Consensus control method for heterogeneous multi-agent system based on event-triggered control

Abstract

The application discloses a kind of event trigger control-based heterogeneous multi-agent system consistency control method, the heterogeneous multi-agent system contains m first-order multi-agent, N-m second-order multi-agent, communication is carried out through weighted undirected network;First, according to the convergence of the heterogeneous multi-agent system to consistency, the position of agent converges to the average value of position, and the speed converges to 0, define the average value of position convergence;Then the consistency problem of the heterogeneous multi-agent system is converted into a stability problem, and the consistency control of the heterogeneous multi-agent system is realized by piecewise control input rate and event trigger control.The application combines the event trigger control of combined measurement method, inherits the consistency of first-order second-order heterogeneous multi-agent system, reduces the loss of communication resources.The condition of matrix Q is that its minimum singular value is greater than 0, to reduce the conservativeness of event trigger condition.

Description

Technical Field

[0001] This invention belongs to the field of distributed control technology and relates to a consensus control method for multi-agent systems, specifically a consensus control method for heterogeneous multi-agent systems based on event-triggered control. Background Technology

[0002] Distributed coordinated control of multi-agent systems has attracted widespread attention due to its extensive applications in formation control, swarm control, and swarm control. In contrast, centralized control requires each node to have a reliable network communication connection with the central controller. However, in practical applications, due to factors such as communication latency, centralized control often fails to achieve the intended control effect effectively. Furthermore, due to potential single points of failure, the probability of failure in centralized control is higher than in distributed control. Distributed control reduces the impact of communication delays between the central controller and individual nodes in centralized control, enabling the system to adapt to dynamically changing operating environments, reducing reliance on global communication, and improving the system's fault tolerance and robustness.

[0003] The consistency problem, as one of the most fundamental distributed coordination control problems, is an intersection of control system theory and graph theory. It involves a series of intelligent agents achieving a common goal through information interaction and sharing. Consistency refers to the fact that the various states of an intelligent agent system eventually converge to the same value at a certain point in time. This state can be the attitude of a satellite, the direction of movement of a school of fish or a flock of birds, data fusion, or the filtered values ​​of distributed sensors.

[0004] Currently, research on the consensus problem mainly focuses on the cooperative consensus control of first-order, second-order, higher-order, and heterogeneous systems. The paper "Distributed event-triggered control of multi-agent systems with combinational measurements" proposes an event-triggered control method using combinational measurements. Unlike previous event-triggered control methods, agents trigger only at their own event times without considering the triggering times of their neighbors. This reduces communication overhead and lowers the frequency of controller updates in practice. This scheme demonstrates the feasibility of a method, but it does not consider first-order and second-order heterogeneous multi-agent systems. The paper "Distributed event-triggered consensus control for leaderless heterogeneous multi-agent systems" uses a distributed event-triggered control method to control first-order and second-order heterogeneous multi-agent systems to achieve average position consensus and velocity convergence to zero, eliminating the zeno behavior of the system. However, this scheme does not consider event-triggered control using combinational measurements and cannot better mitigate the energy consumption of control input updates. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a consistency control method for heterogeneous multi-agent systems based on event-triggered control.

[0006] The technical solution adopted by the method of the present invention is: a consistency control method for heterogeneous multi-agent systems based on event-triggered control, wherein the heterogeneous multi-agent system contains m first-order multi-agents and Nm second-order multi-agents, and communicates through a weighted undirected network;

[0007] First, based on the principle that when the heterogeneous multi-agent system converges to consistency, the agent's position converges to the average position and the velocity converges to 0, the average position convergence is defined. Then, the consistency problem of the heterogeneous multi-agent system is transformed into a stability problem, and the consistency control of the heterogeneous multi-agent system is achieved by segmented control of the input rate and event-triggered control.

[0008] This invention also provides a heterogeneous multi-agent system consistency control system based on event-triggered control, comprising:

[0009] One or more processors;

[0010] A storage device for storing one or more programs, which, when executed by one or more processors, enable the one or more processors to implement the event-triggered control-based heterogeneous multi-agent system consistency control method.

[0011] The present invention also provides a storage medium storing a program, which, when executed by a processor, implements the event-triggered control-based heterogeneous multi-agent system consistency control method.

[0012] Compared with the prior art, the advantages of the present invention are:

[0013] (1) It combines event-triggered control with combined measurement methods, inherits the consistency of first-order and second-order heterogeneous multi-agent systems, and reduces communication resource consumption.

[0014] (2) The condition for matrix Q is that its smallest singular value is greater than 0, in order to reduce the conservatism of the event triggering condition. Attached Figure Description

[0015] The technical solutions described herein are further illustrated below using examples and specific implementation methods. Additionally, accompanying drawings are used in the description of the technical solutions. Those skilled in the art can, without any creative effort, obtain other drawings and the intent of the present invention based on these drawings.

[0016] Figure 1 This is a topology diagram of a multi-agent system according to an embodiment of the present invention;

[0017] Figure 2 This is a location status update diagram according to an embodiment of the present invention;

[0018] Figure 3 This is a speed state update diagram according to an embodiment of the present invention;

[0019] Figure 4 This is a control input update diagram according to an embodiment of the present invention;

[0020] Figure 5 This is a diagram showing the number of triggers for heterogeneous multi-agent systems in an embodiment of the present invention. Detailed Implementation

[0021] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0022] This invention provides a consistency control method for a heterogeneous multi-agent system based on event-triggered control. The heterogeneous multi-agent system contains m first-order multi-agents and Nm second-order multi-agents, which communicate through a weighted undirected network.

[0023] First, based on the principle that when the heterogeneous multi-agent system converges to consistency, the agent's position converges to the average position and the velocity converges to 0, the average position convergence is defined. Then, the consistency problem of the heterogeneous multi-agent system is transformed into a stability problem, and the consistency control of the heterogeneous multi-agent system is achieved by segmented control of the input rate and event-triggered control.

[0024] In one implementation, the topology of the weighted undirected network is defined as G = {V, ε, A}, where V = {V1, V2, ..., V}. N} represents a set of nodes, V i Let i represent the agent with the number i, where 1 ≤ i ≤ N; Represents the edge set; A = [a ij ]∈R N×N Represents a weighted adjacency matrix, where a is a link between agents i and j if there is an information link between them. ij =1, otherwise a ij =0; Define D as the degree matrix, and the Laplace matrix L = DA;

[0025] When i = 1, 2, ..., m, the dynamic equation of a first-order agent is defined as follows: When i = m+1, m+2, ..., N, the dynamic equation of the second-order agent is defined as follows: Where t represents time; each agent stores its own state information, and the position and state value of the i-th agent at time t is defined as x. i (t), the velocity state value of the last Nm agents at time t is v. i (t);

[0026] Define a consensus protocol:

[0027]

[0028] Where, x i (t), x j (t) represent the position and state information of the i-th and j-th agents at time t, respectively; v i (t), v j (t) represent the velocity state information of the i-th and j-th agents at time t, respectively; I m I represents the set of the first m agents out of N agents, i.e., the first-order agents. N-m This represents the set of the last Nm agents out of N agents, i.e., the second-order agents; b ij The weights of the weighted adjacency matrix corresponding to the velocity topology of the second-order agent are represented by α and β, which are the feedback gains of the system satisfying α>0 and β>0; L A =[a ij ] N×N ,L B=[b ij ] (N-m)×(N-m) It is location map G p and velocity graph G v The corresponding matrix, j∈N i It is the set of neighbors of agent i;

[0029] Define the trigger time of the k-th event for agent i as Represent the roles of agents i and j in... Substituting the position sampling state and velocity sampling state at each moment into equation (3), we get:

[0030]

[0031] Substituting equation (4) into equations (1) and (2), we get:

[0032]

[0033] The combined measurement position and combined measurement velocity of agent i in its neighbor agent j are:

[0034]

[0035] Substituting equation (6) into equation (5), we get: Define the measurement error of the sampling data as: Where e f,x (t)=(e 1,x (t),e 1,x (t),...,e m,x (t)) T ,e s,x (t)=(e m+1,x (t),e m+2,x (t),...,e N,x (t)) T ,e s,v (t)=(e m+1,v (t),e m+2,v (t),...,e N,v (t)) T x f (t)=(x1(t),x2(t),...,x m (t)) T ,x s (t)=(x m+1 (t),x m+2 (t),...,x N (t)) T ,v s (t)=(v m+1 (t),v m+2 (t),...,v N(t)) T ;

[0036] Substituting equation (8) into equation (7), we get:

[0037] Equation (9) can be further written as:

[0038]

[0039] make The system is then rewritten in matrix form:

[0040]

[0041] in L 11 L 12 L 21 L 22 L represents A The block matrix, L 11 ∈R m*m L 12 ∈R m*(N-m) L 21 ∈R (N-m)*m L 22 ∈R (N-m)*(N-m) .

[0042] From the system's dynamic equations, we know that when a first-order and second-order heterogeneous multi-agent system converges to uniformity, the agents' positions converge to the average position, and their velocities converge to zero. Therefore, we define the average position convergence value as:

[0043] Define a column vector

[0044] Let the system's error signal The error system is then:

[0045]

[0046] when hour, Equivalent to

[0047] Therefore, the consistency problem of the heterogeneous multi-agent system (11) is transformed into the stability problem of the research system (12).

[0048] Let ε(t) be ε, and construct a Lyapunov function:

[0049] V(t)=ε T Pε (13);

[0050] Where P is a positive definite symmetric matrix;

[0051] Differentiating V(t), we get:

[0052]

[0053] Where P is a positive definite symmetric matrix, a matrix Q = G is defined. T Given P+PG-PK, there exists a matrix P such that svd min (Q)>0; svd min (Q) denotes the smallest singular value of matrix Q;

[0054] Define λ max (P) is the largest eigenvalue of matrix P, and ||K|| is the spectral norm of matrix K; then equation (14) can be further written as:

[0055]

[0056] Forced e i satisfy When σ i When ∈(0,1), we obtain a negative definite value. As time goes on, once the condition (16) changes, the agent i will trigger an event; at the same time, the measurement error of the agent i is set to 0, and the control law is updated according to equation (4), otherwise the control law remains unchanged;

[0057] Based on the Lasalle invariant principle, define the Lasalle invariant set. express

[0058] Further results were obtained:

[0059]

[0060]

[0061]

[0062] That is, the consistency problem of heterogeneous multi-agent systems is solved.

[0063] Systems (1) and (2) in an undirected connected topology G, through piecewise control of the input rate (4) and the event triggering function (16), ensure that for any initial condition, there exists at least one agent r∈V whose time interval... Strictly positive, lower bound τ r >0.

[0064] The proof is as follows: Define r = arg max i ||ε i||and believes||e i ||≤||e|| holds for all agents i, therefore: Define τ r for From 0 to Time, τ * for From 0 to From the above inequality, we can obtain the time τ. r Ratio to τ * It needs to be big.

[0065]

[0066] definition achievable Assume θ(t,θ0) is an equation The solution is found, and θ(0,θ0)=θ0, therefore φ≤θ(t,θ0). The minimum time interval can be obtained by calculating the time of this differential equation:

[0067] Assuming the system starts when the first event is triggered, θ0 = 0; otherwise, the system will continue to evolve, and for at least one agent, its absolute measurement error will increase without being reset.

[0068] Define τ as a solution to equation (17), and we can obtain make The minimum time interval between any two agents Obviously τ * The value >0 proves that the event will not be triggered indefinitely, thus ruling out Zeno's behavior.

[0069] The present invention will be further illustrated by the following experiments.

[0070] This experiment considers the following system: Its topology diagram is as follows Figure 1 As shown.

[0071] Agents 1 and 2 are first-order integral agents, while agents 3 and 4 are second-order integral agents. The Laplace matrix L of the positional topology... A and L B They are respectively: With feedback gain α = 1 and β = 1, the initial position of the system is x = (2, -1, -2, 3). T The initial velocity is v = (-1, 1). T , the parameter δ is set to δ1=δ2=δ3=δ4=δ5=δ6=0.9. Figure 2 and Figure 3 These represent the agent's position and velocity reaching the same level, respectively. Figure 4 Indicates the system's control input, by Figure 4 It can be seen that once the agent reaches the consensus goal, the agent's control protocol is 0. Figure 5 The system displays the trigger count for each agent. Through simulation, the timestamp [0s, 10s] is divided into 1000 intervals, each with h = 0.01s. The trigger counts for each agent are 47, 47, 81, and 81 times respectively. If no event is triggered, control updates require at least 1000 updates. Figure 5 It can be seen that the number of times the input is updated has been effectively reduced.

[0072] This invention realizes first- and second-order heterogeneous multi-agent consensus in event-triggered control of a combined measurement method. The event-triggered control of the combined measurement method reduces communication resource consumption. Its key points are as follows:

[0073] 1. Feedback gains α, β, and design constant σ i All are kept within a reasonable range.

[0074] 2. Agents only trigger at their own event time without considering the triggering time of their neighbors, reducing communication frequency and energy consumption, and avoiding the "Zeno's phenomenon".

[0075] 3. The discussion of first-order and second-order heterogeneous multi-agent system models is more consistent with some real-world situations.

[0076] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A consensus control method for heterogeneous multi-agent systems based on event-triggered control, characterized in that: The heterogeneous multi-agent system contains A first-order multi-agent system Two second-order multi-agent communication networks are used to communicate. First, based on the principle that when the heterogeneous multi-agent system converges to consistency, the agent's position converges to the average position and the velocity converges to 0, the average position convergence is defined. Then, the consistency problem of the heterogeneous multi-agent system is transformed into a stability problem, and the consistency control of the heterogeneous multi-agent system is achieved by segmented control of the input rate and event-triggered control. Define a consensus protocol: (3)； in, , They represent the first , An intelligent agent in Location status information at any given time; , They represent the first , An intelligent agent in Velocity status information at any given moment; express Among the intelligent agents, the first An intelligent agent is a set of first-order intelligent agents. Represents the last of N intelligent agents A set of intelligent agents, namely, a set of second-order intelligent agents; The weight values ​​of the weighted adjacency matrix represent the velocity topology of a second-order agent. , Is the system's feedback gain satisfied? >0, >0; , It is a location map and velocity diagram The corresponding matrix, It is an intelligent agent The neighbor set; Define intelligent agents The k The event is triggered at the time of the event. , , , , Representing intelligent agents respectively and exist Substituting the position sampling state and velocity sampling state at time t into equation (3), we get: (4)； Substituting equation (4) into equations (1) and (2), we get: (5)； intelligent agent In its neighboring intelligent agent The combined measurement position and combined measurement speed are: (6)； Substituting equation (6) into equation (5), we get: (7); Define the measurement error of the sampling data as: (8); in , ； Substituting equation (8) into equation (7), we get: (9); Equation (9) can be further written as: (10)； make The system is then rewritten in matrix form: (11)； in , , ; , , , express The block matrix, , , , ; From the system's dynamic equations, we know that when a first-order and second-order heterogeneous multi-agent system converges to uniformity, the agents' positions converge to the average position, and their velocities converge to zero. Therefore, we define the average position convergence value as: Define a column vector ; Let the system's error signal Then the error system is: (12)； when hour, , equivalent to , Therefore, the consistency problem of the heterogeneous multi-agent system (11) is transformed into the stability problem of the research system (12).

2. The consensus control method for heterogeneous multi-agent systems based on event-triggered control according to claim 1, characterized in that: The topology graph of the weighted undirected network is defined as follows: , Represents a set of nodes. Indicates the number is i intelligent agents, 1≤ i ≤N; Represent edge set; Represents a weighted adjacency matrix, if the agent and intelligent agents If there are information links between them =1, otherwise =0; definition For degree matrix, Laplace matrix ; when At that time, the dynamic equation of a first-order intelligent agent is defined as follows: (1); when At that time, the dynamic equation of the second-order intelligent agent is defined as follows: (2); among which t Represents time; each agent stores its own state information, specifying the first... An intelligent agent in t The position state value at time 1 After N- m An intelligent agent in t The velocity state value at time t is .

3. The consensus control method for heterogeneous multi-agent systems based on event-triggered control according to claim 2, characterized in that: Construct a Lyapunov function: (13)； in Let be a positive definite symmetric matrix, denoted as for ; right Differentiating, we get: (14)； Define a matrix There exists a matrix Make >0; Representation matrix The smallest singular value; definition For matrix The largest eigenvalue, Let K be the spectral norm of matrix K; then equation (14) can be further written as: (15)； Forced satisfy (16); when At that time, we obtain a negative definite value. , As time goes on, once the conditions (16) change, the agent... An event will be triggered; at the same time, the intelligent agent The measurement error is set to 0, and the control law is updated according to equation (4); otherwise the control law remains unchanged. Based on the Lasalle invariant principle, define the Lasalle invariant set. , express , Further results were obtained: ， ， ； That is, the consistency problem of heterogeneous multi-agent systems is solved.

4. A consensus control system for heterogeneous multi-agent systems based on event-triggered control, characterized in that, include: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the event-triggered control-based heterogeneous multi-agent system consistency control method as described in any one of claims 1 to 3.

5. A storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the event-triggered control-based consistency control method for heterogeneous multi-agent systems as described in any one of claims 1 to 3.

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