Multi-agent system finite time consensus control method and communication device

Abstract

The application provides a multi-agent system finite time consensus control method and communication equipment, first, a multi-agent system is constructed, the multi-agent system comprises one leader agent and q follower agents, and a dynamic model of the agent system is obtained; then when the follower agent cannot obtain the state of the leader agent, a tracking error estimator is designed; considering the unknown state of the leader agent to part of the follower agents, an event-triggered control protocol is constructed; finally, according to the event-triggered control protocol, the control of the finite time consensus of the multi-agent system is realized. The application has the beneficial effect that the convergence speed and the convergence precision of the system are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of agent system, and particularly relates to a multi-agent system finite time consensus control method and a communication device. BACKGROUND

[0002] In the prior art, event-triggered leader-follower tracking control of a directed topological first-order linear multi-agent system is studied. Generally, a distributed event-triggered estimator is first proposed to estimate the state of the leader, to ensure that the estimation error of the estimator is maintained within a certain range, and the estimator system does not exhibit Zeno behavior. Then, the estimator is used to construct an event-triggered controller in a completely distributed manner, to achieve a bounded tracking error. Although the event-triggered manner can effectively reduce communication and save resources, the implementation is still gradual convergence consensus. In combination with actual needs, it is necessary to conduct further research on the convergence speed of the first-order linear multi-agent system. SUMMARY

[0003] To solve the above problems, the present application provides a multi-agent system finite time consensus control method and a communication device. The multi-agent system finite time consensus control method mainly comprises the following steps:

[0004] S1: constructing a multi-agent system, the multi-agent system comprising one leader agent and q follower agents, to obtain a dynamic model of the agent system;

[0005] S2: designing a tracking error estimator when the follower agent cannot obtain the state of the leader agent;

[0006] S3: considering the unknown state of the leader agent to some follower agents, constructing an event-triggered control protocol;

[0007] S4: implementing control of the finite time consensus of the multi-agent system according to the event-triggered control protocol.

[0008] Further, the dynamic model of the multi-agent system is:

[0009]

[0010] wherein i={1,2,…,q}, q∈N, u i (t)∈R represents a control input, represents the derivative of the state of the i-th follower agent, represents the disturbance of the i-th follower agent, represents the derivative of the state of the leader agent, u0(t) represents the control input of the leader agent, represents the disturbance of the leader agent.

[0011] Further, the designed tracking error estimator is:

[0012]

[0013] where a1, a2, a3 are three positive numbers as adjustable feedback gains, is the estimation value of is the estimation value of is the estimation value of j = 0, …, q, m, n are two odd numbers, satisfying n > m > 0, represents the state tracking error between the follower agent and the leader agent; sign() represents the sign function, a ij is an adjacent matrix element, representing the communication relationship between agents, x j (t) represents the state of the jth follower agent, j = {1, 2, …, q}.

[0014] Further, the event-triggered control protocol is:

[0015]

[0016] where the error feedback gains κ1, κ2, κ3 are all greater than 0, is the pth triggering time of the ith follower agent, u i (t) represents updating only at the triggering moment, and after updating, it remains unchanged until the next triggering moment; represents the m / n power of represents the value at

[0017] Further, the Lyapunov function shown below is constructed to prove that the method realizes the finite-time consensus control of the multi-agent system:

[0018]

[0019] where H is a positive definite matrix and H = L + B, L represents the Laplacian matrix, and B represents the diagonal matrix;

[0020] Through calculation, when the time is achieved, that is, finite-time consensus is achieved, where θ represents a real number greater than zero and less than 1, and x(0) represents the state of the agent at 0 time.

[0021] ​A communication device includes a processor and a storage device; the storage device stores instructions and data, and the processor loads and executes the instructions and data in the storage device to implement the multi-agent system finite time consensus control method.

[0022] The technical solution provided by the application has the beneficial effects that: a new control protocol based on an event triggering mechanism is proposed for a first-order multi-agent system with a leader agent, and under the control of the control protocol, the system can achieve finite time consensus. Compared with progressive stability and consensus final bounded stability control, finite time stability control can not only ensure that the system can obtain faster convergence speed and convergence accuracy, but also has better anti-interference ability when there is interference outside the system. BRIEF DESCRIPTION OF DRAWINGS

[0023] The application will be further described below with reference to the accompanying drawings and examples, wherein:

[0024] Figure 1 is a flowchart of a multi-agent system finite time consensus control method in an embodiment of the application.

[0025] Figure 2 is a system topology diagram in an embodiment of the application.

[0026] Figure 3 is a state diagram of an agent in an embodiment of the application.

[0027] Figure 4 is a control input change diagram of an agent in an embodiment of the application.

[0028] Figure 5 is a triggering time diagram of an agent in an embodiment of the application.

[0029] Figure 6 is a schematic diagram of the working of a hardware device in an embodiment of the application. DETAILED DESCRIPTION

[0030] In order to have a clearer understanding of the technical features, objectives and effects of the application, the specific embodiments of the application will be described in detail with reference to the accompanying drawings.

[0031] Embodiments of the application provide a multi-agent system finite time consensus control method and a communication device, which are realized based on an event triggering mechanism and an estimator.

[0032] Please refer to Figure 1 , Figure 1 is a flowchart of a multi-agent system finite time consensus control method in an embodiment of the application, specifically including:

[0033] S1: a multi-agent system is constructed, the multi-agent system comprises a leader agent and q follower agents, and a dynamic model of the multi-agent system is obtained;

[0034] S2: when the follower agent cannot obtain the state of the leader agent, a tracking error estimator is designed;

[0035] S3: considering that the state of the leader agent is unknown to part of the follower agents, an event-triggered control protocol is constructed;

[0036] S4: according to the event-triggered control protocol, control of finite-time consensus of the multi-agent system is realized.

[0037] The event-triggered control protocol proposed in the application, that is, based on an event-triggering mechanism, can realize finite-time consensus and avoid the occurrence of the Zeno phenomenon when the system has a bounded disturbance, under the condition that the state of the leader agent is unknown to part of the follower agents. Considering a first-order multi-agent system with a leader agent, the communication topology graph G between the follower agents is connected, and at least one follower agent communicates with the leader agent, and the dynamic model of the multi-agent system is as follows:

[0038]

[0039] wherein x i (t)∈R represents the state of the i-th follower agent, i={1, 2, …, q}, u i (t)∈R represents a control input, represents a disturbance of the system, represents the derivative of the state of the i-th follower agent, represents the disturbance of the i-th agent, x0(t)∈R represents the state of the leader agent, represents the derivative of the state of the leader agent, u0(t) represents the control input of the leader agent, represents the disturbance of the leader agent. It is assumed that u0(t) satisfies |u0(t)|≤η, η and γ are two non-negative constants. The state tracking error between the follower agent and the leader agent is defined as wherein In actual application, considering that the follower agent cannot obtain the state of the leader agent in some cases, the tracking error estimator is designed as follows:

[0040]

[0041] wherein a1, a2, and a3 are three positive numbers, and k is an adjustable feedback gain, ​The estimated value of the error satisfies m, n are two odd numbers, n>m>0, and the estimation error of the estimator is defined The derivative of which is Wherein, F(t)=[F1(t), F2(t),..., F q (t)] T , And H is a positive definite matrix and H=L+B, L represents a Laplace matrix, B represents a diagonal matrix, λ min is the minimum eigenvalue of H, and it is easy to obtain a positive definite matrix M, Wherein, As part of the Lyapunov function V(t).

[0042] The control protocol is designed as Wherein, the error feedback gain κ1, κ2, κ3>0, is the pth trigger time of the ith agent, and u i (t) is only updated at the trigger time, and after updating, it remains unchanged until the next trigger time. The measurement error is defined as The time trigger function is designed The adjustable event trigger parameters τ1, τ2∈(0, 1), Q xi (t) is the absolute value of the m / n power of the defined Q i (t), when g (t)>0, i The control protocol u min (t) is updated. When 2γ+η-(1-τ2)κ2<0 and 2a3λ x -a1>0, the system realizes finite-time consensus, and no "Zeno" phenomenon occurs. The proof is as follows:

[0043] First, the Lyapunov function V(t) is constructed Here e x (t) is is Let

[0044] The derivative of V1(t) is obtained as

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] where,

[0051] Similarly, the next V2(t) derivative can be obtained:

[0052]

[0053]

[0054] where, c4=2a3l min -a1.

[0055] Therefore, we can get

[0056] Let It is easy to get f(V2(t)) has a maximum value

[0057] Finally, we can get:

[0058]

[0059] So the system can achieve consistency when , that is, it achieves finite-time consensus. θ represents a real number greater than zero and less than 1, and x(0) represents the state of the agent at time 0.

[0060] Next, it is proved that the "Zeno" phenomenon is excluded, the process is as follows:

[0061]

[0062] Because q i is the number of neighbors of the ith agent. Positive numbers ξ1, ξ2 are the upper bounds of , from which we can get:

[0063]

[0064] Since the event triggers g i (t)>0, so Let It is easy to see that there exists a unique zero point x0 > 0, therefore we have That is, the "Zeno's phenomenon" will not occur.

[0065] To demonstrate the effectiveness of the control protocol proposed in this invention, Figure 2 Taking the multi-agent system topology diagram shown as an example, 0 represents the leader agent, and 1-4 represent the four follower agents. The initial values ​​of the follower agents are selected as x(0) = [5,8,-10,14]. T The initial values ​​of the leader agent are: x0 = 4.25, m = 21, n = 25, τ1 = 0.6, τ2 = 0.04, η = 0.12, γ = 0.15, κ1 = 5.8, κ2 = 0.64, κ3 = 0.27, a1 = 1.5, a2 = 0.51, a3 = 5.21, u0(t) = 0. Under the control protocol of this invention, the state of the intelligent agent is as follows: Figure 3 As shown, from Figure 3 It can be seen that, under the control of the control protocol, the four follower agents changed from initial states of 5, 8, -10, and 14 respectively, eventually aligning with the leader agent's state. When the trigger condition is met, the control inputs of these four follower agents are updated, and during this period, the changes in their control inputs are as follows: Figure 4 As shown, the moment when the control input is updated is the trigger moment. The trigger moments of these four follower agents are as follows: Figure 5 As shown, the control output is 0 when the four follower agents maintain the same position and state as the leader agent. By continuously updating the control input at each event trigger, finite-time consistent leader-follower control is ultimately achieved.

[0066] Please see Figure 6 , Figure 6 This is a schematic diagram of the hardware device operation according to an embodiment of the present invention. The hardware device specifically includes: a communication device 401, a processor 402, and a storage device 403.

[0067] The communication device 401 includes a processor 402 and a storage device 403; the storage device 403 stores instructions and data.

[0068] Processor 402: The processor 402 loads and executes the instructions and data in the storage device 403 to implement the finite-time consistency control method for a multi-agent system.

[0069] The present application has the beneficial effects that a new event-triggered control protocol based on a first-order multi-agent system with a leader agent is proposed, and the system can realize finite-time consensus under the control of the control protocol. Compared with the gradual stability and the consensus final bound stability control, the finite-time stability control can not only ensure that the system can obtain faster convergence speed and convergence accuracy, but also has better anti-interference ability when there is interference outside the system.

[0070] The above merely describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A finite-time consistency control method for a multi-agent system, characterized in that: include: S1: Construct a multi-agent system, which includes one leader agent and q follower agents, and obtain the dynamic model of the agent system; S2: Design a tracking error estimator when the follower agent cannot obtain the state of the leader agent; S3: Considering the situation where the leader agent's state is unknown to some follower agents, construct an event-triggered control protocol; S4: Implement finite-time consistency control of the multi-agent system according to the event-triggered control protocol; The event triggering control protocol is as follows: Among them, error feedback gain , For the first The first follower agent's first Trigger time, This means that the update only occurs at the trigger time and remains unchanged until the next trigger time. express m / n power, Indicates in The value at time, , , For adjustable feedback gain, for The estimated value, , Indicates in The state of the leader agent at all times. These are the elements of the adjacency matrix, representing the communication relationships between agents.

2. The finite-time consistency control method for a multi-agent system as described in claim 1, characterized in that: The dynamic model of a multi-agent system is as follows: in, , q , Indicates control input, This indicates the state of the leader agent. Indicates the first The derivative of the state of a follower agent. Indicates the first The disturbance of a follower agent The derivative representing the state of the leader agent. This represents the control input for the leader agent. This represents the disturbance of the leader agent.

3. The finite-time consistency control method for a multi-agent system as described in claim 2, characterized in that: The designed tracking error estimator is as follows: in, , , Three positive numbers represent the adjustable feedback gain. for The estimated value, for The estimated values, j=0,…, q , , Two odd numbers satisfying , , This represents the state tracking error between the follower agent and the leader agent. The elements of the adjacency matrix represent the communication relationships between agents. Indicates the first The state of a follower agent .

4. The finite-time consistency control method for a multi-agent system as described in claim 1, characterized in that: Construct the Lyapunov function shown below to prove that this method enables finite-time consistency control of multi-agent systems: in, It is a positive definite matrix and , Represents the Laplace matrix, Represents a diagonal matrix; Calculations show that when time At that time, finite-time consistency is achieved, where, Represents real numbers that are greater than zero and less than 1. This represents the state of the agent at time 0.

5. A communication device, characterized in that: The communication device includes a processor and a storage device; the storage device stores instructions and data, and the processor loads and executes the instructions and data in the storage device to implement the finite-time consistency control method for multi-agent systems as described in any one of claims 1 to 4.

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