CN114415517B - Multi-agent consistency control method based on time synchronization stability - Google Patents
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Abstract
The invention discloses a multi-agent consistency control method based on time synchronization stability, which comprises the following steps: establishing a second-order dynamic model of multiple intelligent agents, and designing a formation auxiliary function; based on the mathematical principle of unit direction vector, a novel direction symbol function is designed, and a novel fixed time sliding mode surface is constructed by utilizing the function; aiming at the multi-agent system, the convergence time of the multi-agent system is designed, and a fixed time synchronous convergence controller is constructed to realize the consistent tracking of the positions of the multi-agent system; the states of all the multiple agents cooperate to reach the equilibrium point. The control method has the characteristics of strong robustness, high control precision and the like, and is suitable for being applied to the problem of synchronous convergence consistency tracking of all states of a plurality of intelligent agents in fixed time.
Description
Technical Field
The invention relates to a multi-agent consistency control method based on time synchronization stability, which is mainly applied to spacecraft constellation formation, unmanned ship distribution tracking and the like, and belongs to the technical field of multi-agent control.
Background
With the rapid development of modern communications and intelligent computing, multiple intelligent systems have gained increased attention from students. The advantages of low cost, networking operation and high flexibility are proved to be effective in a plurality of practical applications. The multi-agent cooperative control is to form regular and orderly movement through mutual cooperation of a plurality of multi-agents. The multi-agent distributed tracking control has basic theoretical value and important engineering application prospect. Aiming at practical system models capable of widely representing spacecrafts, robots, unmanned vehicles and the like, the design of a distributed cooperative control algorithm for researching multiple intelligent agents is a problem to be solved urgently by the technicians in the field.
Aiming at the problem of multi-agent consistency control, patent CN108181926A discloses a rapid finite time consistency protocol, which improves the convergence rate of the multi-agent. Patent CN113269297a considers a multi-agent scheduling method with time constraints, improving the reaction speed and operational reliability of the multi-agent. However, the above two methods cannot meet the control requirement that all states of multiple agents in a specific task are synchronized at the same time. Patent 20210707354.X provides a controller design scheme for synchronous convergence of multiple dimensional states of a monomer system, but the method is not applicable to a distributed multi-agent system.
In conclusion, the multi-agent second-order dynamic system is taken as one of main research directions of the multi-agent system, and the development of the distributed time synchronization consistency control method has quite enough engineering and theoretical research significance.
Disclosure of Invention
The invention solves the technical problems: the method is used for solving the problem that the system state reaches the sliding die surface at fixed time; the multi-agent consistent tracking is performed for a fixed time; the problem that the states of all the multiple agents cooperatively reach the balance point can realize the control of the precision above 10-4 orders of magnitude under the interference of 10-3 orders of magnitude, and the precision is improved by one order of magnitude. The method is suitable for being applied to the problem of synchronous convergence consistency tracking of all states of the multi-agent fixed time.
The invention discloses a multi-agent consistency control method based on time synchronization stability, which comprises the following steps:
s1: establishing a second-order dynamic model of multiple intelligent agents, and designing a formation auxiliary function;
s2: based on the mathematical principle of unit direction vector, a novel direction symbol function is designed, and a novel fixed time sliding mode surface is constructed by utilizing the function;
s3: designing a fixed time synchronous convergence controller aiming at a multi-agent system model;
s4: based on the sliding mode surface construction in the step S2 and the controller designed in the step S3, verifying that the state of the multi-agent system reaches the sliding mode surface at fixed time; the multiple intelligent agents realize consistent tracking in fixed time; the states of all the multiple agents cooperate to reach the equilibrium point.
In step S1, a second-order dynamic model of the multi-agent is built as follows:
wherein the position and velocity vectors arei∈{1,2,…,N}，/>Is a control law of the present invention,for the state transition function +.>Is a reversible input function.
Auxiliary variables are defined as follows:
wherein,
the novel direction symbol function in step S2 is designed and defined as follows:
wherein the method comprises the steps ofAs an arbitrary n-dimensional vector, 0 n Is an n-dimensional zero vector. The exponentiation of the sign function may be defined as follows:
wherein p is a power exponent.
Based on the above sign function, a novel time synchronization stable sliding mode surface can be constructedThe method comprises the following steps:
wherein,middle sliding mode surface switching condition->Threshold epsilon>0, design the sliding mode surface gain parameter alpha 1 >0,β 1 >0,The sliding mode face power exponent satisfies 0<p 1 <1,g 1 >1。
In step S3, the boundary process of the time for the multi-intelligent system to converge is designed as follows:
first, design Lyapunov functionAnd its time partial derivative is designed in the form of:
wherein the gain parameter alpha is designed 2 >0,β 2 >0, the exponent parameter satisfies p 2 <1,g 2 >1. From this, it can be analyzed that the state of the multi-agent system reaches the slip plane s at a fixed time i =0, the boundary of convergence time is:
then, redesign the second Lyapunov functionLyapunov function V m2 The derivative of (2) is:
the boundary for realizing the tracking of the consistent convergence time by the multi-agent system is as follows:
after analyzing the boundary of the design convergence time, a fixed time synchronous convergence controller is constructed as follows:
the design of the multi-agent consistency control with time synchronization and stability is completed through the design.
The multi-agent consistency control method based on time synchronization and stability is characterized by firstly establishing a second-order dynamic model of the multi-agent and designing auxiliary variables; then, based on the mathematical principle of unit direction vector, a novel direction symbol function is designed, and a novel fixed time sliding mode surface is constructed by utilizing the function; then, a fixed time synchronous convergence controller is designed aiming at the multi-agent system model; finally, based on the constructed sliding surface and the controller, verifying that the state of the multi-agent system reaches the sliding surface at a fixed time; the multiple intelligent agents realize consistent tracking in fixed time; the states of all the multiple agents cooperate to reach the equilibrium point.
Compared with the prior art, the invention has the advantages that:
(1) Compared with the traditional fixed time attitude control method, the construction of the sign function of the invention enables the position and the speed in the multi-agent system to realize the synchronous convergence of limited time.
(2) Because the error constructed by the direction symbol function is an actual vector error, compared with the control method based on the traditional symbol function, the control energy consumption of the invention can be obviously reduced, the control performance can be effectively improved, and the design of the controller of the control method of the invention has no numerical singular, so that stable collaborative tracking can be realized.
Drawings
FIG. 1 is a flow chart of a multi-agent consistency tracking control method based on time synchronization stabilization of the present invention;
FIG. 2 is a graph showing the results of a trajectory simulation for synchronization of multiple agents using the control method of the present invention;
FIG. 3 is a simulation result of state quantity using the control method of the present invention;
FIG. 4 is a simulation result of the control amount using the control method of the present invention;
fig. 5 shows simulation results of formation tracking errors using the control method of the present invention.
Detailed Description
The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is apparent that the described embodiments are merely examples and are not intended to limit the present invention.
As shown in fig. 1, the specific implementation of the multi-agent consistency tracking control method based on time synchronization stabilization of the present invention is described in detail.
In step S1, a second-order dynamic model of the multi-agent is built as follows:
wherein the position and velocity vectors arei∈{1,2,3,4}，/>Is a control law.
Selecting
q i ＝-i(-1) i [4,-6,8] T (3)
The incidence matrix is:
the novel direction symbol function in step S2 is designed and defined as follows:
wherein the method comprises the steps ofAs an arbitrary n-dimensional vector, 0 n Is an n-dimensional zero vector. The exponentiation of the sign function may be defined as follows:
wherein p is a power exponent.
Based on the above sign function, a novel time synchronization stable sliding mode surface can be constructedThe method comprises the following steps:
wherein,
medium sliding mode surface switching conditionDesign of the sliding mode surface gain parameter alpha 2 ＝0.5,β 2 ＝0.1/>The sliding mode face power exponent is designed as p 1 ＝0.7,g 1 ＝1.2。
In step S3, the time limit for the convergence of the multi-intelligent system is designed as follows:
design of Lyapunov functionAnd its time partial derivative is designed in the form of:
wherein the parameter is alpha 2 ＝1,β 2 =0.05, power exponent designed as p 2 ＝0.7,g 2 From this, it can be analyzed that the multi-agent system state reaches the slip plane s at a fixed time i =0, the convergence time is bounded by
Then, redesign the second Lyapunov functionLyapunov function V m2 The derivative of (2) is:
the boundary for realizing the tracking of the consistent convergence time by the multi-agent system is as follows:
after analyzing the boundary of the design convergence time, a fixed time synchronous convergence controller is constructed as follows:
simulation results of multi-agent synchronous convergence stabilization control can be obtained based on the implementation method, and are shown in fig. 2-5.
FIG. 2 shows simulation results of motion trajectories of various agents that achieve synchronization and coincidence of multiple agents by adopting the control method of the present invention; the control method provided by the invention is capable of controlling the movement of multiple intelligent agents to a desired position, and four different curves represent the tracks of the four intelligent agents in xyz space respectively.
FIG. 3 is a state diagram of a control method according to the present invention, wherein x i1 ，x i2 And x i3 The 1 st, 2 nd and 3 rd position components of the ith agent are respectively represented, and it can be seen that three components of the 4 multi-agent arrive at a stable state at the same time; FIG. 4 is a plot of control torque output using the control method of the present invention, where u i1 ，u i2 And u i3 The 1 st, 2 nd and 3 rd control components of the ith agent are respectively represented, and it can be seen that the control amounts of the 4 multi-agents converge to 0 at the same moment; fig. 3 and 4 illustrate that the present control method enables time synchronization stabilization.
FIG. 5 is a graph of a formation tracking error designed by the method of the present invention, in whichAnd->The 1 st, 2 nd and 3 rd consistency error components of the ith agent are respectively represented, and the formation tracking error can be seen to converge to 10 in 24s -4 Magnitude.
The simulation result fully shows that the method can realize high-precision fixed time state synchronous convergence control under the condition of the control method provided by the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (2)
1. The multi-agent consistency control method based on time synchronization stabilization is characterized by comprising the following steps:
s1: establishing a second-order dynamic model of multiple intelligent agents, and designing a formation auxiliary function;
s2: based on the mathematical principle of unit direction vector, a novel direction symbol function is designed, and a novel fixed time sliding mode surface is constructed by utilizing the function;
s3: aiming at a second-order dynamic model of the multi-agent system in S1, designing convergence time of the multi-agent system, constructing a fixed time synchronous convergence controller by utilizing the Lyapunov stability principle, and calculating to obtain a control value by utilizing information of positions and speeds and the second-order dynamic model information of the multi-agent in S1 so as to realize multi-agent consistency control of time synchronous stability;
in the step S1, a second-order dynamic model of the multi-agent is established as follows:
wherein the position and velocity vectors are Is control law,/->For the state transition function +.>Is a reversible input function;
defining auxiliary variables for characterizing the degree of synchronicity of position and velocity between the respective agents:
wherein,
in the step S2, the novel direction symbol function is designed and defined as follows:
wherein the method comprises the steps ofAs an arbitrary n-dimensional vector, 0 n Is an n-dimensional zero vector;
the exponentiation of the sign function is defined as follows:
wherein p is a power exponent;
construction of novel time-synchronous stable sliding mode surface based on above sign functionThe method comprises the following steps:
wherein,
medium sliding mode surface switching conditionThe threshold epsilon > 0, the sliding mode surface gain parameters in the design controller are as follows: /> The power exponent of the sliding mode surface satisfies 0 < p 1 ＜1,g 1 ＞1。
2. The method according to claim 1, characterized in that: in the step S3, the boundary process of the time for designing the multi-agent system to converge is as follows:
first, design Lyapunov functionAnd its time partial derivative is designed in the form of:
wherein the gain parameter alpha is designed 2 ＞0,β 2 > 0, the exponent parameter satisfies p 2 ＜1,g 2 > 1, thereby obtaining that the multi-agent system state reaches the slip plane s at a fixed time i =0, the boundary of convergence time is:
then, redesign the second Lyapunov functionLyapunov function V m2 The derivative of (2) is:
the boundary for realizing the tracking of the consistent convergence time by the multi-agent system is as follows:
after determining the boundary of the design convergence time, constructing a fixed time synchronous convergence controller into the following form:
the value of the control quantity is calculated by the above formula, namely by utilizing the information of the position and the speed and the second-order dynamic model information of the multi-agent, and the control quantity is acted in the control of the multi-agent.
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