness of system control. The introduction of a symbolic network extends the behavior of heterogeneous multi-agent systems to two-part consistency tracking, expanding the application scenarios of the algorithm. Attached Figure Description

[0044] Figure 1 This is a flowchart of a heterogeneous multi-agent tracking control method for a neural network coupled output regulator according to the present invention.

[0045] Figure 2 This is a heterogeneous multi-agent communication topology diagram in an embodiment of the present invention.

[0046] Figure 3 This is a positional response diagram of the leader and followers in an embodiment of the present invention.

[0047] Figure 4 This is a tracking position error diagram in an embodiment of the present invention.

[0048] Figure 5 This is a system coupling gain diagram in an embodiment of the present invention.

[0049] Figure 6 This is a diagram showing the neural network estimation error in an embodiment of the present invention. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] like Figure 1 The flowchart shown below illustrates a heterogeneous multi-agent tracking control method for a neural network coupled output regulator according to the present invention. The specific steps are as follows:

[0052] S1. Establish a third-order model of the leader agent and a dynamic model of the follower agent in a multi-agent system to form a heterogeneous multi-agent system;

[0053] S2. For multi-agent systems, a fusion framework with a neural network coupled output regulator is designed to estimate the uncertainty in the follower model and solve the model mismatch problem between the follower and the leader in heterogeneous multi-agent systems.

[0054] S3. The estimated value obtained in step S2 is compensated to the controller, and then a robust two-part tracking control protocol is designed.

[0055] S4. Design the adaptive law of the control protocol established in step S3 to complete the design of the neural network adaptive parameters.

[0056] S5. Apply the control protocol to the dynamic model of the follower agent to complete the bipartition of the multi-agent system under the symbolic network. One group of agents tracks the trajectory of the leader, while the other group tracks the trajectory away from the leader, thus completing the bipartition of the followers and the bipartition of the leader's output consistency tracking.

[0057] In this embodiment, in step S1, in civilian application scenarios, the task of swarming unmanned vehicles to track aerial moving targets (UAVs) frequently occurs. The leader is the aerial UAV, and the followers are the swarming unmanned vehicle formation, as detailed below:

[0058] S11. In a heterogeneous multi-agent system, there exists one leader and n followers, connected by a symbolic network G. Let... , Let the set of all followers be represented. The model of the leader in a multi-agent system is as follows:

[0059] (1)

[0060] in, Indicates time, and These represent the leader's state and output, respectively. The derivative representing the leader's state, This represents the state matrix.

[0061] S12, the integer-order model of n follower agents is as follows:

[0062] (2)

[0063] in, and They represent the first The state and output of each follower. The derivative of the follower state, Indicates control input, It is a smooth and continuous unknown function, related to the state and time of the follower, representing the model uncertainty of the follower, and the state matrix is... and The dimensions are compatible.

[0064] S13. To achieve two-part output consistency tracking control in a heterogeneous multi-agent system, the following definition is given:

[0065] (3)

[0066] in, This means that if the output states of the i-th agent and the leader eventually converge, then... ,otherwise When the above conditions are met, it means that the two-part output consistency tracking control is completed.

[0067] In this embodiment, step S2 addresses the issue of differing configurations between leaders and followers in a multi-agent system using an output regulator. A neural network is used to estimate the uncertainties present in the follower agent model, as detailed below:

[0068] S21. Using the linear parameterization method in adaptive control theory, in equation (2) It can be parameterized in the following form:

[0069] (4)

[0070] in, Denotes the basis functions. Represents an unknown parameter vector; each agent For parameter vectors The estimated value is denoted as ; This represents the estimation error of the neural network, assuming... There exists a bound for an unknown constant. ,Right now , The estimated value is written as , The estimated value is denoted as Assuming It has the following forms:

[0071] (5)

[0072] S22. Introduce the following output regulation equation:

[0073] (6)

[0074] Among them, for The above equation has a solution. The state matrix is ​​obtained. and The goal is to ensure consistent two-part output tracking control in heterogeneous multi-agent systems.

[0075] In this embodiment, step S3 is specifically as follows:

[0076] S31. The robust adaptive state feedback protocol composed of dynamic compensators is as follows:

[0077] (7)

[0078] in, Let T denote the coupling gain, and let T denote the transpose of the matrix. , Indicates the first The follower's state of mind towards the leader The estimated quantity, Indicates the first Follower-leader status The estimated quantity, The derivative of the leader's state estimator, It is a matrix with a value greater than zero. Indicates the first A follower-leader state matrix The estimated quantity, Indicates the first An estimate of the leader's state matrix by each follower. The derivative of the leader state matrix estimator is given by... Represents a constant greater than zero. and This indicates the control parameters that need to be determined. It represents the set of all followers. Represent the adjacency matrix, if the agent Acquire intelligent agent The information, ,on the contrary, . and Representing intelligent agents respectively and intelligent agents The relationship of cooperation and confrontation between them, defined Represent a diagonal matrix, if the follower Upon receiving a message from the leader, ;otherwise .

[0079] S32. To achieve convergence of the two-part tracking error in step S13, the robust adaptive control algorithm, i.e., equation (7), needs to satisfy the following two conditions. Then, the algorithm equation (7) will solve the two-part output consistency tracking problem of system equations (1) and (2):

[0080] Condition 1: For , Represent the Herwitz matrix, and at the same time , The output regulation equation (6) is satisfied.

[0081] Condition 2: The following inequalities have a solution. :

[0082] (8)

[0083] In this embodiment, step S4 is specifically as follows:

[0084] S41. To achieve adaptive estimation in a neural network, the following adaptive law is designed:

[0085] (9)

[0086] in, , Let represent a positive definite matrix, and the Laplace matrix is ​​defined as follows: , The degree matrix is ​​defined as follows: , , , With the state matrix Consistent, ( (representing a block diagonal matrix) express 3D identity matrix Indicates the parameter The adaptive law, Indicates the parameter The update rate.

[0087] S42. Using the control protocol designed in step S41, complete the adaptive parameter... and The updated values ​​of both are then substituted into the control protocol in step S31.

[0088] The heterogeneous multi-agent communication topology diagram in this embodiment is as follows: Figure 2 As shown, there are 6 follower agents and 1 leader agent, where the node numbered 0 represents the leader. According to the principle of bipartite partitioning in symbolic networks, the above multi-agent system will be divided into two groups. : and Only the follower numbered 3 can obtain the leader's location information, and the leader's system matrix is ​​defined as follows:

[0089]

[0090] The system matrix of followers is defined as follows:

[0091]

[0092] The feedback control gain matrix of the controller shown in equation (7) is defined as follows:

[0093]

[0094] The control parameters are set as follows: .

[0095] The uncertainty design of the model in the follower system shown in equation (2) is as follows:

[0096]

[0097] for The basis functions were chosen as , and The initial value is set to any number or any matrix.

[0098] Figure 3 This represents the positional state responses of the leader and followers in a heterogeneous multi-agent system. Figure 4 This indicates that the tracking error is bounded. Figure 5 Coupling gain It can converge to a constant value. Figure 6 This represents the estimation error due to model uncertainty. It is bounded.

[0099] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A heterogeneous multi-agent tracking control method for a neural network coupled output regulator, comprising the following steps: S1. Establish a third-order model of the leader agent and a dynamic model of the follower agent in a multi-agent system to form a heterogeneous multi-agent system; in, The leader is an aerial drone, and the followers are a swarm of unmanned vehicles. S2. For multi-agent systems, a fusion framework with a neural network coupled output regulator is designed to estimate the uncertainty in the follower model and solve the model mismatch problem between the follower and the leader in heterogeneous multi-agent systems. S3. The estimated value obtained in step S2 is compensated to the controller, and then a robust two-part tracking control protocol is designed. Step S3 is as follows: S31. The robust adaptive state feedback protocol composed of dynamic compensators is as follows: （1）； in, Indicates time, Indicates control input, Indicates the first The state of a follower Denotes the basis functions, for each agent. For parameter vectors The estimated value is denoted as , A bound representing an unknown constant representing the estimation error of a neural network. The estimated value, Let T denote the coupling gain, and let T denote the transpose of the matrix. , Indicates the first The follower's state of mind towards the leader The estimated quantity, Indicates the first Follower-leader status The estimated quantity, The derivative of the leader's state estimator, It is a matrix with a value greater than zero. This means that if the output states of the i-th agent and the leader eventually converge, then... ,otherwise , Indicates the first A follower-leader state matrix The estimated quantity, Indicates the first An estimate of the leader's state matrix by each follower. The derivative of the leader state matrix estimator is given by... Represents a constant greater than zero. and This indicates the control parameters that need to be determined. It represents the set of all followers. Represent the adjacency matrix, if the agent Acquire intelligent agent The information, ,on the contrary, ; and Representing intelligent agents respectively and intelligent agents The relationship of cooperation and confrontation between them, defined Represent a diagonal matrix, if the follower Upon receiving a message from the leader, ;otherwise ; S32. To achieve convergence of the two-part tracking error, the robust adaptive control algorithm, i.e., equation (1), needs to satisfy the following two conditions. Then, equation (1) will solve the two-part output consistency tracking problem of the leader and follower models of the system: Condition 1: For , Represent the Herwitz matrix, and at the same time , Satisfy the output regulation equation ; Among them, for The above equation has a solution. The state matrix is ​​obtained. and The objective is to ensure consistent output tracking control in heterogeneous multi-agent systems. Condition 2: The following inequalities have a solution. : （2）； S4. Design the adaptive law of the control protocol established in step S3 to complete the design of the neural network adaptive parameters. S5. Apply the control protocol to the dynamic model of the follower agent to complete the bipartition of the multi-agent system under the symbolic network. One group of agents tracks the trajectory of the leader, while the other group tracks the trajectory away from the leader, thus completing the bipartition of the followers and the bipartition of the leader's output consistency tracking.

2. The heterogeneous multi-agent tracking control method for a neural network coupled output regulator according to claim 1, characterized in that, The specific steps of S1 are as follows: S11. In a heterogeneous multi-agent system, there exists one leader and n followers, connected by a symbolic network G. Let... , Let the set of all followers be represented. The model of the leader in a multi-agent system is as follows: （3）； in, Indicates time, and These represent the leader's state and output, respectively. The derivative representing the leader's state, Represents the state matrix; S12, the integer-order model of n follower agents is as follows: （4）； in, and They represent the first The state and output of each follower. The derivative of the follower state, Indicates control input, It is a smooth and continuous unknown function, related to the state and time of the follower, representing the model uncertainty of the follower, and the state matrix is... and The dimensions are compatible; S13. To achieve two-part output consistency tracking control in a heterogeneous multi-agent system, the following definition is given: （5）； in, This means that if the output states of the i-th agent and the leader eventually converge, then... ,otherwise When the above conditions are met, it means that the two-part output consistency tracking control is completed.

3. The heterogeneous multi-agent tracking control method for a neural network coupled output regulator according to claim 2, characterized in that, Step S2 is as follows: S21. Using the linear parameterization method in adaptive control theory, in equation (4) It can be parameterized in the following form: （6）； in, Denotes the basis functions. Represents an unknown parameter vector; each agent For parameter vectors The estimated value is denoted as ; This represents the estimation error of the neural network, assuming... There exists a bound for an unknown constant. ,Right now , The estimated value is written as , The estimated value is denoted as Assuming It has the following forms: （7） S22. Introduce the following output regulation equation: （8）； Among them, for The above equation has a solution. The state matrix is ​​obtained. and The goal is to ensure consistent two-part output tracking control in heterogeneous multi-agent systems.

4. The heterogeneous multi-agent tracking control method for a neural network coupled output regulator according to claim 3, characterized in that, Step S4 is as follows: S41. To achieve adaptive estimation in a neural network, the following adaptive law is designed: （9）； in, , Let represent a positive definite matrix, and the Laplace matrix is ​​defined as follows: , The degree matrix is ​​defined as follows: , , , With the state matrix Consistent Represents a block diagonal matrix. express 3D identity matrix Indicates the parameter The adaptive law, Indicates the parameter The update rate; S42. Using the control protocol designed in step S41, complete the adaptive parameter... and The updated values ​​of both are then substituted into the control protocol in step S31.

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