Multi-agent data-driven adaptive bisection tracking control method and device

Abstract

The application relates to the technical field of automatic control, and discloses a kind of multi-agent data-driven adaptive two-part tracking control method and device.The application designs a kind of completely distributed direct data-driven adaptive consensus protocol for the cooperative control problem of multi-agent system under unknown dynamics model and the complex scene that dynamic leader control input is non-zero and unknown, the protocol only uses input data matrix, state data matrix and state derivative data matrix in the sampling measurement value of leader agent and follower agent, and on-line adaptive adjustment control parameter and coupling weight matrix.Thereby, without the condition of system accurate model and global network information, two-part tracking consensus of leader-follower multi-agent system is realized under the condition that dynamic leader exists.The method significantly improves the flexibility, scalability and engineering applicability of the control system.

Description

Technical Field

[0001] This application relates to the field of automatic control technology, and in particular to a multi-agent data-driven adaptive binary tracking control method and apparatus. Background Technology

[0002] Consistency in multi-agent systems is a core fundamental problem in distributed control, demonstrating significant application value in modern engineering fields such as sensor networks, UAV swarms, and robot collaboration. The key to solving this problem lies in designing a distributed consensus protocol for each agent that relies solely on local neighbor information to collaboratively adjust its behavior and achieve group goals. Significant progress has been made in research on this protocol, with existing results broadly covering various agent models, from simple single / dual integrator dynamics to general linear and nonlinear dynamics, and fully considering different communication topologies such as undirected and directed communication. The leader-tracking problem is a deepening and extension of the consensus problem. This problem requires that the states of all agents be synchronized to the state of a dynamic leader, and its core is also the design of a distributed controller. However, traditional research is mostly based on the ideal assumption of pure cooperation between agents. In practical applications, such as social networks and offensive / defensive scenarios, mixed interactions of cooperation and competition are common.

[0003] Therefore, the "binary consensus tracking" problem has been proposed as an important branch and has attracted widespread attention. Within this framework, agents are explicitly divided into two groups: one group strives to reach consensus with the leader's reference signal (cooperation), while the other group strives to have its state opposite to the reference signal (competition), thus more accurately characterizing complex hybrid interaction networks. However, existing modeling of leader dynamics still has significant limitations. In many cutting-edge applications (such as obstacle avoidance in unmanned swarms), the leader's control system typically needs to introduce non-zero and time-varying control inputs to achieve complex global tasks. This constitutes a new technical challenge. Unfortunately, most current research, in order to simplify the problem, makes unrealistic assumptions: that the leader's control input is either always zero, or its precise value or upper bound information can be directly obtained by all or some of the follower agents. This severely limits the applicability of existing protocols in practical engineering.

[0004] Furthermore, existing consensus protocols for multi-agent systems face a dual technical bottleneck in practical applications: First, mainstream protocols generally adopt a model-based design paradigm, and their control performance is highly dependent on the accurate understanding of the agent's dynamic model. However, in complex engineering environments, due to factors such as parameter perturbations, external interference, and unmodeled dynamics, obtaining an accurate mathematical model is often extremely difficult. Second, model-free methods proposed to overcome the problem of unknown models (such as system identification and adaptive dynamic programming) utilize data to reconstruct the model through the "identify first, then control" paradigm, but they suffer from high computational costs due to the identification process. Summary of the Invention

[0005] This application provides a multi-agent data-driven adaptive binary tracking control method and apparatus. Addressing the cooperative control problem of multi-agent systems with unknown dynamic models, and complex scenarios where the dynamic leader's control input is non-zero and unknown, this application designs a fully distributed direct data-driven adaptive consensus protocol. This protocol utilizes only the input data matrix, state data matrix, and state derivative data matrix from the sampled measurements of the leader and follower agents to adaptively adjust control parameters and coupling weight matrices online. This enables multiple follower agents to achieve binary tracking consensus in the presence of a dynamic leader, even without a system model or global network information. This method plays a significant role in improving the flexibility, scalability, and engineering applicability of control systems.

[0006] In a first aspect, embodiments of this application provide a multi-agent data-driven adaptive binary tracking control method, including: Establish a multi-agent system and communication topology; determine the Laplace matrix based on the communication topology; wherein the multi-agent system includes one leader agent and... A follower agent; the communication topology is used to describe The information interaction relationship between the follower agents; the Laplace matrix is ​​used to describe the structural characteristics of the communication topology; Regarding the Any one of the follower agents collects sampled measurement values ​​offline at discrete time points to form a control input data matrix, a state data matrix, and a state derivative data matrix; Based on the leader agent and the follower agent, a binary tracking error is defined; the time derivative of the binary tracking error is calculated to establish an error system. Based on the communication topology, a data-driven adaptive consensus protocol is established; the data-driven adaptive consensus protocol includes an adaptive rate and control parameters, and the adaptive rate includes a coupling weight matrix. Based on the follower agent, the leader agent, and the Laplace matrix, the data-driven adaptive consistency protocol and the error system are introduced to establish a complete error system. Based on the adaptive rate and Lyapunov function, the stability conditions of the complete error system are established. Using the control input data matrix, state data matrix, and state derivative data matrix, the stability condition is solved to determine the control parameters and coupling weight matrix. Control using the aforementioned control parameters and coupling weight matrix The aforementioned follower agent operates.

[0007] In some embodiments, the dynamic process of the follower agent is represented by the following formula: ; in, Indicates the first A follower intelligent agent in time The state derivative under the given conditions, for A set of 3D real vectors; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; Indicates the first A follower intelligent agent in time The following state; This represents the unknown second coefficient matrix; Indicates the first A follower intelligent agent in time The control input below, express A set of 3D real vectors; This represents the total number of follower agents.

[0008] In some embodiments, the dynamic process of the leader agent is represented by the following formula: ; in, This indicates that the leader agent is in time. The state derivative under the given conditions; This represents the first coefficient matrix, which is unknown. This indicates that the leader agent is in time. The following state, This indicates that the leader agent is in time. The state of the next One component; This represents the unknown second coefficient matrix; This indicates that the leader agent is in time. Non-zero control inputs below.

[0009] In some embodiments, the communication topology is represented as: ; in, Represents the communication topology; Represents a set of nodes, the set of nodes including A follower agent, wherein each follower agent is a node; Let the set of edges be represented, which includes several edges, and each edge represents an information interaction channel between two different follower agents. This represents a symbolic weighted adjacency matrix. Indicates the first The follower agent and the first Information interaction relationships between follower agents. ; ; Indicating cooperation, It indicates competition. and These represent the indices of the follower agents.

[0010] In some embodiments, the Laplace matrix is ​​represented as: ; in, Let the Laplace matrix be denoted as . matrix; Represents a diagonal matrix; ; ; This represents a symbolic weighted adjacency matrix. ,for matrix; Indicates the first The follower agent and the first Information interaction relationships between follower agents. ; ; Denotes the first Laplace matrix Line number Column elements, ; ; when middle hour, , , ; when middle hour, , .

[0011] In some embodiments, the error system is expressed according to the following formula: ; in, Indicates the first Follower and leader agents in time The time derivative of the binary tracking error under the given conditions; Indicates the first A follower intelligent agent in time The state derivative under the given conditions; Indicates the first A binary symbol for a follower agent. ; This indicates that the leader agent is in time. The state derivative under the given conditions; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; Indicates the first Follower and leader agents in time The following binary tracking error; This represents the unknown second coefficient matrix; Indicates the first A follower intelligent agent in time The control input below; This indicates that the leader agent is in time. Non-zero control inputs below.

[0012] In some embodiments, the data-driven adaptive consensus protocol is represented by the following formula: ; in, Indicates the first A follower intelligent agent in time The control input below; Indicates the first A follower intelligent agent in time Adaptive rate under; This represents the first gain matrix; ; This represents the control input data matrix; Represents the controller parameter matrix. express A set of 3D real matrices; Represents the state data matrix; Indicates the first A follower intelligent agent in time Local neighborhood error; ; The total number of follower agents. For indexing follower agents, Indicates the first The follower agent and the first Information interaction relationships between follower agents. Indicates the first A follower intelligent agent in time The following state, Indicates the first A follower intelligent agent in time The following state, Indicates the connection weights of the leader agent. Indicates the first A binary symbol for a follower agent. This indicates that the leader agent is in time. The following state; Represents a symbolic function; This represents the second gain matrix; ; Represents the state derivative data matrix; Represents a block matrix with two rows and one column; express transpose and The inverse matrix of the product; express OK A matrix of columns; express OK The identity matrix of columns, express OK The zero matrix of the column; the control parameters include the first gain matrix and the second gain matrix; The adaptive rate is expressed by the following formula: ; in, Indicates the first A follower intelligent agent in time The rate of change of the adaptive rate under the condition; Represents the coupling weight matrix; ; Represents the auxiliary matrix. .

[0013] In some embodiments, the complete error system is represented by the following formula: ; in, The time derivative of the augmented error vector; Represents a column vector; for Indicates the first Follower and leader agents in time The transpose of the binary tracking error; express identity matrix; Indicates the Kronecker product; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; express 3D diagonal matrix Indicates the first A follower intelligent agent in time Adaptive rate under; Represents the symbolic Laplace matrix; ; Represents the Laplace matrix; Represents the restraint matrix. , ; Indicates the connection weights of the leader agent; This represents the unknown second coefficient matrix; This represents the first gain matrix; This represents the second gain matrix; Indicated by The sign function for the element; Represents a diagonal matrix; Indicates the first A binary symbol for a follower agent; Indicates that all elements are 1 3D column vector; This indicates that the leader agent is in time. Non-zero control inputs below.

[0014] In some embodiments, the stability condition is expressed by the following formula: ; ; ; in, Represents the state derivative data matrix; Represents the controller parameter matrix. express A set of 3D real matrices; Represents the state data matrix; , Represents the target data matrix; Represents a block matrix with two rows and one column; This represents the control input data matrix; Represents the state data matrix; express transpose and The inverse matrix of the product; Represents a matrix with m+n rows and 2m columns; express OK The identity matrix of columns, express OK The zero matrix of columns.

[0015] Secondly, this application provides a multi-agent data-driven adaptive binary tracking control device, comprising: The first establishment unit is used to establish a multi-agent system and a communication topology; and to determine a Laplace matrix based on the communication topology; wherein the multi-agent system includes one leader agent and... A follower agent; the communication topology is used to describe The information interaction relationship between the follower agents; the Laplace matrix is ​​used to describe the structural characteristics of the communication topology; Collection unit, used for the collection of the Any one of the follower agents collects sampled measurement values ​​offline at discrete time points to form a control input data matrix, a state data matrix, and a state derivative data matrix; The second establishment unit is used to define a binary tracking error based on the leader agent and the follower agent; and to calculate the time derivative of the binary tracking error to establish an error system. The third establishment unit is used to establish a data-driven adaptive consensus protocol based on the communication topology; the data-driven adaptive consensus protocol includes an adaptive rate and control parameters, and the adaptive rate includes a coupling weight matrix; The fourth establishment unit is used to establish a complete error system based on the follower agent, the leader agent, and the Laplace matrix, by introducing the data-driven adaptive consistency protocol and the error system. The fifth establishment unit is used to establish the stability conditions of the complete error system based on the adaptive rate and the Lyapunov function. The determining unit is used to solve the stability condition using the control input data matrix, the state data matrix, and the state derivative data matrix to determine the control parameters and the coupling weight matrix. Control unit, used to control using the control parameters and coupling weight matrix The aforementioned follower agent operates.

[0016] The above embodiments provide a multi-agent data-driven adaptive binary tracking control method and apparatus. This method addresses the cooperative control problem of multi-agent systems with unknown dynamic models, as well as complex scenarios where the dynamic leader's control input is non-zero and unknown. This application designs a fully distributed direct data-driven adaptive consensus protocol. This protocol utilizes only the input data matrix, state data matrix, and state derivative data matrix from the sampled measurements of the leader and follower agents to adaptively adjust control parameters and coupling weight matrices online. This enables multiple follower agents to achieve binary tracking consensus in the presence of a dynamic leader, even without a system model or global network information. This method plays a crucial role in improving the flexibility, scalability, and engineering applicability of control systems. Attached Figure Description

[0017] Figure 1 An exemplary flowchart is shown for a multi-agent data-driven adaptive binary tracking control method provided according to some embodiments; Figure 2 An exemplary communication topology diagram is shown in one embodiment; Figure 3 An example is shown showing the adaptation rates for different follower agents in one embodiment; Figure 4(a) shows a schematic diagram of the first component consistency of the leader-following state achieved by 5 follower agents under data-driven control and the consistency achieved by 2 additional follower agents after 20 seconds. Figure 4(b) is a schematic diagram showing the consistency of the second component of the leader-following state achieved by 5 follower agents under data-driven control, and the consistency achieved by 2 additional follower agents after 20 seconds. Figure 5 An exemplary schematic diagram of a multi-agent data-driven adaptive binary tracking control device is shown, according to some embodiments. Detailed Implementation

[0018] To make the objectives and implementation methods of this application clearer, the exemplary implementation methods of this application will be clearly and completely described below with reference to the accompanying drawings of the exemplary embodiments of this application. Obviously, the exemplary embodiments described are only some embodiments of this application, and not all embodiments.

[0019] It should be noted that the brief descriptions of terms in this application are only for the convenience of understanding the embodiments described below, and are not intended to limit the embodiments of this application. Unless otherwise stated, these terms should be understood in their ordinary and common meaning.

[0020] The terms "first," "second," "third," etc., used in the specification and accompanying drawings of this application are used to distinguish similar or related objects or entities, and do not necessarily imply a specific order or sequence, unless otherwise specified. It should be understood that such terms can be used interchangeably where appropriate.

[0021] The terms “comprising” and “having”, and any variations thereof, are intended to cover but not exclude inclusion, for example, a product or device that includes a range of components is not necessarily limited to all of the components that are clearly listed, but may include other components that are not clearly listed or that are inherent to such product or device.

[0022] To address the aforementioned technical problems, this application provides a multi-agent data-driven adaptive binary tracking control method and apparatus. This method addresses the cooperative control problem of multi-agent systems with unknown dynamic models, as well as complex scenarios where the dynamic leader's control input is non-zero and unknown. This application designs a fully distributed direct data-driven adaptive consensus protocol. This protocol utilizes only the input data matrix, state data matrix, and state derivative data matrix from the sampled measurements of the leader and follower agents to adaptively adjust control parameters and coupling weight matrices online. This enables multiple follower agents to achieve binary tracking consensus in the presence of a dynamic leader, even without a system model or global network information. This method plays a crucial role in improving the flexibility, scalability, and engineering applicability of control systems.

[0023] Figure 1 A flowchart of a multi-agent data-driven adaptive binary tracking control method according to some embodiments is illustrated. The method includes steps S100-S700.

[0024] S100. Establish a multi-agent system and communication topology; determine the Laplace matrix based on the communication topology.

[0025] The multi-agent system includes one leader agent and... A follower agent; the communication topology is used to describe The information interaction relationship between the follower agents; the Laplace matrix is ​​used to describe the structural characteristics of the communication topology.

[0026] In this embodiment of the application, by A multi-agent system consists of several agents, including one leader agent and... It consists of a group of follower intelligent agents.

[0027] In some embodiments, it is assumed Each follower agent possesses a general linear dynamic characteristic. The dynamic process of the follower agent is expressed by the following formula: (1) in, Indicates the first A follower intelligent agent in time The state derivative under the given conditions, for A set of 3D real vectors; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; Indicates the first A follower intelligent agent in time The following state; This represents the unknown second coefficient matrix; Indicates the first A follower intelligent agent in time The control input below, express The set of 3D real vectors serves as the external control input; Let be the total number of follower agents. Assume ( and ) Matrix pairs are stable.

[0028] In some embodiments, the dynamic process of the leader agent is represented by the following formula: (2) in, This indicates that the leader agent is in time. The state derivative under the given conditions; This represents the first coefficient matrix, which is unknown. This indicates that the leader agent is in time. The following state, This indicates that the leader agent is in time. The state of the next One component; This represents the unknown second coefficient matrix; This indicates that the leader agent is in time. Non-zero control inputs below. It can represent the state vector of an agent network.

[0029] In some embodiments, the communication topology is shown in the figure. definition.

[0030] The communication topology is represented as follows: (3) in, Represents the communication topology; Represents a set of nodes, the set of nodes including A follower agent, wherein each follower agent is a node; Let the set of edges be represented, which includes several edges, and each edge represents an information interaction channel between two different follower agents. This represents a symbolic weighted adjacency matrix. Indicates the first The follower agent and the first Information interaction relationships between follower agents. ; ; Indicating cooperation, It indicates competition. and These represent the indices of the follower agents.

[0031] In some embodiments, the Laplace matrix is ​​represented as: (4) in, Let the Laplace matrix be denoted as . matrix; Represents a diagonal matrix; ; ; This represents a symbolic weighted adjacency matrix. ,for matrix; Indicates the first The follower agent and the first Information interaction relationships between follower agents. ; ; Denotes the first Laplace matrix Line number Column elements, ; ; when middle hour, , , ; when middle hour, , .

[0032] S200, regarding the above Any one of the follower agents collects sampled measurements offline at discrete time points, forming a control input data matrix, a state data matrix, and a state derivative data matrix.

[0033] In this embodiment of the application, due to the first coefficient matrix Second coefficient matrix The fact that all these elements are unknown constitutes the core challenge in designing the controller in the embodiments of this application, rendering all existing design methods that rely on model knowledge inapplicable. Therefore, the key to this application lies in constructing a novel data-driven framework that does not depend on a system model, in order to achieve model-free adaptive control law design.

[0034] Assuming that data for each follower agent can be collected offline at discrete time points ( Measurements sampled during the dynamic process of the follower agent: (5) in, Indicates the first Measurements of each follower agent; Indicates the first A follower intelligent agent in time The control input below; Indicates the sampling time interval. ; Indicates the number of samples collected. ; Indicates the first A follower intelligent agent in time The following state; Indicates the first A follower intelligent agent in time The state derivative under the given conditions.

[0035] In the embodiments of this application, Including the The control inputs, states, and state derivatives of each follower agent are used to obtain a set of input-state samples to verify the dynamic process of the follower agent (Equation (1)). Within the scope of the situation. Based on the dynamic process of the follower agent (Equation (1)), it is assumed that each agent has the same system matrix. and For ease of discussion, we can choose one of the follower agents (labeled as...). The corresponding first coefficient matrix and second coefficient matrix are labeled as follows: and These measurements were collected offline to form the following data matrix: (6) (7) (8) in, This represents the control input data matrix; Represents the state data matrix; This represents the state derivative data matrix. These data satisfy... ;in, for A set of 3D real matrices.

[0036] S300. Based on the leader agent and the follower agent, define a binary tracking error; calculate the time derivative of the binary tracking error to establish an error system.

[0037] In this embodiment, binary tracking consistency is achieved based on the dynamic process of the leader agent (Formula (2)) and the dynamic process of the follower agent (Formula (1)), requiring the definition of tracking error. From Formula (1) and Formula (2), we can obtain the... The binary tracking error of the follower agent relative to the leader agent is as follows: (9) in, Indicates the first Follower and leader agents in time The following binary tracking error; Indicates the first A follower intelligent agent in time The following state; Indicates the first A binary symbol for a follower agent. ; This indicates that the leader agent is in time. The current state.

[0038] when Time The relationship between the follower agent and the leader agent is cooperative; when Time The follower and leader agents are in a competitive relationship.

[0039] In some embodiments, the error system is expressed according to the following formula: (10) in, Indicates the first Follower and leader agents in time The time derivative of the binary tracking error under the given conditions; Indicates the first A follower intelligent agent in time The state derivative under the given conditions; Indicates the first A binary symbol for a follower agent. ; This indicates that the leader agent is in time. The state derivative under the given conditions; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; Indicates the first Follower and leader agents in time The following binary tracking error; This represents the unknown second coefficient matrix; Indicates the first A follower intelligent agent in time The control input below; This indicates that the leader agent is in time. Non-zero control inputs below.

[0040] S400. Based on the communication topology, establish a data-driven adaptive consensus protocol; the data-driven adaptive consensus protocol includes an adaptive rate and control parameters, and the adaptive rate includes a coupling weight matrix.

[0041] In this embodiment, an adaptive consensus protocol is adopted, and considering the non-zero control input of the leader agent, a new distributed data-driven protocol is proposed, namely the data-driven adaptive consensus protocol. This protocol only uses the input data matrix, state data matrix and state derivative data matrix in the sampled measurement values ​​of the leader agent and the follower agent to adaptively adjust the control parameters and coupling weight matrix online, and can achieve binary tracking consensus without any global information.

[0042] In some embodiments, the data-driven adaptive consensus protocol is represented by the following formula: (11) in, Indicates the first A follower intelligent agent in time The control input below; Indicates the first A follower intelligent agent in time Adaptive rate under; Represents the first gain matrix; ; This represents the control input data matrix; Represents the controller parameter matrix. express A set of 3D real matrices; Represents the state data matrix; Indicates the first A follower intelligent agent in time Local neighborhood error; ; The total number of follower agents. For indexing follower agents, Indicates the first The follower agent and the first The information interaction relationship between the following intelligent agents (also known as the first) The follower agent and the first (coupling strength value between follower agents) Indicates the first A follower intelligent agent in time The following state, Indicates the first A follower intelligent agent in time The following state, This represents the connection weights between the leader agent and the second agent (also known as the connection weights between the leader agent and the third agent). (the binding connection weight of each follower agent). Indicates the first A binary symbol for a follower agent. This indicates that the leader agent is in time. The following state; Represents a symbolic function; This represents the second gain matrix; ; Represents the state derivative data matrix; Represents a block matrix with two rows and one column; express transpose and The inverse matrix of the product; express OK A matrix of columns; express OK The identity matrix of columns, express OK The zero matrix of the column; the control parameters include the first gain matrix and the second gain matrix; The adaptive rate is expressed by the following formula: (12) in, Indicates the first A follower intelligent agent in time The rate of change of the adaptive rate under the condition; Represents the coupling weight matrix; ; Represents the auxiliary matrix. ; This represents the second gain matrix.

[0043] S500: Based on the follower agent, the leader agent, and the Laplace matrix, the data-driven adaptive consistency protocol and the error system are introduced to establish a complete error system.

[0044] In this embodiment, a complete error system is established by introducing a data-driven adaptive consensus protocol (formula (11)) and an error system (formula (10) based on the dynamic process of the follower agent (formula (1)), the dynamic process of the leader agent (formula (2)) and the Laplace matrix (formula (4)).

[0045] The complete error system is expressed by the following formula: (13) in, The time derivative of the augmented error vector; Represents a column vector; for Indicates the first Follower and leader agents in time The transpose of the binary tracking error; express identity matrix; Indicates the Kronecker product; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; express 3D diagonal matrix Indicates the first A follower intelligent agent in time Adaptive rate under; Represents the symbolic Laplace matrix; ; Represents the Laplace matrix; Represents the restraint matrix. , ; Indicates the connection weights of the leader agent; This represents the unknown second coefficient matrix; This represents the first gain matrix; This represents the second gain matrix; Indicated by The sign function for the element; Represents a diagonal matrix; Indicates the first A binary symbol for a follower agent; Indicates that all elements are 1 3D column vector; This indicates that the leader agent is in time. Non-zero control inputs below.

[0046] In this embodiment of the application, the first If a follower agent has a connection with the leader agent, i.e., there is information exchange, then ,otherwise .

[0047] S600. Based on the adaptive rate and Lyapunov function, establish the stability conditions of the complete error system.

[0048] In this embodiment, to ensure the effectiveness of the data-driven adaptive consensus protocol, the core task is to establish sufficient conditions to guarantee the asymptotic stability of the closed-loop error system. Specifically, graph theory, Lyapunov stability theory, and matrix analysis techniques are comprehensively applied: First, graph theory is used to characterize the cooperative-competitive topology of the agent network; then, a suitable Lyapunov function is constructed, and its derivative along the error system trajectory is analyzed; finally, matrix theory is used to process the coupling weight matrix in the system dynamics, deriving sufficient conditions to ensure the global asymptotic stability of the error system, thereby theoretically guaranteeing the implementation of binary tracking consensus.

[0049] In some embodiments, the Lyapunov function is expressed according to the following formula: (14) in, This represents the total energy of the error system; This indicates that follower and leader agents are in time. The transpose of the binary tracking error; Represents the symbolic Laplace matrix; ; Represents the Laplace matrix; Represents the restraint matrix. , ; Indicates the connection weights of the leader agent; This represents a symmetric positive definite metric matrix, used to define the quadratic norm of the bisection tracking error; This indicates that follower and leader agents are in time. The following binary tracking error; Indicates the first A follower intelligent agent in time Adaptive rate under; Represents positive constants; This represents the total number of follower agents.

[0050] The control objective of the method described in this application is to make the complete error system between all follower agents and the leader agent asymptotically converge to zero under the action of the data-driven adaptive consensus protocol.

[0051] In this embodiment of the application, the stability condition, that is, the sufficient condition for the asymptotic stability of the complete error system (Equation (13)), includes: (15) (16) (17) in, Represents the state derivative data matrix; Represents the controller parameter matrix. express A set of 3D real matrices; Represents the state data matrix; , Represents the target data matrix; Represents a block matrix with two rows and one column; This represents the control input data matrix; Represents the state data matrix; express transpose and The inverse matrix of the product; Represents a matrix with m+n rows and 2m columns; express OK The identity matrix of columns, express OK The zero matrix of columns.

[0052] The controller parameter matrix Y needs to satisfy the three inequalities in formulas (15), (16) and (17).

[0053] S600. Using the control input data matrix, state data matrix, and state derivative data matrix, solve the stability condition to determine the control parameters and coupling weight matrix.

[0054] The control parameters include a first gain matrix and a second gain matrix.

[0055] In this embodiment, the controller parameter matrix that guarantees the asymptotic stability of the complete error system is determined by constructing linear matrix inequality conditions based on matrix theory (formulas (15), (16) and (17)). This transforms the distributed binary consensus problem between multiple followers and a leader into an equivalent stability problem of an error system; and it is achieved by designing the first gain matrix in a data-driven adaptive controller. Second gain matrix This enables the tracking error system to achieve asymptotic stability, thus strictly guaranteeing the realization of binary consistency between the multi-follower agent system and the dynamic leader under the condition that the system model is completely unknown.

[0056] S700: Control the operation of N follower agents using the control parameters and coupling weight matrix.

[0057] In this application, addressing the cooperative control problem of multi-agent systems under unknown dynamic models and complex scenarios where the dynamic leader's control input is non-zero and unknown, a fully distributed direct data-driven adaptive consensus protocol is designed. This protocol utilizes only the input data matrix, state data matrix, and state derivative data matrix from the sampled measurements of the leader and follower agents to adaptively adjust control parameters and coupling weight matrices online. This enables multiple follower agents to achieve binary tracking consensus in the presence of a dynamic leader, even without a system model or global network information. This method plays a crucial role in improving the flexibility, scalability, and engineering applicability of control systems, completely eliminating the dependence on precise mathematical models and global information, and providing a general solution for achieving reliable cooperative control in uncertain environments.

[0058] This application overcomes the dependence of traditional methods on precise system mathematical models and global communication network information, improving the reliability, flexibility, and scalability of the system in real uncertain scenarios. The technical solution mainly includes the following points: (1) Direct data-driven: The design and implementation of the control protocol does not depend on the system's dynamic model, utilizing only offline collected measurements. (2) Fully distributed adaptive consensus protocol: An adaptive law is designed that can automatically adjust controller parameters or coupling weight matrices online, allowing each agent to exchange information only with its neighbors without needing to know the global information of the entire network. This application provides a model-free, fully distributed adaptive control solution. It is particularly suitable for scenarios where system models are difficult to obtain accurately, communication topologies are complex or may change, and high reliability and self-organization capabilities are required, such as UAV formation collaborative search, smart grid distributed frequency recovery, and robot swarm collaborative operations.

[0059] Compared with traditional multi-agent cooperative control methods that rely on precise mathematical models, only support pure cooperative relationships, and have limited adaptive capabilities, this application achieves fundamental breakthroughs and significant innovations in the following aspects: (1) Existing multi-agent consensus protocols heavily rely on precise dynamic models of agents. This application innovatively proposes a direct data-driven control framework that requires no system model. The design and online operation of all controllers depend only on local measurements, fundamentally eliminating the dependence on any prior model knowledge and exhibiting inherent robustness to model uncertainties.

[0060] (2) Existing research is almost entirely limited to networks where agents only have cooperative relationships. This application innovatively introduces symbolic graph theory to solve the binary tracking consistency problem in cooperative-adversarial hybrid relationship networks. This enables the system to achieve structured collaboration even in scenarios with competitive or adversarial relationships (such as competitive tasks and opinion formation).

[0061] (3) Breakthrough in Problem Scenarios: Handling Unknown and Active Dynamic Leaders. Traditional Limitations: In tracking control involving leaders, it is usually assumed that the leader's control input is zero or can be obtained by all followers. This application innovatively overcomes the extremely challenging problem that the leader's control input is non-zero and completely unknown to all followers. This enables the method to be applied to real-world scenarios where leaders are performing complex dynamic tasks, greatly expanding the application boundaries.

[0062] (4) Comprehensive upgrade of adaptive architecture. Most traditional adaptive consensus protocols rely on global network information for parameter tuning or cannot be dynamically adjusted online, thus lacking true scalability. This application innovatively designs a fully distributed non-smooth protocol and adaptive law, which automatically adjusts control parameters, eliminating the dependence on global network information and enabling the system to have excellent scalability and deployment convenience.

[0063] This application constructs an unprecedented, powerful, and flexible multi-agent cooperative control solution through data-driven approaches, fully distributed adaptive mechanisms, and comprehensive processing capabilities for complex network relationships (including symbolic graphs and directed graphs) and dynamic scenarios (including unknown active leaders). It is particularly suitable for high-level tasks such as cooperative encirclement of drone swarms in adversarial environments, autonomous frequency recovery of distributed energy resources in smart grids, and exploration and collaboration of robot teams in unknown model environments, laying a core technological foundation for the reliable and autonomous operation of complex systems in the real world.

[0064] The method in this embodiment is a distributed adaptive control protocol that does not rely on system models and global network information. By utilizing the input data matrix, state data matrix, and state derivative data matrix from the sampled measurements of the leader and follower agents to adjust control parameters online, this protocol can simultaneously solve two types of problems: first, achieving group consistency among heterogeneous multi-agent groups when the agent model is unknown; and second, achieving binary tracking consistency among followers when a dynamic leader with unknown non-zero control input exists. This method is fully distributed, highly adaptive, and highly scalable, making it suitable for a wider range of engineering applications.

[0065] The embodiments of this application design an adaptive law for each edge in the communication topology, enabling it to adjust the coupling weights online. It utilizes only the relative state information between the agent and its neighbors, without requiring any system model knowledge or global network information. This effectively solves the problem of dual dependence on accurate models and global information in existing technologies, while ensuring asymptotic tracking performance in cooperative-competitive hybrid interactive networks.

[0066] In a specific example, the system consists of a leader agent and five follower agents, whose interaction network includes both cooperative and competitive relationships.

[0067] Step 1: Propose a dynamic model description for the multi-agent system: ; ; In the formula Indicates the first A follower intelligent agent in time The state is defined by two components: a first component and a second component. Assume... and unknown.

[0068] A topology is proposed for a multi-follower agent with five agents. Used to represent the cooperative and competitive communication relationships between intelligent agents, where Represents the set of following nodes. Represents an edge set. This represents a symbolic weighted adjacency matrix. Indicates the first The follower agent and the first Information interaction relationships between follower agents (symbolic representation of interaction relationships between agents): Indicating cooperation, This indicates competition. The leader node is marked as 0. This represents the constraint matrix. In this embodiment, the communication topology diagram is as follows: Figure 2 As shown, in Figure 2 In the diagram, the node marked 0 in the circle is the leader agent, and the nodes marked 2, 1, 3, 5, and 4 in the circle (hereinafter referred to as node 2, node 1, node 3, node 5, and node 4) are the follower agents. Figure 2 In the communication topology, the constraint connection weight between the leader agent and node 1 is 2, the coupling strength between node 1 and node 2 is 1, the coupling strength between node 1 and node 3 is -1.5, the coupling strength between node 2 and node 5 is -1, and the coupling strength between node 4 and node 5 is 1.

[0069] The Laplace matrix is ​​as follows: ; .

[0070] Step 2: Collecting and measuring experimental data: Assuming system matrix and Unknown. To verify the effectiveness of the proposed distributed data-driven adaptive consensus protocol, system data was collected through open-loop experiments. Control input. The initial state of the system was uniformly and randomly selected within the interval [0,1]. A total of 10 sets of data samples were collected in the experiment: ; ; ; Sampling interval The amount of data is sufficient to satisfy the assumptions.

[0071] Step 3: Design the adaptive controller In this example, to achieve data-driven binary state consistency for leader-following multi-agent systems, a data-based distributed adaptive controller for the five followers is designed as follows: Non-zero leader control input: Data-driven adaptive control protocol: ; Adaptive rate Designed as follows: ; Based on the data from the second step, solve the system of inequalities: ; ; This leads to the data-driven controller gain matrix. and The key matrix for coupling weight design, namely the coupling weight matrix. as follows: ; ; .

[0072] In the simulation, for all edges Set initial adaptive weights The dynamic evolution of these weights is as follows: Figure 3 As shown, in Figure 3 The display shows the adaptation rates corresponding to different follower agents. These represent the adaptation rates corresponding to different follower agents. From 0s to 20s, there are 5 follower agents with corresponding adaptation rates. After 20s, 2 more follower agents are added. Figure 3 This reflects the protocol's self-regulating ability during operation. Finally, the system's state convergence results are shown in Figures 4(a) and 4(b). Indicates the first A follower intelligent agent in time The state is two-dimensional. Figure 4(a) shows a schematic diagram of the first component consistency of the leader-following state achieved by five follower agents under data-driven control, and the consistency achieved by two additional follower agents added after 20 seconds. The first component representing the state of the leader agent. The first component represents the state of the seven follower agents. Figure 4(b) shows a schematic diagram illustrating the consistency of the second component of the leader-following state achieved by five follower agents under data-driven control, and the continued consistency achieved by two additional follower agents added after 20 seconds. The second component represents the state of the follower agent. The second component represents the state of the seven follower agents. Simulation results show that the adaptive control protocol designed based on the collected data can successfully drive the binary convergence of the state trajectories of all agents to the same value, thus effectively solving the distributed consistency problem under the condition that the system model is not fully known.

[0073] Figure 5 An exemplary schematic diagram of a multi-agent data-driven adaptive binary tracking control device is shown. This application also provides a multi-agent data-driven adaptive binary tracking control device, comprising: The first establishment unit 501 is used to establish a multi-agent system and a communication topology; and to determine a Laplace matrix based on the communication topology; wherein the multi-agent system includes one leader agent and... A follower agent; the communication topology is used to describe The information interaction relationship between the follower agents; the Laplace matrix is ​​used to describe the structural characteristics of the communication topology; Collection unit 502, used for collecting the Any one of the follower agents collects sampled measurement values ​​offline at discrete time points to form a control input data matrix, a state data matrix, and a state derivative data matrix; The second establishment unit 503 is used to define a binary tracking error based on the leader agent and the follower agent; and to calculate the time derivative of the binary tracking error to establish an error system. The third establishment unit 504 is used to establish a data-driven adaptive consensus protocol based on the communication topology; the data-driven adaptive consensus protocol includes an adaptive rate and control parameters, and the adaptive rate includes a coupling weight matrix; The fourth establishment unit 505 is used to establish a complete error system based on the follower agent, the leader agent, and the Laplace matrix, by introducing the data-driven adaptive consistency protocol and the error system. The fifth establishment unit 506 is used to establish the stability conditions of the complete error system based on the adaptive rate and the Lyapunov function; The determining unit 507 is used to solve the stability condition using the control input data matrix, the state data matrix, and the state derivative data matrix to determine the control parameters and the coupling weight matrix. Control unit 508 is used to control using the control parameters and coupling weight matrix. The aforementioned follower agent operates.

[0074] The above embodiments provide a multi-agent data-driven adaptive binary tracking control method and apparatus. This method addresses the cooperative control problem of multi-agent systems under unknown dynamic models, as well as complex scenarios where the dynamic leader's control input is non-zero and unknown. This application designs a fully distributed direct data-driven adaptive consensus protocol. This protocol utilizes only the input data matrix, state data matrix, and state derivative data matrix from the sampled measurements of the leader and follower agents to adaptively adjust control parameters and coupling weight matrices online. This enables multiple follower agents to achieve binary tracking consensus in the presence of a dynamic leader, even without a system model or global network information. This method plays a crucial role in improving the flexibility, scalability, and engineering applicability of control systems.

[0075] It will be readily understood by those skilled in the art that the above-described advantageous methods can be freely combined and superimposed without conflict. The above are merely preferred embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application. The above are merely preferred embodiments of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of this application, and these improvements and modifications should also be considered within the protection scope of this application.

Claims

1. A multi-agent data-driven adaptive binary tracking control method, characterized in that, include: Establish a multi-agent system and communication topology; determine the Laplace matrix based on the communication topology; wherein the multi-agent system includes one leader agent and... A follower agent; the communication topology is used to describe The information interaction relationship between the follower agents; the Laplace matrix is ​​used to describe the structural characteristics of the communication topology; Regarding the Any one of the follower agents collects sampled measurement values ​​offline at discrete time points to form a control input data matrix, a state data matrix, and a state derivative data matrix; Based on the leader agent and the follower agent, a binary tracking error is defined; the time derivative of the binary tracking error is calculated to establish an error system. Based on the communication topology, a data-driven adaptive consensus protocol is established; the data-driven adaptive consensus protocol includes an adaptive rate and control parameters, and the adaptive rate includes a coupling weight matrix. Based on the follower agent, the leader agent, and the Laplace matrix, the data-driven adaptive consistency protocol and the error system are introduced to establish a complete error system. Based on the adaptive rate and Lyapunov function, the stability conditions of the complete error system are established. Using the control input data matrix, state data matrix, and state derivative data matrix, the stability condition is solved to determine the control parameters and coupling weight matrix. Control using the aforementioned control parameters and coupling weight matrix The aforementioned follower agent operates.

2. The method according to claim 1, characterized in that, The dynamic process of the follower agent is expressed by the following formula: ； in, Indicates the first A follower intelligent agent in time The state derivative under the given conditions, for A set of 3D real vectors; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; Indicates the first A follower intelligent agent in time The following state; This represents the unknown second coefficient matrix; Indicates the first A follower intelligent agent in time The control input below, express A set of 3D real vectors; This represents the total number of follower agents.

3. The method according to claim 1, characterized in that, The dynamic process of the leader agent is represented by the following formula: ； in, This indicates that the leader agent is in time. The state derivative under the given conditions; This represents the first coefficient matrix, which is unknown. This indicates that the leader agent is in time. The following state, This indicates that the leader agent is in time. The state of the next One component; This represents the unknown second coefficient matrix; This indicates that the leader agent is in time. Non-zero control inputs below.

4. The method according to claim 1, characterized in that, The communication topology is represented as follows: ； in, Represents the communication topology; Represents a set of nodes, the set of nodes including A follower agent, wherein each follower agent is a node; Let the set of edges be represented, which includes several edges, and each edge represents an information interaction channel between two different follower agents. This represents a symbolic weighted adjacency matrix. Indicates the first The follower agent and the first Information interaction relationships between follower agents. ; ; Indicating cooperation, It indicates competition. and These represent the indices of the follower agents.

5. The method according to claim 1, characterized in that, The Laplace matrix is ​​represented as follows: ； in, Let the Laplace matrix be denoted as . matrix; Represents a diagonal matrix; ； ； This represents a symbolic weighted adjacency matrix. ,for matrix; Indicates the first The follower agent and the first Information interaction relationships between follower agents. ; ; Denotes the first Laplace matrix Line number Column elements, ; ; when middle hour, , , ; when middle hour, , .

6. The method according to claim 1, characterized in that, The error system is expressed by the following formula: ； in, Indicates the first Follower and leader agents in time The time derivative of the binary tracking error under the given conditions; Indicates the first A follower intelligent agent in time The state derivative under the given conditions; Indicates the first A binary symbol for a follower agent. ; This indicates that the leader agent is in time. The state derivative under the given conditions; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; Indicates the first Follower and leader agents in time The following binary tracking error; This represents the unknown second coefficient matrix; Indicates the first A follower intelligent agent in time The control input below; This indicates that the leader agent is in time. Non-zero control inputs below.

7. The method according to claim 4, characterized in that, The data-driven adaptive consensus protocol is expressed by the following formula: ； in, Indicates the first A follower intelligent agent in time The control input below; Indicates the first A follower intelligent agent in time Adaptive rate under; This represents the first gain matrix; ； This represents the control input data matrix; Represents the controller parameter matrix. express A set of 3D real matrices; Represents the state data matrix; Indicates the first A follower intelligent agent in time Local neighborhood error; ； The total number of follower agents. For indexing follower agents, Indicates the first The follower agent and the first Information interaction relationships between follower agents. Indicates the first A follower intelligent agent in time The following state, Indicates the first A follower intelligent agent in time The following state, Indicates the connection weights of the leader agent. Indicates the first A binary symbol for a follower agent. This indicates that the leader agent is in time. The following state; Represents a symbolic function; This represents the second gain matrix; ； Represents the state derivative data matrix; Represents a block matrix with two rows and one column; express transpose and The inverse matrix of the product; express OK A matrix of columns; express OK The identity matrix of columns, express OK The zero matrix of the column; the control parameters include the first gain matrix and the second gain matrix; The adaptive rate is expressed by the following formula: ； in, Indicates the first A follower intelligent agent in time The rate of change of the adaptive rate under the condition; Represents the coupling weight matrix; ； Represents the auxiliary matrix. .

8. The method according to claim 5, characterized in that, The complete error system is expressed by the following formula: ； in, The time derivative of the augmented error vector; Represents a column vector; for Indicates the first Follower and leader agents in time The transpose of the binary tracking error; express identity matrix; Indicates the Kronecker product; This represents the first coefficient matrix, which is unknown. for A set of 3D real matrices; express 3D diagonal matrix Indicates the first A follower intelligent agent in time Adaptive rate under; Represents the symbolic Laplace matrix; ； Represents the Laplace matrix; Represents the restraint matrix. , ; Indicates the connection weights of the leader agent; This represents the unknown second coefficient matrix; This represents the first gain matrix; This represents the second gain matrix; Indicated by The sign function for the element; Represents a diagonal matrix; Indicates the first A binary symbol for a follower agent; Indicates that all elements are 1 3D column vector; This indicates that the leader agent is in time. Non-zero control inputs below.

9. The method according to claim 1, characterized in that, The stability condition is expressed by the following formula: ； ； ； in, Represents the state derivative data matrix; Represents the controller parameter matrix. express A set of 3D real matrices; Represents the state data matrix; , Represents the target data matrix; Represents a block matrix with two rows and one column; This represents the control input data matrix; Represents the state data matrix; express transpose and The inverse matrix of the product; Represents a matrix with m+n rows and 2m columns; express OK The identity matrix of columns, express OK The zero matrix of columns.

10. A multi-agent data-driven adaptive binary tracking control device, characterized in that, include: The first establishment unit is used to establish a multi-agent system and a communication topology; and to determine a Laplace matrix based on the communication topology; wherein the multi-agent system includes one leader agent and... A follower agent; the communication topology is used to describe The information interaction relationship between the follower agents; the Laplace matrix is ​​used to describe the structural characteristics of the communication topology; Collection unit, used for the collection of the Any one of the follower agents collects sampled measurement values ​​offline at discrete time points to form a control input data matrix, a state data matrix, and a state derivative data matrix; The second establishment unit is used to define a binary tracking error based on the leader agent and the follower agent; and to calculate the time derivative of the binary tracking error to establish an error system. The third establishment unit is used to establish a data-driven adaptive consensus protocol based on the communication topology; the data-driven adaptive consensus protocol includes an adaptive rate and control parameters, and the adaptive rate includes a coupling weight matrix; The fourth establishment unit is used to establish a complete error system based on the follower agent, the leader agent, and the Laplace matrix, by introducing the data-driven adaptive consistency protocol and the error system. The fifth establishment unit is used to establish the stability conditions of the complete error system based on the adaptive rate and the Lyapunov function. The determining unit is used to solve the stability condition using the control input data matrix, the state data matrix, and the state derivative data matrix to determine the control parameters and the coupling weight matrix. Control unit, used to control using the control parameters and coupling weight matrix The aforementioned follower agent operates.

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