A finite time cooperative control method using distributed event-triggered control

Abstract

The application belongs to the field of multi-agent cooperative control, and particularly relates to a finite time cooperative control method using distributed event-triggered control; comprising establishing a dynamic model of each agent in a nonlinear multi-agent system, and constructing a communication topology structure of the nonlinear multi-agent system; setting a distributed event-triggered controller and an event-triggering condition based on the dynamic model; realizing finite time consistency of the multi-agent system according to the distributed event-triggered controller and the event-triggering condition; the application realizes finite time optimization of a nonlinear first-order multi-agent system, adopts a non-continuous event-triggering mechanism, can effectively reduce the communication burden of the system, and better enables the system to cope with complex environments.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control, specifically relating to a finite-time cooperative control method employing distributed event-triggered control. Background Technology

[0002] Many real-world problems are highly complex and difficult to solve with a single agent. This has led to the introduction of Multi-Agent Systems (MASs) to address complex issues such as traffic management and power grid allocation. MASs also play a crucial role in automation, particularly in drone swarm control and autonomous driving control for automobiles. In recent years, research on cooperative control of MASs has received significant attention, with consensus control being the most fundamental and core issue. To address consensus control, numerous scholars have proposed control methods such as finite-time control, sliding mode control, and adaptive control, which satisfy various control objectives or performance requirements.

[0003] Multi-agent systems (MAS) used in industrial control typically embed a controller within each agent and are powered by a power supply. Traditional continuous control methods consume significant resources, and frequent information transmission within the system consumes limited bandwidth, negatively impacting system performance and potentially causing system crashes. Non-continuous control methods, on the other hand, reduce resource consumption and communication bandwidth usage because they are triggered only when needed, rather than executed continuously. For example, event-triggered control, unlike continuous control, does not execute control operations at fixed time intervals; instead, control operations are only triggered when certain conditions are met. This significantly reduces the frequency of control operations and lowers resource consumption.

[0004] In distributed control of multi-agent systems, each agent can communicate and coordinate with its neighbors to achieve a common control objective. This control method distributes the computational and communication burden across all agents, so even if one agent fails, the system can still complete the control task through cooperation among the others. This approach improves the coordination of multi-agent systems and offers advantages such as robustness, flexibility, and ease of expansion. Therefore, to address the aforementioned issues, we need to consider distributed control, which offers greater flexibility and resilience, and is easier to update and expand in the future.

[0005] Meanwhile, considering that nonlinear multi-agent systems can better simulate complex real-world systems and handle various nonlinear dynamics and interactions, this invention also targets nonlinear multi-agent systems. These systems exhibit stronger robustness, effectively coping with system parameter variations, external disturbances, and uncertainties, thereby increasing system reliability. Finally, most consensus controls achieve asymptotic convergence, meaning they can only guarantee that agents achieve consensus within an infinite timeframe. This does not meet real-world requirements. The control proposed in this paper, however, can achieve consensus within a finite timeframe. Since finite-time consensus defines a time limit within which the agent system must reach consensus, it saves system resources and improves efficiency.

[0006] Based on the above discussion, considering that control and communication between agents under continuous control will increase the communication burden, that consistency needs to be achieved within a finite time in actual control systems, and that most control tasks are based on discontinuous systems, this paper aims to design a distributed event-triggered control strategy to achieve finite-time consistency of nonlinear multi-agent systems for the finite-time consistency problem of nonlinear multi-agent systems. Summary of the Invention

[0007] To address the above problems, this invention provides a finite-time cooperative control method employing distributed event-triggered control, characterized by the following steps:

[0008] S1. Establish the dynamic model of each agent in the nonlinear multi-agent system and construct the communication topology of the nonlinear multi-agent system;

[0009] S2. Set up a distributed event triggering controller and event triggering conditions based on the dynamics model;

[0010] S3. Achieve finite-time consistency in a multi-agent system based on a distributed event-triggered controller and event triggering conditions.

[0011] Furthermore, step S1 includes:

[0012] S11. A nonlinear multi-agent system comprises N agents, each representing a node. Its communication topology is represented by a weighted undirected graph G = (V, ε, A); where V represents the node set, ε represents the edge set, and the adjacency matrix A = (a...). ij ) N×N a represents the connectivity relationship in a nonlinear multi-agent system. ij This represents the value of the element in the i-th row and j-th column of the adjacency matrix, if node v i With node v j There exists an edge that belongs to the edge set, i.e. (v i ,vj If )∈ε, then a ij >0, otherwise a ij =0; Determine the degree matrix D and the Laplacian matrix L based on the undirected graph G, where D = diag{d1,d2,…,d...} N}, L = DA;

[0013] S12. The dynamic model of each agent in a nonlinear multi-agent system is as follows:

[0014]

[0015] Where, x i (t) represents the state information of the i-th agent at time t, u i (t) represents the control input of the i-th agent at time t, and f(,) represents the nonlinear equation.

[0016] Furthermore, step S2 sets the distributed event triggering controller based on the dynamic model as follows:

[0017] S21. Based on the state information of a multi-agent system x i (t) Design the joint state function q i (t), represented as:

[0018]

[0019] Where, n i Let a represent the number of neighboring agents of the i-th agent. If the i-th agent and the j-th agent can communicate, then a ij =1, otherwise a ij =0;

[0020] S22. Based on the joint state function q i (t) Defines the event-triggered measurement error e i (t), represented as:

[0021]

[0022] in, This indicates that the i-th agent is triggered at the k-th event trigger time, and α and β represent error coefficients;

[0023] S23. Based on the joint state function q i (t) Design a distributed event triggering controller u i (t), represented as:

[0024]

[0025] Where, γ iThis represents the gain parameter of the i-th agent.

[0026] Furthermore, the event triggering condition is expressed as follows:

[0027]

[0028] Among them, f i (t,e i (t),q i (t) is the trigger function value of the i-th agent at time t.

[0029] Furthermore, in step S3, each agent in the nonlinear multi-agent system transmits information according to the distributed event-triggered controller and event-triggered conditions, including:

[0030] S31. Calculate the trigger function value f of the i-th agent (i = 1, 2, ..., N) at time t. i ;

[0031] S32. If the trigger function value f i If the value is greater than 0, then the i-th agent satisfies the event triggering condition, and the i-th agent is updated in state using a non-continuous event triggering control protocol;

[0032] S33. If the trigger function value f i If the value is less than or equal to 0, then the i-th agent does not meet the event triggering condition, and the state of the i-th agent is not updated.

[0033] Furthermore, the formula for calculating the trigger function value of the i-th agent at time t is:

[0034]

[0035] Among them, f i (t,e i (t),q i (t) represents the trigger function value of the i-th agent at time t, q i (t) represents the joint state function value of the i-th agent at time t, e i (t) represents the event-triggered measurement error of the i-th agent at time t, ε i Let represent the gain parameter of the i-th agent, N represent the total number of agents, and α and β represent the error coefficients.

[0036] Furthermore, the finite time τ is set as follows:

[0037]

[0038]

[0039]

[0040] γ=min{γ i ,i=1,2,…,N}

[0041] Where α represents the error coefficient, x(0) represents the initial position of the agent, and U represents the Lyapunov function (CLF) equation. γ, ε i γ i Let λ represent the gain, λ2 represent the second smallest eigenvalue of the Laplace matrix, and N represent the number of agents.

[0042] The beneficial effects of this invention are:

[0043] This invention proposes a distributed event-triggered control protocol for achieving finite-time consistency coordination in first-order nonlinear multi-agent systems, addressing the challenge of achieving consistency within a finite timeframe. The proposed distributed event-triggered condition effectively reduces the system's communication burden. Furthermore, it achieves finite-time consistency, enabling convergence within a limited time and reducing system resource usage. Finally, specifically targeting nonlinear multi-agent systems, it enhances system robustness and better addresses complex system environments. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method of the present invention;

[0045] Figure 2 This is a schematic diagram of the communication topology according to an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram of the time convergence results in an embodiment of the present invention;

[0047] Figure 4 This is an analysis diagram of the results of an embodiment of the present invention. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] This invention provides a finite-time cooperative control method employing distributed event-triggered control, such as... Figure 1 As shown, it includes the following steps:

[0050] S1. Establish the dynamic model of each agent in the nonlinear multi-agent system and construct the communication topology of the nonlinear multi-agent system.

[0051] Specifically, step S1 includes:

[0052] S11. A nonlinear multi-agent system comprises N agents, each representing a node. Its communication topology is represented by a weighted undirected graph G = (V, ε, A); where V represents the node set, ε represents the edge set, and the adjacency matrix A = (a...). ij ) N×N a represents the connectivity relationship in a nonlinear multi-agent system. ij This represents the value of the element in the i-th row and j-th column of the adjacency matrix, if node v i With node v j There exists an edge that belongs to the edge set, i.e. (v i ,v j If )∈ε, then a ij >0, otherwise a ij =0; Determine the degree matrix D and the Laplacian matrix L based on the undirected graph G, where D = diag{d1,d2,…,d...} N}, L = DA;

[0053] S12. The dynamic model of each agent in a nonlinear multi-agent system is as follows:

[0054]

[0055] Where, x i (t) represents the state information of the i-th agent at time t, u i (t) represents the control input of the i-th agent at time t, and f(,) represents the nonlinear equation. This invention uses nonlinear equations in the dynamic model of the agent, which, compared to continuous systems, can increase the system's flexibility and anti-interference capability.

[0056] S2. Set up a distributed event triggering controller and event triggering conditions based on the dynamic model;

[0057] Specifically, step S2 sets the distributed event triggering controller based on the dynamic model as follows:

[0058] S21. Based on the state information of a multi-agent system x i (t) Design the joint state function q i (t), joint state function q i (t) is the sum of the state information of all neighboring agents of the i-th agent at time t, expressed as:

[0059]

[0060] Where, n i Let a represent the number of neighboring agents of the i-th agent. If the i-th agent and the j-th agent can communicate, then a ij =1, otherwise a ij =0;

[0061] S22. Based on the joint state function q i (t) Defines the event-triggered measurement error e i (t), represented as:

[0062]

[0063] in, This indicates that the i-th agent is triggered at the k-th event trigger time, and α and β represent error coefficients;

[0064] S23. Based on the joint state function q i (t) Design a distributed event triggering controller u i (t), represented as:

[0065]

[0066] Where, γ i This represents the gain parameter of the i-th agent. This invention designs a distributed control method, which significantly enhances anti-interference capability compared to a centralized control method.

[0067] Specifically, the event triggering condition is expressed as follows:

[0068]

[0069] Among them, f i (t,e i (t),q i (t) is the trigger function value of the i-th agent at time t.

[0070] S3. Achieve finite-time consistency in a multi-agent system based on a distributed event-triggered controller and event triggering conditions.

[0071] Specifically, in step S3, each agent in the nonlinear multi-agent system transmits information according to the distributed event-triggered controller and event-triggered conditions, including:

[0072] S31. Calculate the trigger function value f of the i-th agent (i = 1, 2, ..., N) at time t. i ;

[0073] S32. If the trigger function value f iIf the value is greater than 0, then the i-th agent satisfies the event triggering condition, and the i-th agent is updated in state using a non-continuous event triggering control protocol;

[0074] S33. If the trigger function value f i If the value is less than or equal to 0, then the i-th agent does not meet the event triggering condition, and the state of the i-th agent is not updated.

[0075] Specifically, the formula for calculating the trigger function value of the i-th agent at time t is:

[0076]

[0077] Among them, f i (t,e i (t),q i (t) represents the trigger function value of the i-th agent at time t, q i (t) represents the joint state function value of the i-th agent at time t, e i (t) represents the event-triggered measurement error of the i-th agent at time t, ε i Let represent the gain parameter of the i-th agent, N represent the total number of agents, and α and β represent the error coefficients.

[0078] Each agent in the system can independently complete a series of information monitoring tasks, ultimately achieving system consistency.

[0079] Specifically, the finite time τ is set as follows:

[0080]

[0081]

[0082]

[0083] γ=min{γ i ,i=1,2,…,N}

[0084] Where α represents the error coefficient, and x(0) represents the initial position of the agent. γ, ε i γ i Let λ represent the gain, λ² represent the second smallest eigenvalue of the Laplace matrix, and N represent the number of agents. U represents the Control Lyapunov Function (CLF) equation, expressed as:

[0085]

[0086] I n This represents a column vector whose elements are all 1s. This represents the Kronecker product.

[0087] The communication topology and communication framework in this embodiment are as follows: Figure 2 As shown. The numerical simulation process of an embodiment of the present invention is as follows: The above control strategy is verified through a system composed of four agents, and the Laplace matrix L is shown below:

[0088]

[0089] The initial state of the four agents is selected as x(0) = [1.8 1.2 -0.15 -2]. T And this coefficient α=β=0.8, γ i =0.5 and ε i =1.9.

[0090] according to Figure 3 It can be seen that the system's state input can eventually converge within the finite time we calculated, and the set time τ≈88.249s. From Figure 4 It can be seen that the distributed event triggering mechanism introduced by the system reduces the system's communication cost to a certain extent.

[0091] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "setting," "connection," "fixing," "rotation," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two components or the interaction between two components. Unless otherwise explicitly limited, those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0092] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A finite-time cooperative control method employing distributed event-triggered control, characterized in that, Includes the following steps: S1. Establish the dynamic model of each agent in the nonlinear multi-agent system and construct the communication topology of the nonlinear multi-agent system; Step S1 includes: S11. A nonlinear multi-agent system consists of N agents, each representing a node, and its communication topology uses a weighted undirected graph. Indicated by; where V represents the node set, Represents the edge set and adjacency matrix This represents the connectivity relationships in a nonlinear multi-agent system. This represents the value of the element in the i-th row and j-th column of the adjacency matrix, if node v i With node v j There exists an edge that belongs to the edge set, i.e. ,but ,otherwise Based on the degree matrix D and Laplace matrix L of the undirected graph G, where , L=DA; S12. The dynamic model of each agent in a nonlinear multi-agent system is as follows: in, This represents the state information of the i-th agent at time t. This represents the control input of the i-th agent at time t. Represents nonlinear equations; S2. Set up a distributed event triggering controller and event triggering conditions based on the dynamics model; S3. Achieve finite-time consistency in a multi-agent system based on a distributed event-triggered controller and event triggering conditions; Limited time Set as: in, Let x(0) represent the error coefficient, x(0) represent the initial position of the agent, and U represent the Lyapunov function equation. , , , , Indicates gain. Let represent the second smallest eigenvalue of the Laplace matrix, and N represent the number of agents.

2. The finite-time cooperative control method using distributed event-triggered control according to claim 1, characterized in that, Step S2 sets the distributed event triggering controller based on the dynamic model as follows: S21. Based on the state information of a multi-agent system Design the joint state function , is represented as: in, Let represent the number of neighboring agents of agent i. If agent i and agent j can communicate, then... ,otherwise ; Let N represent the state information of the j-th agent at time t, and N represent the number of agents. S22. Based on the joint state function Define event-triggered measurement error , represented as: in, This indicates that the i-th agent is triggered at the k-th event trigger time. Indicates the error coefficient; S23. Based on the joint state function Design a distributed event triggering controller. , represented as: in, This represents the gain parameter of the i-th agent.

3. The finite-time cooperative control method using distributed event-triggered control according to claim 2, characterized in that, The event triggering condition is expressed as follows: in, Let be the trigger function value of the i-th agent at time t.

4. The finite-time cooperative control method using distributed event-triggered control according to claim 1, characterized in that, Step S3: In the nonlinear multi-agent system, each agent transmits information according to the distributed event-triggered controller and event triggering conditions, including: S31. Calculate the trigger function value of the i-th agent (i=1,2,…,N) at time t. ; S32. If the trigger function value If the i-th agent satisfies the event triggering condition, the i-th agent's state is updated using a non-continuous event triggering control protocol. S33. If the trigger function value If the event triggering condition is not met, then the i-th agent will not be updated.

5. A finite-time cooperative control method employing distributed event-triggered control according to any one of claims 3 or 4, characterized in that, The formula for calculating the trigger function value of the i-th agent at time t is: in, This represents the trigger function value of the i-th agent at time t. This represents the joint state function value of the i-th agent at time t. Let represent the event-triggered measurement error of the i-th agent at time t. Let represent the gain parameter of the i-th agent, N represent the total number of agents, and α and β represent the error coefficients.

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