A distributed weighted average tracking control method with communication delay

Abstract

The present invention provides a distributed weighted average tracking control method with communication delay, which relates to the field of information technology. The present invention first constructs a multi-agent network topology diagram, gives the state equation and weighted average signal of the system, then designs a distributed control law according to the dynamic equation and the control target, and finally analyzes the convergence of the algorithm. This method can make the state tracking of all agents the weighted average of multiple time-varying signals using only the past state information of the agent's neighbors. Tracking the average value of weighted signals is often more in line with actual needs. When the weights of all signals are the same, the distributed weighted average tracking is degraded to distributed average tracking, so the technology of the present invention is more general than the general distributed average tracking method, and can be applied to many fields such as smart grids and sensor fusion. This invention not only has profound theoretical value, but also has rich practical significance.

Description

Technical Field

[0001] The present invention relates to the field of information technology, and in particular to a distributed weighted average tracking control method with communication delay. Background Art

[0002] With the advancement of communication and computing technologies, distributed cooperative control of multi-agent systems has received increasing attention and has been widely studied in the past few decades. Distributed average tracking, as an important type of cooperative control problem, has attracted much attention in recent years due to its wide application in many fields such as distributed optimization, smart grid, sensor fusion, etc. The goal of distributed average tracking is to make all agents track the average of multiple time-varying signals using only local information, where each agent can only access its own time-varying signal. Distributed average tracking under constant signals is degraded to static average consistency. Compared with static average consistency, distributed average tracking is more general and challenging because the desired trajectory (i.e., the average of multiple time-varying signals) is time-varying and unknown to any agent.

[0003] However, in practice, multi-agent systems are usually affected by communication delays, which can make the system less stable. Many scholars have done a lot of research on the processing of delays, but the signals that can be tracked in existing studies are only the average values ​​of reference signals. In practice, the signal to be tracked is often not the average value of a time-varying signal, so the present invention proposes a distributed weighted average tracking control method with communication delay, which can use only the past state information of the agent's neighbors to make the state tracking of all agents the weighted average of multiple time-varying signals. Tracking the average value of weighted signals is often more in line with actual needs. When the weights of all signals are the same, distributed weighted average tracking is downgraded to distributed average tracking, so the research of the present invention is more extensive than the research on distributed average tracking. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a distributed weighted average tracking control method with communication delay. Compared with the prior art, the distributed weighted average tracking method with communication delay provided by the present invention is more in line with the actual situation, more general, and has important value in practical application.

[0005] A distributed weighted average tracking control method with communication delay comprises the following steps:

[0006] Step 1: Construct a multi-agent network topology graph, which is an undirected connected graph G = (V, E, A), where V = {1, ..., n} represents a set of n nodes. represents the set of edges, represents the adjacency matrix, represents a set of n×n dimensional real number matrices; in the adjacency matrix, if there is an edge connecting nodes i and j, then a ij =

[0007] a ji =1, otherwise a ij =a ji =0;

[0008] Step 2: Given the state equation of the system; consider a multi-agent system consisting of n agents that interact with each other on an undirected graph, where the agents are described by the following single integrator dynamics:

[0009]

[0010] in, and Represent the state and control input of the ith agent, i=1,…,n, represents the set of real numbers, .

[0011] Step 3: Given a weighted average signal, the time-varying reference signal of the i-th agent is r i (t), the goal is to make each agent track the following time-varying weighted reference signal in the presence of communication delay:

[0012]

[0013] Among them, ω i >0 represents the weight of the i-th time-varying reference signal. When all weights are the same, distributed weighted average tracking degrades to distributed average tracking.

[0014] Step 4: Design the distributed control law u according to the dynamic equation and control objectives i (t):

[0015]

[0016] i=1,…,n (4)

[0017] The initial conditions should meet the following conditions:

[0018]

[0019] Among them, z i (t) represents the auxiliary variable of the ith agent, τ(t) represents the time-varying communication delay, parameters α>0, β>0, x i (0) represents the initial condition of the ith agent, r i (0) represents the initial condition of the time-varying reference signal of the ith agent, z i(0) represents the initial condition of the auxiliary variables of the i-th agent.

[0020] Step 5: Convergence analysis; according to the following error function

[0021]

[0022] A Lyapunov function is constructed and a linear matrix inequality condition is obtained which makes the derivative of the Lyapunov function less than 0. When the consistency is satisfied, the system can track the weighted average of the time-varying reference signal.

[0023] The beneficial effects of adopting the above technical solution are:

[0024] The present invention provides a distributed weighted average tracking control method with communication delay. The distributed control law designed by the method can effectively solve the problem of communication delay and can track any weighted average signal, which is more general in practical applications.

[0025] Compared with the prior art, the specific beneficial technical effects of the present invention are: (1) It can solve the communication delay problem between intelligent agents, thereby improving the robustness of the system. (2) The designed control law can make the state tracking of all intelligent agents on any weighted average signal, which is more applicable and more feasible than the general distributed average tracking method. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A block diagram of a distributed weighted average tracking control method provided in an embodiment of the present invention;

[0027] Figure 2 A schematic diagram of a multi-agent network topology structure established in an embodiment of the present invention;

[0028] Figure 3 This is a state trajectory diagram of the intelligent agent obtained by using the designed distributed control law in the embodiment of the present invention. DETAILED DESCRIPTION

[0029] The present invention is described in detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0030] A distributed weighted average tracking control method with communication delay, such as Figure 1 As shown, the following steps are included:

[0031] Step 1: Construct a multi-agent network topology graph, which is an undirected connected graph G = (V, E, A), where V = {1, ..., n} represents a set of n nodes. represents the set of edges, represents the adjacency matrix, represents a set of n×n dimensional real number matrices; in the adjacency matrix, if there is an edge connecting nodes i and j, then a ij =a ji =1, otherwise a ij =a ji =0.

[0032] In this embodiment, an undirected connected topological graph is constructed, and the structure is as follows: Figure 2 As shown in the figure, the nodes numbered 1, 2, 3, 4, 5, and 6 represent 6 agents respectively.

[0033] Step 2: Given the state equation of the system. Consider a multi-agent system consisting of n agents that interact with each other on an undirected graph, where the agents are described by the following single integrator dynamics:

[0034]

[0035] in, and Represent the state and control input of the i-th agent, i=1,…,n, Represents the set of real numbers.

[0036] Step 3: Given a weighted average signal, the time-varying reference signal of the i-th agent is r i (t), the goal is to make each agent track the following time-varying weighted reference signal in the presence of communication delay:

[0037]

[0038] Among them, ω i >0 represents the weight of the i-th time-varying reference signal. When all weights are the same, distributed weighted average tracking degrades to distributed average tracking.

[0039] Step 4: Design the distributed control law u according to the dynamic equation and control objectives i (t):

[0040]

[0041] i=1,…,n (4)

[0042] The initial conditions should meet the following conditions:

[0043]

[0044] Among them, z i (t) represents the auxiliary variable of the ith agent, τ(t) represents the time-varying communication delay, parameters α>0, β>0, xi (0) represents the initial condition of the ith agent, r i (0) represents the initial condition of the time-varying reference signal of the ith agent, z i (0) represents the initial condition of the auxiliary variables of the i-th agent.

[0045] Step 5: Convergence analysis. According to the following error function

[0046]

[0047] By constructing a Lyapunov function, a linear matrix inequality condition is obtained, which makes the derivative of the Lyapunov function less than 0. When the consistency is satisfied, the system can track the weighted average of the time-varying reference signal.

[0048] The parameters used in this embodiment are as follows:

[0049] Reference signal: r i (t) = i*(cos(t)+2);

[0050] Communication delay: τ = 0.0012;

[0051] Weight parameters: ω1=5; ω2=9; ω3=5; ω4=5; ω5=6; ω6=8; α=1; β=100;

[0052] Initial state: x1(0)=3; x2(0)=6; x3(0)=9; x4(0)=15; x5(0)=12; x6(0)=18;

[0053] z1(0)=0; z2(0)=0; z3(0)=0; z4(0)=0; z5(0)=0; z6(0)=0.

[0054] from Figure 3 It can be seen that by applying the distributed weighted average tracking control algorithm designed in the present invention, the state of each intelligent agent eventually converges to the weighted average of all time-varying reference signals, thereby achieving the control target.

[0055] Finally, it should be noted that the above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form a technical solution.

Claims

1. A distributed weighted average tracking control method with communication delay, characterized in that: The following steps are involved: Step 1: Construct a multi-agent network topology diagram; The network topology graph in step 1 is an undirected connected graph G = (V, E, A), where V = {1, ..., n} represents a set of n nodes, represents the set of edges, represents the adjacency matrix, represents a set of n×n dimensional real number matrices; in the adjacency matrix, if there is an edge connecting nodes i and j, then a ij =a ji =1, otherwise a ij =a ji =0; Step 2: Given the state equation of the system; Specifically, step 2 is to consider a multi-agent system including n agents, which interact with each other on an undirected graph, wherein the agents are described by the following single integrator dynamic state equation: in, and Represent the state and control input of the ith agent respectively, represents the set of real numbers; Step 3: Given the weighted average signal; the time-varying reference signal of the i-th agent is r i (t), the goal is to make each agent track the time-varying weighted reference signal in the presence of communication delay; The time-varying weighted reference signal described in step 3: Among them, ω i >0 represents the weight of the i-th time-varying reference signal. When all weights are the same, the distributed weighted average tracking is degraded to the distributed average tracking; Step 4: Design the distributed control law u according to the dynamic equation and control objectives i (t); The distributed control law u described in step 4 i (t): i=1,…,n (4) The initial conditions should meet the following conditions: Among them, z i (t) represents the auxiliary variable of the ith agent, τ(t) represents the time-varying communication delay, parameters α>0, β>0, x i (0) represents the initial condition of the ith agent, r i (0) represents the initial condition of the time-varying reference signal of the ith agent, z i (0) represents the initial condition of the auxiliary variables of the i-th agent; Step 5: Convergence analysis; construct the Lyapunov function and obtain a linear matrix inequality condition that makes the derivative of the Lyapunov function less than 0. When the consistency is satisfied, the system can track the weighted average of the time-varying reference signal. The step 5 is specifically as follows: A Lyapunov function is constructed, and a linear matrix inequality condition is obtained which makes the derivative of the Lyapunov function less than 0. When the consistency is satisfied, the system can track the weighted average of the time-varying reference signal.

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