Multi-agent formation control method of finite time event trigger control strategy

Abstract

The invention belongs to the technical field of multi-agent formation control, and particularly relates to a multi-agent formation control method of a finite time event trigger control strategy. Comprising the following steps: constructing a network communication topological graph of the multi-agent system; establishing an agent position state model under an event triggering mechanism according to the communication topological graph; setting a target position of the intelligent agent; and designing a control law and an event triggering condition of a controller according to the target position, sampling the position state of the intelligent agent by using a finite time formation control algorithm under an event triggering mechanism, and realizing formation control of the intelligent agent arriving at the target position within finite time. According to the method disclosed by the invention, a large amount of communication resources can be saved, the system can converge in finite time, the flexibility is higher, and the method is more in line with engineering practice.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent formation control, and in particular relates to a multi-agent formation control method of a finite time event triggering control strategy. Background Art

[0002] Formation control is a core issue in the study of multi-agent systems. It requires multiple agents to maintain a predetermined geometric shape, i.e., formation, while adapting to environmental constraints, such as avoiding obstacles, while moving toward a specific target or direction. Formation control can not only improve the overall performance and efficiency of the multi-agent system, but also enhance the robustness and adaptability of the system. Completing formation control within a limited time further improves the system's response speed and task execution capability.

[0003] How to achieve effective collaboration among multiple agents is the core issue of formation control research. This involves the design and optimization of distributed algorithms, protocols, and communication methods. Multi-agent systems need to maintain a stable formation in a complex and changing environment, and also need to have the ability to avoid obstacles and plan paths. With the development of artificial intelligence technology, the formation control of multi-agent systems will be more intelligent, able to make autonomous decisions, learn, and adapt to environmental changes. In recent years, with the continuous development of science and technology, research on finite-time control of multi-agent systems has made significant progress. However, as a fundamental property of the system, stability reflects the ability of distributed control of the system. Studying the stability of the system helps to deeply understand how individuals can achieve stable operation of the system through information interaction and collaboration. There is no result in finite-time formation control under event-triggered control strategy. The present invention proposes a multi-agent system formation control method based on a finite-time event-triggered strategy.

[0004] In the future, with the continuous advancement of technologies such as artificial intelligence and network communications, the research on finite-time formation control of multi-agent systems will become more in-depth and extensive. Researchers will continue to explore more efficient and stable control algorithms and strategies to meet the higher requirements for the performance of multi-agent systems in practical applications. Summary of the invention

[0005] The present invention provides a method for realizing multi-agent finite-time formation control based on an event-triggered control strategy, so as to solve the problems of limited communication resources and long convergence time in the prior art.

[0006] The technical solution adopted by the present invention to solve the technical problem is as follows: a multi-agent formation control method with a finite time event triggering control strategy comprises the following steps: S1. Construct the network communication topology diagram of the multi-agent system; S2, establish the agent position state model under the event trigger mechanism according to the communication topology diagram; S3, set the target position of the agent; S4. Design the control law and event triggering conditions of the controller according to the target position, and use the finite time formation control algorithm under the event triggering mechanism to sample the position state of the intelligent agent to achieve formation control of the intelligent agent to reach the target position within a limited time.

[0007] Preferably, in step S1, the network communication topology diagram , in the communication topology graph, nodes represent agents, where Represents a multi-agent set, that is, a set of nodes in the communication topology graph; represents the edge set, edge Representing multi-agent Can accept multiple agents information, and said yes Neighbors.

[0008] Preferably, step S4 comprises: S41, according to the estimated position value of the neighboring agent and the position vector of the agent, the trigger function value is calculated according to the event trigger condition, and whether the event trigger condition is met is determined, if the event trigger condition is met, communication is performed, if not, communication is not performed; S42. Each agent calculates the estimated value of its own position and the position of its neighboring agents based on its latest position and the position of its neighboring agents, brings it into the control law, generates formation control instructions, and finally the agent executes autonomously, continuously executing steps S41 and S42 to achieve formation control.

[0009] Preferably, in step S2, The system model of the intelligent agent is modeled as ,in For intelligent agents The actual status of For intelligent agents The control input, and are the system matrix and input matrix respectively; In step S4, the control law of the controller is as follows: ;in, For intelligent agents Internal interaction protocols; For intelligent agents External control input; For intelligent agents The estimated value of the trigger time, For intelligent agents At the triggering moment The location at the moment; Representing an Agent The error at time t is ; is the feedback gain matrix, is a solution to a positive definite moment and satisfies the algebraic Riccati equation; is the gain coefficient; exponent ; It is a default agent Target location; Representing an Agent Is it subject to external control? The impact of Representing an Agent take over ,otherwise ; It is an intelligent agent The edge weight of the edge pointing to agent j; The trigger function is designed as ;in, For intelligent agents Trigger error norm; For intelligent agents and neighbors Position error at the time of triggering; To design the threshold item; Represents the trigger error coefficient, represents the state error coefficient, Represents the target position coefficient.

[0010] Preferably, the gain coefficient is determined to satisfy the condition ,in is the algebraic connectivity of the topological graph G.

[0011] Preferably, step S4 includes: if the trigger function is greater than 0, the system samples the position of the agent, and the position of the agent at the sampling time is .

[0012] Preferably, an event is triggered to calculate an estimated value of the position of the neighboring agent at the current moment based on the initial value of the position of the neighboring agent.

[0013] Preferably, in step S41, >0, the communication trigger condition is met, and the agent communicates once to obtain the latest location status of neighboring agents through the network topology.

[0014] Preferably, in step S42, using Compute estimates of the positions of this agent and its neighbors.

[0015] Preferably, when an event occurs, the error Will be reset to 0.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention can reduce the number of communications and the frequency of controller updates by introducing event-triggered control, so it can save a lot of communication resources, is suitable for situations where communication resources are limited, and is more in line with engineering practice; 2. The present invention ensures the realization of system stability and formation control within a limited time by introducing dynamic variables that converge within a limited time; 3. The present invention can adjust the frequency of system triggering by setting the parameters in the event triggering conditions, and the autonomous control operation efficiency of the formation is high, and the application scope in practice is wider. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the multi-agent formation control method of the present invention.

[0018] Figure 2 This is the aircraft system communication topology diagram in Example 1.

[0019] Figure 3 This is a diagram of the positions of aircraft during the formation control process in Example 1.

[0020] Figure 4 The trigger error diagram of the aircraft during the formation control process in Example 1 (the horizontal axis is time t, the vertical axis is the aircraft error, and the three figures on the left correspond from top to bottom to Figure 2 The three figures on the right correspond from top to bottom to the following aircraft: Figure 2 Aircraft 2, 4 and 6). DETAILED DESCRIPTION

[0021] In order to facilitate the understanding of the present invention, the present invention is described in more detail below in conjunction with the accompanying drawings and specific embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described in this specification. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive.

[0022] The present invention provides a multi-agent system formation control method based on event-triggered finite time, combined with Figure 1 Understanding includes the following steps: S1. Constructing a multi-agent communication topology graph , in the communication topology graph, nodes represent multiple agents, where Represents a multi-agent set, that is, a set of nodes in the communication topology graph; represents the edge set, edge Representing multi-agent Can accept multiple agents information, and said yes Neighbors; If the communication topology If there is a path between any two nodes, it is called a communication topology graph. is connected; An independent strongly connected component iSCC is the largest strongly connected induced subgraph , which satisfies any node have , V 1 is a subset of V; S2. According to the system position state model of multiple agents under the communication topology diagram, The multi-agent system model is modeled as ,in, Multi-agent The actual status of Multi-agent The control input, and are the system matrix and the input matrix respectively; definition The triggering time and position of multiple agents The estimated value of Multi-agent The time when the most recent event was triggered, Trigger moment for multi-agents The measurement error vector is defined as ; S3, set the target position r of the agent; S4, the control law of the controller is designed as follows: in, Represents the output signal of the controller; For intelligent agents Internal interaction protocols; For intelligent agents External control input; For intelligent agents The estimated value of the trigger time, Neighbor Agent An estimate of the triggering moment; For intelligent agents At the triggering moment The location at the moment; It is a default agent Target location, is the default neighbor agent Target location; Representing an Agent The trigger error at time t is ; is the feedback gain matrix, is a positive definite moment and satisfies the algebraic Riccati equation The solution; is the gain coefficient, which is also the feedback control coefficient. Determine the gain coefficient to meet the condition ,in is the algebraic connectivity of the topological graph G; Representing an Agent Is it subject to external control? The impact of Representing an Agent take over ,otherwise ;index . represents the adjacency weighted matrix, is the adjacency weight matrix No. Line Column elements, i.e. agents The edge weight of the edge pointing to agent j, express OK A real matrix of columns, , .

[0023] The trigger function is designed as , if the trigger function value is greater than 0, the system samples the agent's position, and the agent's position at the sampling moment is . For intelligent agents Trigger error norm; For intelligent agents and neighbors Position error at the time of triggering; To design the threshold item; reflects the sensitivity of the trigger error to the threshold, where Represents the trigger error coefficient, represents the state error coefficient, Indicates the target position coefficient. By adjusting The larger the value, the lower the trigger frequency. Once the threshold parameters are determined, you can To further reduce the trigger frequency. When an event occurs, the error Will be reset to 0.

[0024] The initialization event triggers the formation controller to obtain the initial value of the neighboring agent's position through the communication network.

[0025] S5. Based on the initial value of the position of the neighboring agent, use the formula Calculate the estimated position of the neighboring agent at the current moment, where the position vector Take the initial value.

[0026] S6. Based on the estimated position of the neighboring agent and the position vector of the agent, the trigger function value is calculated according to the event triggering condition, and it is determined whether the event triggering condition is met: if the event triggering condition is met, the agent communicates once and obtains the latest position status of the neighboring agent through the network topology. If the event triggering condition is not met, no communication is performed. When >0, the communication trigger condition is met.

[0027] S7, each agent uses the latest position of itself and the position of neighboring agents to Calculate the estimated values ​​of the positions of the agent and neighboring agents, bring them into the control law, generate formation control instructions, and finally execute them autonomously by the agent, continuously executing steps S6 and S7 to achieve formation control. Under the designed control law, the time for the agent to reach the formation position is limited.

[0028] The output signal of the controller is calculated by comprehensively considering both the internal interaction protocol and the external control input; starting from the preset target position, the trigger error and position error are considered, the norm calculation is performed, and the parameters are set, and the threshold items are designed to adjust the system trigger frequency. The multi-agent system formation control method in this application can reduce the number of communications and the frequency of controller updates through the introduction of event-triggered control, so it can save a lot of communication resources, is suitable for situations where communication resources are limited, and is more in line with engineering practice; by introducing dynamic variables that converge in a finite time, the system stability and formation control are guaranteed within a finite time; by setting the parameters in the event trigger conditions, the system trigger frequency can be adjusted, and the application range in practice is wider.

[0029] Embodiment 1: The application of the multi-agent system formation control method based on event-triggered finite time in aircraft system formation control includes the following steps: Step 1: construct a communication topology diagram of the aircraft, where the nodes in the communication topology diagram represent the aircraft. Specifically, a 6-node network topology diagram is constructed, such as Figure 2 As shown, it is a weakly connected graph. Consider a two-dimensional aircraft system and assume that the initial state of the aircraft is random.

[0030] Step 2: Select a certain flight position of the aircraft and design a distributed formation controller based on the formation control algorithm. The dynamic model of the selected aircraft is constructed as a general linear system model. ,in For aircraft status, For aircraft The control input, and are the system matrix and the input matrix, satisfying the matrix pair It is calmable.

[0031] Step 3, set the target position r; Step 4: The finite-time formation control algorithm proposed in this invention designs a formation controller for aircraft with general linear system dynamics. Before a given event triggers the formation control algorithm, it is necessary to define the aircraft position estimation vector and measurement error vector used in the algorithm. The position estimation vector is defined as ,in For aircraft At the triggering moment The position at the moment.

[0032] The measurement error vector is defined as , represents the error between the true position and the estimated position.

[0033] Select the aircraft's location is the formation control quantity, and a formation controller is designed according to the event-triggered finite-time formation control algorithm. The control algorithm is as follows: ; Where K is the gain matrix, is the gain coefficient, is the element of the adjacency matrix A in the topological graph; It is a preset aircraft Target location; represents the trigger error of aircraft i at time t, where . is the feedback gain matrix obtained by solving the Riccati equation, is the positive definite matrix in the Riccati equation, is the gain coefficient. Select any node k in all iSCCs and let ,the remaining .index .

[0034] Furthermore, the positive definite matrix P can be obtained by calculating the algebraic Riccati equation, and the gain matrix K=BP can be calculated.

[0035] Next, the event trigger function is given as ;

[0036] in, For aircraft Trigger error norm, For aircraft and neighbors State error at the time of triggering. is the design threshold item. Reflects the sensitivity of the trigger error to the threshold. Represents the trigger error coefficient, represents the state error coefficient, Indicates the target position coefficient. By adjusting The larger the value, the lower the trigger frequency. Once the threshold parameters are determined, you can To further reduce the trigger frequency. When an event occurs, the error Will be reset to 0.

[0037] Specifically, take ; ; ; ; The target location is .

[0038] Step 5, the initialization event triggers the formation controller, obtains the initial position value of the neighboring aircraft through the communication topology, records it in the state storage, and records the start time of the algorithm, and resets the event trigger timer.

[0039] Step 6: Calculate and estimate the position state of the neighbor aircraft at the current moment based on the event trigger timer, the initial value of the neighbor aircraft and the state transfer matrix.

[0040] Step 7: Calculate the trigger function value based on the estimated position of the neighboring aircraft, the event trigger timer and the position of the aircraft to determine whether the communication trigger condition is met.

[0041] Step 8: If the event triggering condition is met, the aircraft will communicate once, obtain the latest state of the adjacent aircraft through the communication topology, update the state memory data, and reset the event triggering timer. If the event triggering condition is not met, no communication will be performed.

[0042] Step 9: Each aircraft calculates and generates formation control instructions in a distributed manner according to the estimated coordination status of adjacent node aircraft and the flight status of the aircraft itself.

[0043] Step 10, the generated formation control command is transmitted to the next control link of the aircraft, and finally the aircraft executes it autonomously to realize the aircraft formation control. When multiple aircraft perform formation control, steps 6 to 9 should be executed in each controller beat until the multi-aircraft control position is completed.

[0044] Within 0~20s, the positions of the six aircraft are as follows: Figure 3 As shown, it can be seen from the figure that the aircraft system formation controlled by the method in this application operates stably within a limited time. Figure 4 The change of trigger error during the formation control process is shown. It can be seen from the figure that there is no Zeno behavior in this process. That is to say, the introduction of event-triggered control reduces the number of communications and the frequency of controller updates, which can save a lot of communication resources. It is suitable for situations where communication resources are limited and is more in line with engineering practice.

[0045] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A multi-agent formation control method based on a finite-time event-triggered control strategy, characterized in that: The following steps are involved: S1. Construct the network communication topology diagram of the multi-agent system; S2, establish the agent position state model under the event trigger mechanism according to the communication topology diagram; S3, set the target position of the agent; S4. Design the control law and event triggering conditions of the controller according to the target position, and use the finite time formation control algorithm under the event triggering mechanism to sample the position state of the intelligent agent to achieve formation control of the intelligent agent to reach the target position within a limited time.

2. The multi-agent formation control method according to the finite time event triggering control strategy of claim 1, characterized in that: In step S1, the network communication topology diagram , in the communication topology graph, nodes represent agents, where Represents a multi-agent set, that is, a set of nodes in the communication topology graph; represents the edge set, edge Representing multi-agent Can accept multiple agents information, and said yes Neighbors.

3. The multi-agent formation control method according to the finite time event triggering control strategy of claim 2, characterized in that: Step S4 includes: S41, according to the estimated position value of the neighboring agent and the position vector of the agent, the trigger function value is calculated according to the event trigger condition, and whether the event trigger condition is met is determined, if the event trigger condition is met, communication is performed, if not, communication is not performed; S42. Each agent calculates the estimated value of its own position and the position of its neighboring agents based on its latest position and the position of its neighboring agents, brings it into the control law, generates formation control instructions, and finally the agent executes autonomously, continuously executing steps S41 and S42 to achieve formation control.

4. The multi-agent formation control method according to the finite time event triggering control strategy of claim 3 is characterized in that: In step S2, The system model of the intelligent agent is modeled as ,in For intelligent agents The actual status of For intelligent agents The control input, and are the system matrix and input matrix respectively; In step S4, the control law of the controller is as follows: ;in, For intelligent agents Internal interaction protocols; For intelligent agents External control input; For intelligent agents The estimated value of the trigger time, For intelligent agents At the triggering moment The location at the moment; Representing an Agent The error at time t is ; is the feedback gain matrix, is a solution to a positive definite moment and satisfies the algebraic Riccati equation; is the gain coefficient; exponent ; It is a default agent Target location; Representing an Agent Is it subject to external control? The impact of Representing an Agent take over ,otherwise ; It is an intelligent agent The edge weight of the edge pointing to agent j; The trigger function is designed as ;in, For intelligent agents Trigger error norm; For intelligent agents and neighbors Position error at the time of triggering; To design the threshold item; Represents the trigger error coefficient, represents the state error coefficient, Represents the target position coefficient.

5. The multi-agent formation control method according to the finite time event triggering control strategy of claim 4 is characterized in that: Determine the gain coefficient to meet the conditions ,in is the algebraic connectivity of the topological graph G.

6. The multi-agent formation control method according to the finite time event triggering control strategy of claim 4, characterized in that: Step S4 includes: if the trigger function is greater than 0, the system samples the agent position.

7. The multi-agent formation control method according to the finite time event triggering control strategy of claim 4, characterized in that: When an event is triggered, the estimated position of the neighboring agent at the current moment is calculated based on the initial position value of the neighboring agent.

8. The multi-agent formation control method according to the finite time event triggering control strategy of claim 4, characterized in that: In step S41, >0, the communication trigger condition is met, and the agent communicates once to obtain the latest location status of neighboring agents through the network topology.

9. The multi-agent formation control method according to the finite time event triggering control strategy of claim 4, characterized in that: In step S42, using Compute estimates of the positions of this agent and its neighbors.

10. The multi-agent formation control method according to the finite time event triggered control strategy of claim 4, characterized in that: When an event occurs, the error Will be reset to 0.

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