Multi-agent consistency tracking control method based on observer

Abstract

The invention discloses a multi-agent consistency tracking control method based on an observer, and belongs to the technical field of multi-agent systems, and the method comprises the steps: constructing a second-order leader following multi-agent dynamic model with external disturbance; determining a network communication topology structure of the multi-agent system; constructing a fixed time tracking error observer; establishing a dynamic event triggering protocol; establishing a consistency tracking control protocol according to the output of the observer and based on a backstepping method; and enabling each multi-agent to communicate according to the communication topology, when a trigger condition is met, the agent sends own state information to a neighbor, the observer updates output information according to the state information, and the controller outputs the output information to the actuator at the same time. According to the invention, the anti-interference capability of the system can be improved, and the consumption of communication resources and energy of the system is reduced.

Description

Technical Field

[0001] This invention relates to the field of multi-agent system technology, and in particular to an observer-based multi-agent consensus tracking control method. Background Technology

[0002] Multi-agent systems (MASs) are composed of many interacting individual agents that accomplish a large number of complex tasks that a single agent cannot perform, through communication, cooperation, and competition among themselves. In recent decades, with the continuous development of industrial technology, many large-scale and complex control systems have emerged. To systematically complete specific tasks, it is essential to rely on the mutual communication and collaborative effects between the various parts of the system. MASs possess characteristics of high autonomy, high flexibility, scalability, and high collaborative capabilities. Currently, MASs are widely used in aircraft formation, sensor networks, multi-robotic arm collaborative equipment, multi-robot cooperative control, transportation vehicle control, and smart grids.

[0003] Among the many research hotspots in intelligent agent systems, consistency is a core research problem. The consistency problem refers to the process by which each agent communicates with its neighbors to adjust and update its state, ultimately ensuring that every individual in the system reaches the same state. Examples include target tracking in aircraft and formation control in flight control. In practical engineering applications and industrial production, many controlled systems are required to repeatedly track certain specific trajectories within a certain time frame, such as trajectory tracking for high-speed trains, automatic driving, and parking. Furthermore, modern production and practical applications are subject to various environmental disturbances, such as wave disturbances in ship control. To meet the tracking control requirements of systems under disturbed conditions, improving the robustness of consistent tracking in multi-agent systems for air traffic control has become an urgent problem to be solved.

[0004] Meanwhile, as production tasks and requirements continue to increase, the structure of the system becomes more complex, and the communication between various parts becomes more frequent. In many applications, the frequency of mutual communication and controller updates is limited. How to save communication resources and controller update frequency while ensuring that control performance meets requirements is also a problem that needs to be studied and solved. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an observer-based multi-agent consensus tracking control method, which can improve the anti-interference capability of the system while reducing the consumption of communication resources and energy.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a multi-agent consensus tracking control method based on an observer, comprising the following steps:

[0007] Step 1: Construct a second-order leader-follower multi-agent dynamics model with external perturbations;

[0008] Step 2: Determine the network communication topology of the multi-agent system;

[0009] Step 3: Construct a fixed-time tracking error observer;

[0010] Step 4: Establish a dynamic event triggering protocol;

[0011] Step 5: Establish a consistent tracking control protocol based on the observer's output and the backstepping method;

[0012] Step 6: Enable the various agents to communicate according to the communication topology. When the triggering condition is met, the agent sends its own state information to its neighbors. The observer updates the output information according to the state information, and the controller outputs to the actuator at the same time.

[0013] A further improvement to the technical solution of this invention lies in the following: the second-order leader-follower multi-agent dynamics model with external perturbation constructed in step 1 includes one leader and n followers, wherein each follower is affected by the perturbation, and the specific composition is as follows:

[0014] Leader dynamics model:

[0015]

[0016] in, Indicates the leader's location information. This indicates the leader's speed information. This represents the bounded input of the leader. Indicates time;

[0017] The dynamic model of the disturbed follower is established as follows:

[0018]

[0019] in, Indicates the first Location information of each follower. Indicates the first The speed information of each follower Indicates the first A bounded input for a follower Indicates the application of the first Known external disturbances on an intelligent agent.

[0020] A further improvement to the technical solution of this invention lies in the following: the network communication topology in step 2 is as follows: the leader is marked as: Followers are marked as ; Communication network topology To describe, among which The set of nodes is represented as follows: Denotes the set of edges. The adjacency matrix represents the topology; the network topology among n followers is represented by... describe, Represents a set of nodes. Denotes the set of edges. Represent the adjacency matrix, when The node can receive When the node information is available, ;otherwise, ;at the same time Define nodes in-degree is Then topology in-degree matrix Define the Laplacian matrix. Define the adjacency matrix between leaders and followers as follows: If followers It can communicate with leaders. ;otherwise, ;definition The matrix is ​​as follows: , This represents the connection relationship between every two agents in the system.

[0021] A further improvement to the technical solution of this invention lies in the fact that the fixed-time tracking error observer in step 3 is specifically:

[0022]

[0023] in, The outputs of the tracking error observer represent the agent's position and velocity tracking errors, respectively. Defined as , The tracking error of the system is a function; The time can be estimated very well. The following expression exists:

[0024]

[0025] in, express The smallest eigenvalue of a matrix. .

[0026] A further improvement to the technical solution of this invention lies in the following: the dynamic event triggering protocol in step 4 is as follows:

[0027]

[0028] in, For the first The first intelligent agent Next trigger time A constant greater than 0 For trigger function, As dynamic variables, they respectively satisfy the following equations:

[0029]

[0030]

[0031] in, It is a constant; This refers to the state information at the trigger moment; in the above formula... The state error is represented by the following expression:

[0032]

[0033] in This refers to the state information at the trigger moment.

[0034] A further improvement to the technical solution of this invention lies in the following: Step 5, which establishes a consensus tracking control protocol based on the backstepping method, specifically involves:

[0035]

[0036] in, , It is a constant.

[0037] A further improvement of the technical solution of the present invention is that: Step 6 is specifically the intelligent agent transmitting information through the network communication topology. When the intelligent agent satisfies the dynamic triggering function in step 3, it sends its own state information to the surrounding neighboring intelligent agents. At the same time, the tracking error observation obtains the state information of the leader and the follower and outputs the tracking error value. The control protocol in step 5 ensures that the system achieves consistent tracking. The controller designed based on the backstepping method can effectively avoid the influence of external disturbances in step 1.

[0038] The technological advancements achieved by this invention, due to the adoption of the above technical solutions, are as follows: By setting the controlled object as a perturbed second-order leader-follower model, it achieves greater universality; by applying backstepping to the consensus tracking air traffic control problem in multi-agent systems, and designing a tracking consensus controller based on the observer output using backstepping, the impact of perturbations can be eliminated, effectively improving the robustness of the system. By introducing an error tracking observer, the observer's output update is controlled by a dynamic event-triggered protocol, effectively reducing the communication frequency between followers and between followers and the leader; when the information transmission channel is blocked, the observer can also effectively transmit state information, improving the system's anti-interference capability; by adopting a dynamic event-triggered mechanism, communication between agents is ensured to be discrete, while reducing the number of transmissions and effectively avoiding Zeno's phenomenon, thus reducing the consumption of communication resources; by setting a distributed fixed-time error observer acting between the leader and followers and applying it to dynamic event-triggered consensus control, some special cases can be handled, such as network attacks on the channel between the controller and the agent, improving the robustness of the system. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a framework diagram of the observer-based multi-agent consensus tracking control method of the present invention;

[0041] Figure 2 This is a communication topology diagram of a multi-intelligent system according to an embodiment of the present invention;

[0042] Figure 3 This is a position state error diagram of a fixed-time tracking error sensor according to an embodiment of the present invention;

[0043] Figure 4 This is a speed state error diagram of a fixed-time tracking error sensor according to an embodiment of the present invention.

[0044] Figure 5 This is a control input diagram according to an embodiment of the present invention;

[0045] Figure 6 This is a position state tracking error diagram of a multi-agent system according to an embodiment of the present invention;

[0046] Figure 7 This is a velocity state tracking error diagram of a multi-agent system according to an embodiment of the present invention.

[0047] Figure 8 This is a graph showing the number of event triggers in a multi-agent system according to an embodiment of the present invention. Detailed Implementation

[0048] The present invention will be further described in detail below with reference to embodiments:

[0049] like Figure 1 The diagram illustrates a multi-agent consensus tracking control method based on observers. The system comprises one leader agent and n follower agents, communicating via an undirected network. The specific steps are as follows:

[0050] Step 1: Construct a second-order leader-follower multi-agent dynamics model with external perturbations; the agent system model is as follows:

[0051] The dynamic model for determining the leader is as follows:

[0052]

[0053] in, Indicates the leader's location information. This indicates the leader's speed information. This represents the bounded input of the leader. Indicates time.

[0054] The dynamic model of the disturbed second-order follower is determined as follows:

[0055]

[0056] in, Indicates the first Location information of each follower. Indicates the first The speed information of each follower Indicates the first A follower's control input, Indicates the application of the first Known bounded external perturbations on an intelligent agent.

[0057] Bounded input to leaders External disturbances Make reasonable assumptions:

[0058]

[0059] in, All are non-negative constants.

[0060] Step 2: Determine the network communication topology of the multi-agent system; such as... Figure 2As shown, consider a multi-agent system consisting of a leader and... There are 1 follower, and the leader is labeled as: Followers are marked as ; Communication network topology To describe, among which The set of nodes is represented as follows: Denotes the set of edges. The adjacency matrix represents the topology; the network topology among n followers is represented by... describe, Represents a set of nodes. Denotes the set of edges. Represent the adjacency matrix, when The node can receive When the node information is available, ;otherwise, ;at the same time Define nodes in-degree is Then topology in-degree matrix Define the Laplacian matrix. Define the adjacency matrix between leaders and followers as follows: If followers It can communicate with leaders. ;otherwise, ;definition The matrix is ​​as follows: .

[0061] Step 3: Construct a fixed-time tracking error observer;

[0062] The fixed-time tracking error tracker is constructed as follows:

[0063]

[0064] Among them, among them, The outputs of the tracking error observer represent the estimates of the agent's position and velocity tracking errors, respectively. Defined as , It is a symbolic function.

[0065] The definition is as follows:

[0066]

[0067] The error tracker is transformed into the following:

[0068]

[0069] in

[0070]

[0071] Choose the Lyapunov function:

[0072]

[0073] Differentiating it, we have:

[0074]

[0075] Get time Similarly, for The same process takes time Here It is the time of the location information. It is the time of speed information. The requirement is that the sum of the two numbers must be less than or equal to their sum.

[0076] Step 4: Establish a dynamic event triggering protocol;

[0077]

[0078] Among them, the trigger function The definition is as follows:

[0079]

[0080] in, The measurement error is defined as follows: ; For intelligent agents exist Location and speed information over a time period; Represents intelligent agents The set of neighbors.

[0081] Dynamic threshold The definition is as follows:

[0082]

[0083] Initialization state .

[0084] According to the dynamic event triggering protocol:

[0085]

[0086] Simplifying, we get:

[0087]

[0088] According to the comparison principle, for any intelligent agent... There exists a positive constant. , making .

[0089] The introduction of a dynamic event triggering mechanism indicates that the system state update is not static, but changes with the triggering function. Compared with the ordinary event triggering mechanism, it saves more energy consumption of the system.

[0090] Step 5: Establish a consistent tracking control protocol based on the observer's output and the backstepping method;

[0091] The control protocol is as follows:

[0092] in, , It is a constant.

[0093] The system's control objective is:

[0094]

[0095] Based on Lyapunov's stability theory, it is proven that the above-mentioned second-order leader-follower multi-agent system can achieve the control objective and achieve asymptotic stability under the proposed control law.

[0096] Step 6: Enable communication among the multiple agents according to the communication topology. When the triggering condition is met, the agent sends its own state information to its neighbors. The observer updates its output information based on the state information, and the controller simultaneously outputs to the actuator. Agents transmit information through the network communication topology. When an agent satisfies the dynamic triggering function in Step 3, it sends its own state information to its neighboring agents. Simultaneously, tracking error observation obtains the state information of the leader and followers, outputting the tracking error value. The control protocol in Step 5 ensures consistent tracking. The controller designed based on backstepping effectively avoids the influence of external disturbances in Step 1.

[0097] Numerical simulations were established to verify this. The dynamics of the leader and followers were determined in step S1: constructing a second-order leader-follower multi-agent dynamics model with external perturbations, where... , In the observer, , In the controller, , In the event triggering protocol, , and , .

[0098] The theoretical settling time of the position state is calculated based on the observer parameters. The position state error of the fixed-time tracking error observer in this embodiment of the invention is 2.982s. Figure 3 As shown, the position state stabilization time in the embodiment is consistent with the calculated stabilization time; the theoretical velocity state stabilization time is calculated based on the observer parameters. The velocity state error of the fixed-time tracking error observer in this embodiment of the invention is 3.102s. Figure 4 As shown, the velocity state stabilization time in the embodiment is consistent with the calculated stabilization time, verifying the effectiveness of the designed algorithm; the control input of this embodiment is as follows: Figure 5 As shown, it reflects the dynamic behavior of the four agents in the system control based on the control input; Figure 6 , Figure 7 The figures shown are the position state tracking error diagram and velocity state tracking error diagram of the multi-agent system according to an embodiment of the present invention. Simulation results show that the state trajectories of each follower agent asymptotically converge to the leader's trajectory, verifying the effectiveness of the designed algorithm. Figure 8 The diagram showing the number of event triggers in a multi-agent system according to an embodiment of the present invention demonstrates that the proposed time protocol guarantees the elimination of the Zeno phenomenon.

[0099] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A multi-agent consensus tracking control method based on observers, characterized in that: The steps include the following: Step 1: Construct a second-order leader-follower multi-agent dynamics model with external perturbations; Step 2: Determine the network communication topology of the multi-agent system; Step 3: Construct a fixed-time tracking error observer; Step 4: Establish a dynamic event triggering protocol; Step 5: Establish a consistent tracking control protocol based on the observer's output and the backstepping method; Step 6: Enable the various agents to communicate according to the communication topology. When the triggering condition is met, the agent sends its own state information to its neighbors. The observer updates the output information according to the state information, and the controller outputs to the actuator at the same time.

2. The observer-based multi-agent consensus tracking control method according to claim 1, characterized in that: The second-order leader-follower multi-agent dynamics model with external perturbations constructed in step 1 includes one leader and n followers, where each follower is affected by the perturbation. The specific composition is as follows: Leader dynamics model: in, Indicates the leader's location information. This indicates the leader's speed information. This represents the bounded input of the leader. Indicates time; The dynamic model of the disturbed follower is established as follows: in, Indicates the first Location information of each follower Indicates the first The speed information of each follower Indicates the first A bounded input for a follower Indicates the application of the first Known external disturbances on an intelligent agent.

3. The observer-based multi-agent consensus tracking control method according to claim 1, characterized in that: The network communication topology in step 2 is as follows: The leader is marked as: Followers are marked as ; Communication network topology To describe, among which The set of nodes is represented as follows: Denotes the set of edges. The adjacency matrix represents the topology; the network topology among n followers is represented by... describe, Represents a set of nodes. Denotes the set of edges. Represent the adjacency matrix, when The node can receive When the node information is available, ; otherwise, ;at the same time Define nodes in-degree is Then topology in-degree matrix Define the Laplacian matrix. Define the adjacency matrix between leaders and followers as follows: If followers It can communicate with leaders. ; otherwise, ;definition The matrix is ​​as follows: , This represents the connection relationship between every two agents in the system.

4. The observer-based multi-agent consensus tracking control method according to claim 1, characterized in that: The fixed-time tracking error observer in step 3 is specifically as follows: in, The outputs of the tracking error observer represent the agent's position and velocity tracking errors, respectively. Defined as , The tracking error of the system is a function; The time can be estimated very well. The following expression exists: in, express The smallest eigenvalue of a matrix. .

5. The observer-based multi-agent consensus tracking control method according to claim 1, characterized in that: The dynamic event triggering protocol in step 4 is as follows: in, For the first The first intelligent agent Next trigger time A constant greater than 0 For trigger function, As dynamic variables, they respectively satisfy the following equations: in, It is a constant; in the above formula The state error is represented by the following expression: in This refers to the state information at the trigger moment.

6. The observer-based multi-agent consensus tracking control method according to claim 1, characterized in that: Step 5, which establishes the consistency tracking control protocol based on the backstepping method, specifically involves: in, , It is a constant.

7. The observer-based multi-agent consensus tracking control method according to claim 1, characterized in that: Step 6 specifically involves the agent transmitting information through the network communication topology. When the agent satisfies the dynamic triggering function in step 3, it sends its own state information to neighboring agents. At the same time, the tracking error observation obtains the state information of the leader and followers and outputs the tracking error value. The control protocol in step 5 ensures that the system achieves consistent tracking. The controller designed based on the backstepping method can effectively avoid the influence of external disturbances in step 1.

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