A multi-agent consensus cooperative control method based on event-triggered impulse

Abstract

The application belongs to the field of multi-agent cooperative control, and particularly relates to a multi-agent consensus cooperative control method based on event-triggered impulse; the method comprises the following steps: constructing a communication topology of a nonlinear multi-agent system; constructing a dynamic model of an agent in a second-order discrete system and initializing the system; setting a non-continuous saturation constraint impulse control protocol; each agent communicates with each other according to the communication topology, continuously acquires state information of neighbor agents and saves its own state information in the communication process; all agents are updated by using the non-continuous saturation constraint impulse control protocol at the impulse moment; all agents are updated according to the dynamic model at the non-impulse moment; an error system is constructed according to the state information of the agents, and when the error system is stable, the agents reach the consensus; the application can realize the state consensus at a faster speed and with fewer event triggers.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control, specifically relating to a multi-agent consensus cooperative control method based on event-triggered pulses. Background Technology

[0002] In recent years, consensus in multi-agent systems (MASs) has garnered widespread attention due to its significant applications, such as cooperative control of robots, distributed sensor networks, swarming phenomena in biological and social systems, and chaotic circuit networks. In MASs, agents interact through corresponding topological rules and achieve collaborative goals under the influence of appropriately designed control laws. In this process, the control strategy is a crucial factor influencing the cooperative control process of multi-agent networks, determining the performance of the network in achieving cooperative tasks. In realizing cooperative tasks in multi-agent systems, various cooperative control schemes, such as adaptive control, event-driven control, and model predictive control, have been proposed to achieve their respective control objectives or performance goals. However, these control strategies require continuous control inputs, and in network control, the information exchange between nodes also needs to be real-time. Therefore, there is still considerable room for improvement in conserving resources and increasing the convergence speed of multi-agent systems.

[0003] Impulse control, as a relatively simple discontinuous control method, has been successfully applied in many disciplines. In recent years, to achieve state consensus in dynamic systems (MASs) more quickly, state impulse strategies have been implemented to solve the state consensus problem in MASs. Many scholars have derived consensus criteria for MASs through impulse control schemes, but there are still some aspects that need improvement. For example, since impulse control is periodic, to achieve consensus quickly, some scholars have changed the constraint of the fixed pulse instant to the interval between the center or left endpoint of the time window of adjacent pulses. Although this allows for a larger control region, the pulse occurrence time is still limited by the time window setting, lacking flexibility. While these impulse methods are effective in solving consensus problems, they do not reduce communication and computation costs. To ensure fast convergence, the pulse frequency must be designed to be sufficiently high. Therefore, the results tend to be conservative. Unlike the above control strategies, the triggering time of the event-triggered impulse control strategy is the pulse input time. This control strategy can effectively reduce the number of information transmissions and resource consumption. However, most scholars' work focuses only on first-order dynamical systems, with little attention paid to second-order discrete systems. For general second-order system dynamics models, researchers have mostly focused on using both position and velocity measurements simultaneously to address consistency issues. However, in real-world scenarios, obtaining velocity measurements is often difficult or even impossible. In some cases, it is necessary to design suitable control protocols without using velocity information.

[0004] Furthermore, considering the impact of excessively high instantaneous pulse input on the system, this invention introduces input saturation. Input saturation is a typical control constraint arising from the limited control force of physical actuators. Improper handling can lead to severe performance degradation or even instability. Therefore, designing a consistency controller affected by input saturation is of great significance for practical multi-agent systems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a multi-agent consensus cooperative control method based on event-triggered pulses, which includes:

[0006] S1: Construct a communication topology by treating each agent of the nonlinear multi-agent system as a communication node;

[0007] S2: Construct a dynamic model of the agent in a second-order discrete system based on algebraic graph theory and initialize the system;

[0008] S3: Set the discontinuous saturation constraint pulse control protocol;

[0009] S4: Each agent communicates with each other according to the communication topology, and continuously acquires the state information of its neighboring agents and saves its own state information during the communication process;

[0010] S5: At the pulse moment, a discontinuous saturated constraint pulse control protocol is used to update the state and velocity information of all agents; at the non-pulse moment, the state and velocity information of all agents are updated according to the dynamic model.

[0011] S6: Construct an error system based on the state information of each agent and its neighboring agents. When the error system is stable, all agents reach a consensus.

[0012] Preferably, the process of constructing the communication topology includes:

[0013] Let G = (V, E, A) be an undirected graph of order N, where Let V = {1, 2, ..., N} represent the set of nodes, where N is the total number of nodes in the system. An undirected graph has a weighted adjacency matrix A = (a...). ij ) N×N , where a ij Let a be the weight of the ordered edges from node i to node j, and let a be the weight of the edges if and only if there are no edges between nodes i and j. ij =0; Based on the degree matrix D and Laplace matrix L of the undirected graph, L = DA, and deg(·) represents the diagonalization operation.

[0014] Preferably, the dynamic model of the agent in a second-order discrete system is expressed as follows:

[0015]

[0016] Where, x i (n) represents the position of the i-th agent at time n, v i (n) represents the velocity of the i-th agent at time n, a represents the first coefficient, b represents the second coefficient, and f(v) i (,n) represents a nonlinear function related to velocity, sat(u i (n) represents the constrained control input of the i-th agent. This represents the k-th pulse moment of the i-th agent at time n. Indicates in The change in state at any given time. Indicates in The change in velocity at time step m1 represents the pulse gain constant of the state variable, and m2 represents the pulse gain constant of the velocity variable.

[0017] The preferred, discontinuous saturation-constrained pulse control protocol is expressed as follows:

[0018]

[0019] Among them, u i (n) represents the pulse input of the multi-agent system, and ζ represents the pulse gain. p represents the Dirac function. i (n) represents the joint state error, a ij Let N represent the weight of the ordered edge from node i to node j, and let N represent the total number of nodes in the system. i Let x represent the set of neighboring agents of agent i. i (n-1) represents the state variable of agent i at the time preceding time n, x j (n-1) represents the velocity variable of agent i's neighbor agent j at the time before time n.

[0020] Preferably, in step S5, the process of updating the state information of each agent and its neighboring agents using a discontinuous saturation constraint pulse control protocol includes: at the pulse moment, determining whether the system satisfies the trigger function; if so, calculating the control input according to the discontinuous saturation constraint pulse control protocol and updating the agent state information according to the control input; otherwise, maintaining the agent state information.

[0021] Furthermore, the trigger function is represented as:

[0022]

[0023]

[0024] Where f2(n) represents the trigger function, This represents the intermediate parameter, and α represents the error coefficient. Indicates when The joint state error at time p i (n) represents the state error at time n, n0 represents the initial pulse time, and ε represents the trigger constant.

[0025] Preferably, in step S5, the process of updating the state information of each agent and its neighboring agents according to the dynamic model at non-pulse times includes: at non-pulse times, obtaining the state information of each agent at the previous time according to the dynamic model, and updating the current state information of each agent according to its own and its neighboring agents' state information at the previous time.

[0026] Preferably, the error system is represented as follows:

[0027]

[0028] Where d(n) represents the column vector of the average state errors of all agents at time n, e(n) represents the column vector of the average velocity errors of all agents at time n, P represents a positive definite matrix, and I m Let d(n) represent the m-dimensional identity matrix, F(v,n) represent the column vector consisting of the nonlinear functions of all agents related to velocity at time n, and d(n) represent the velocity-dependent functions of all agents at time n. k ) indicates that in n k The column vector formed by the average state errors of all agents at time n, e(n k ) indicates that in n k The column vector is composed of the average velocity errors of all agents at time t, where m1 represents the state pulse gain constant, m2 represents the velocity pulse gain constant, and sat(u(n)) represents the constrained control input vector of the agent.

[0029] The beneficial effects of this invention are as follows: Based on an event-triggered pulse control strategy, this invention derives a consensus principle for several leaderless second-order discrete systems, which can solve the problem of unavailable velocity information in practical situations. This strategy not only achieves state consistency in multi-agent systems but also avoids continuous communication between adjacent agents. For each agent, input control is injected only at the moment of event triggering, which helps reduce resource consumption. Event-triggered pulse control is more flexible than many existing event-based methods such as pulse control. The multi-agent system using the event-triggered pulse control method of this invention can achieve agent state consistency faster and with fewer event triggers. Attached Figure Description

[0030] Figure 1This is a flowchart of the multi-agent consensus cooperative control method based on event-triggered pulses in this invention;

[0031] Figure 2 This is a topology diagram of an intelligent agent system according to a preferred embodiment of the present invention. Detailed Implementation

[0032] 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.

[0033] This invention proposes a multi-agent consensus cooperative control method based on event-triggered pulses, such as... Figure 1 As shown, the method includes the following:

[0034] S1: Construct a communication topology by treating each agent of the nonlinear multi-agent system as a communication node.

[0035] Algebraic graph theory is an important tool for studying multi-agent consensus. This invention utilizes algebraic graph theory to construct a communication topology graph. Specifically: Let G = (V, E, A) be an N+1 order undirected graph, where... Let V = {1, 2, ..., N} represent the set of nodes, where N is the total number of nodes in the system. An undirected graph has a weighted adjacency matrix A = (a...). ij ) N×N , where a ij Let a be the weight of the ordered edges from node i to node j, and let a be the weight of the edges if and only if there are no edges between nodes i and j. ij =0; Based on the degree matrix D and Laplace matrix L of the undirected graph, L = DA, where deg(·) denotes the diagonalization operation. The Laplacian matrix L = [l ij ] N×N Defined as:

[0036]

[0037] Among them, l ij N represents the element in the i-th row and j-th column of the Laplace matrix. i This represents the set of neighboring intelligent agents related to intelligent agent i.

[0038] S2: Construct a dynamic model of the agent in a second-order discrete system based on algebraic graph theory and initialize the system.

[0039] Assumption 1: Assume that there exist some positive constants Li (i = 1, 2, ..., N), such that |f(x) i (n))|≤L i |x i (n)|, where L f =max{L1,L2,...,L N}

[0040] Based on algebraic graph theory, a dynamic model of an agent in a second-order discrete system is constructed, expressed as:

[0041]

[0042] Wherein, the discrete-time instant n satisfies n = 0, 1, 2, ..., x i (n) represents the position of the i-th agent at time n, v i (n) represents the velocity of the i-th agent at time n, a represents the first coefficient, b represents the second coefficient, and f(v) i (n) represents the velocity variable v of agent i. i A nonlinear function related to time n, whose properties are as shown in Assumption 1, sat(u i (n) represents the constrained input. This represents the k-th pulse moment of the i-th agent at time n. Indicates in The change in state at any given time. Indicates in The change in velocity at time step m1 represents the pulse gain constant of the state variable, and m2 represents the pulse gain constant of the velocity variable.

[0043] S3: Set the discontinuous saturation constraint pulse control protocol.

[0044] The input with constraints is described as follows:

[0045]

[0046] Where u0 represents the input constraint value, u i (n) represents the pulse input of the system.

[0047] To limit the magnitude of the pulse input, different values ​​of u0 can be set according to the actual situation to achieve the purpose of protecting the system. Therefore, the pulse control protocol under saturation constraint, i.e., the discontinuous saturation-constrained pulse control protocol, is as follows:

[0048]

[0049] Where ζ represents the pulse gain, u i(n) represents the pulse input of the multi-agent system, and ζ represents the pulse gain. Describes the Dirac function, only when When p is 1, the function is 1; otherwise, it is 0. i (n) represents the joint state error, a ij Let N represent the weight of the ordered edge from node i to node j, and let N represent the total number of nodes in the system. i Let x represent the set of neighboring agents of agent i. i (n-1) represents the state variable of agent i at the time preceding time n, x j (n-1) represents the state variable of agent i's neighbor agent j at the time before time n, i.e., the position information obtained from the neighbor agent's sensor.

[0050] set up Let the pulse time series of agent i be defined.

[0051] The trigger function f2(n) is defined as follows:

[0052]

[0053]

[0054] in, This represents intermediate parameters; α represents the error coefficient, which is a settable constant. Indicates when The joint state error at time p i (n) represents the state error at time n; n0 represents the initial pulse time, which is generally set to 0; ε represents the trigger constant, which can be set manually.

[0055] S4: Each agent communicates with each other according to the communication topology, and continuously acquires the state information of neighboring agents and saves its own state information during the communication process.

[0056] The agent's sensors receive the agent's state information, including its current position and its previous position.

[0057] S5: At the pulse moment, a discontinuous saturated constraint pulse control protocol is used to update the state and velocity information of all agents; at the non-pulse moment, the state and velocity information of all agents are updated according to the dynamic model.

[0058] The event-triggered pulse control strategy designed in this invention is similar to the classic event-triggered strategy. The feedback loop is activated only when an event occurs, and the system trajectory reaches the design target. At each trigger moment, the pulse generator processes the information collected from the sensor and calculates new state and speed information according to the set control protocol requirements, which is then transmitted to the actuator for execution.

[0059] Each agent updates its state and velocity information at the pulse moment using a discontinuous saturated constraint pulse control protocol, based on the state information of its neighbors and its own position information, as well as the position information obtained by the sensors of its neighbors. Specifically, at the pulse moment, it checks whether the system satisfies the trigger function, i.e., whether f2(n) is greater than 0. If it does, it calculates the control input according to the discontinuous saturated constraint pulse control protocol and updates the agent's state and velocity information accordingly. Otherwise, it maintains the agent's state and velocity information.

[0060] Each agent updates its state and velocity information according to the state information of its neighbors and itself during non-impulse moments, based on the dynamic model. Specifically, as shown by the dynamic model, during non-impulse moments, the state information of the next moment is related to the current state and velocity information; the velocity information of the next moment is determined by a nonlinear function f related to the current velocity information. i (v i ,n) decide.

[0061] S6: Construct an error system based on the state information of each agent and its neighboring agents. When the error system is stable, all agents reach a consensus.

[0062] In this invention, when a discrete multi-agent system satisfies the following condition, all agents can asymptotically achieve consistency: the states and velocities of the agents converge to a single value, i.e. Where i,j=1,2,...,N.

[0063] Given the established control protocol and second-order dynamics model, assuming G is an equilibrium graph and strongly connected, a multi-agent system can achieve second-order consistency of the network topology G when 0 < ξ < 1, where δ1 is 2a 2 and 2b 2 +L f 2 ||P|| 2 The maximum value between θ1 and θ2 is given by ξ = max{θ1, θ2}, where And the constants are a > 0, b > 0, m1 > 0, m2 > 0. Among them, L fThe parameters of the nonlinear function are defined as shown in Assumption 1, where P represents a positive definite matrix, θ1 represents a constant, and I... m Let q be an m-dimensional identity matrix, and let 0 ≤ q be an identity matrix. j ≤1 satisfies D i Let i represent the i-th diagonal matrix, where the diagonal elements are only 0 and 1, i∈[1,2]. m ], D i - Indicates ID i H represents a configurable matrix that satisfies ||Hx|| ∞ ≤1.

[0064] The updated agent can be verified using Lyapunov's stability theorem and graph theory. The process includes:

[0065] definition and in and These are the average position and average velocity values ​​of all agents at time n, respectively.

[0066] An error system is constructed based on the state information of each agent and its neighboring agents. The error system is represented as follows:

[0067]

[0068] Where d(n) represents the column vector consisting of the average state errors of all agents at time n, d(n) = (d1(n),...,dn) N (n)) T , e(n) represents the column vector of the average velocity errors of all agents at time n, e(n) = (e1(n),...,e N (n)) T , P represents a positive definite matrix composed of an N-dimensional identity matrix and N-dimensional column vectors. I N Represents an N-dimensional identity matrix, 1 N I represents a column vector consisting of N 1s; m Let F(v,n) represent an m-dimensional identity matrix, and let F(v,n) represent a column vector consisting of nonlinear functions related to velocity of all agents at time n. F(v,n) = (f(v1,n), f(v2,n), ..., f(v...)). N ,n)) T ;d(n k ) indicates that in n k The column vector formed by the average state errors of all agents at time n, e(n k) indicates that in n k The column vector is composed of the average velocity errors of all agents at time t, where m1 represents the state impulse gain constant and m2 represents the velocity impulse gain constant; sat(u(n)) represents the constrained control input vector of the agent, defined as sat(u(n))=(sat(u1(n)),...,sat(u1(n))=(sat(u1(n)),...,sat(u1(n))=(sat(u1(n))),...,sat(u1(n))). N (n))) T .

[0069] Therefore, a multi-agent system can achieve second-order consistency if and only if the error system is asymptotically stable, that is, the states and velocities of the agents converge to a value, and the agents reach consistency.

[0070] The Lyapunov function is defined as follows:

[0071]

[0072] in, It is a positive definite symmetric matrix.

[0073] From the error system expression, it can be seen that when n k ≤n≤n k+1 When -1, we can get:

[0074]

[0075] Calculate V(n) k ),

[0076]

[0077] From the above formula, we can see that And V(n1)≤ξV)n1-1); and so on, when n k ≤n<n k+1 -1, k∈N + When τ = n k+1 -n k If n0 = 0, we can obtain:

[0078]

[0079] Based on the above conditions, we can conclude that lnδ1 > 0 and lnξ < 0. Therefore, it can be proven that the error system is asymptotically stable, and thus the multi-agent system can achieve second-order consensus, meaning that all agents reach agreement. After the agents reach agreement, the agent system saves the latest state information, and all agents can execute corresponding operations based on the latest control input, achieving the goal of coordinated control of the agent system. If the agent system is a multi-robot system, it can realize the coordinated control of multiple robots.

[0080] In some embodiments, if the number of agents is 4, its topology graph is as follows: Figure 2 As shown, its connectivity weight is: a 12 =a 13 =a 21 =a 24 =a 31 =a 34 =a 42 =a 43 =1, and all other weights are equal to 0.

[0081] Consider the following second-order discrete dynamics model:

[0082]

[0083] Where m1 = 0.32, m2 = 0.18, ζ = -0.6, u0 = 2; let α = 0.06, ε = 5.

[0084] make in:

[0085]

[0086]

[0087] The nonlinear function related to velocity is described as follows:

[0088]

[0089] The tanh(·) function is the hyperbolic tangent function, with a range of [-1, 1]. In f(v i In the setting of the function (n), since the velocity variable is 3-dimensional, the velocities of different dimensions are treated separately. Furthermore, the setting of the nonlinear function is not unique and can be changed according to the actual situation.

[0090] Through calculation, L f =0.5. Set x i (0) = i × [0.1, 0.2, 0.3] T v i (0) = i × [1, 2, 4] T Calculations show that δ1 = 1.7 > 1 and ξ = 0.999 < 1, indicating that the intelligent agent system can achieve consensus by utilizing the event-triggered pulse-based multi-agent consensus cooperative control method of this invention.

[0091] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-agent consensus cooperative control method based on event-triggered pulses, characterized in that, include: S1: Construct a communication topology by treating each agent of the nonlinear multi-agent system as a communication node; S2: Construct a dynamic model of the agent in a second-order discrete system based on algebraic graph theory and initialize the system; S3: Set the discontinuous saturation constraint pulse control protocol; S4: Each agent communicates with each other according to the communication topology, and continuously acquires the state information of its neighboring agents and saves its own state information during the communication process; S5: At pulse moments, a discontinuous saturated constraint pulse control protocol is used to update the state and velocity information of all agents; at non-pulse moments, the state and velocity information of all agents are updated according to the dynamic model; the discontinuous saturated constraint pulse control protocol is expressed as: ； in, This represents the pulse input of a multi-agent system. Indicates pulse gain. Represents the Dirac function, Represents a node To the node The weights of ordered edges, This represents the total number of nodes in the system. Represents intelligent agents A collection of neighboring intelligent agents, Represents intelligent agents The state variable at the time preceding time n Represents intelligent agents Neighbor Intelligent Agent The velocity variable at the time preceding time n; The process of updating the state information of each agent and its neighboring agents using a discontinuous saturation constraint pulse control protocol includes: at the pulse moment, determining whether the system satisfies the trigger function; if so, calculating the control input according to the discontinuous saturation constraint pulse control protocol and updating the agent's state information according to the control input; otherwise, maintaining the agent's state information. The trigger function is expressed as follows: ； ； in, Indicates the trigger function. Indicates intermediate parameters. Indicates the error coefficient. Indicates when Joint state error at time, express Joint state error at time t, Indicates the initial pulse time. Indicates the trigger constant; S6: Construct an error system based on the state information of each agent and its neighboring agents. When the error system is stable, all agents reach a consensus.

2. The multi-agent consensus cooperative control method based on event-triggered pulses according to claim 1, characterized in that, The process of constructing a communication topology includes: set up yes An undirected graph of order, in which It is an edge set. Represents a set of nodes. The undirected graph has a weighted adjacency matrix of non-negative elements, where is the total number of nodes in the system. ,in For nodes To the node The weight of the ordered edges is given if and only if the node and nodes When there is no boundary between them, Based on the degree matrix D and the Laplace matrix L of the undirected graph, , , This indicates a diagonalization operation.

3. The multi-agent consensus cooperative control method based on event-triggered pulses according to claim 1, characterized in that, The dynamic model of the agent in the second-order discrete system is expressed as follows: ； in, Indicates the first An intelligent agent in Location at any given moment Indicates the first An intelligent agent in The speed of time, Indicates the first coefficient. Indicates the second coefficient. This represents a nonlinear function related to velocity. Indicates the first Constrained control inputs for an agent Indicates the first An intelligent agent in The k-th pulse time of time, Indicates in The change in state at any given time. Indicates in The change in velocity at any given moment The pulse gain constant represents the state variable. The pulse gain constant represents the velocity variable.

4. The multi-agent consensus cooperative control method based on event-triggered pulses according to claim 1, characterized in that, In step S5, the process of updating the state information of each agent and its neighboring agents according to the dynamic model at non-pulse times includes: at non-pulse times, obtaining the state information of each agent at the previous time according to the dynamic model, and updating the current state information of each agent according to its own and its neighboring agents' state information at the previous time.

5. The multi-agent consensus cooperative control method based on event-triggered pulses according to claim 1, characterized in that, The error system is represented as follows: ； in, This represents a column vector consisting of the average state errors of all agents at time n. This represents the column vector consisting of the average velocity errors of all agents at time n. Describes a positive definite matrix. express An identity matrix of dimension 1 Let n be a column vector consisting of the nonlinear functions of all agents related to velocity at time n. Indicates in The column vector consisting of the average state errors of all agents at time t. Indicates in The column vector consisting of the average velocity errors of all agents at time t. Represents the state pulse gain constant. Represents the velocity pulse gain constant. Represents the constrained control input vector of the intelligent agent.

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