Research Of Method On Tracking Control Problem For Multi-agent System With Uncertain Factors

Cooperative control for multi-agent systems has been investigated quite intensively and applied to many fields, such as distributed computations, formation control of multi-robot, multi-sensor networks. The study of the impact of various uncertain factors on the performance is the research hotspot of this field. This treatise analyzes and researches the tracking-control problems of multi-agent systems such as unstable communication structure, incomplete information, time-delay and external disturbance.First of all, this thesis proposes the function analysis discriminant method of Joint unicom variable structure system, basing on Lyapunov function. Jointly-connected topologies are a special form of communication topology, and can simulate some of the actual situation in the practical engineering, such as instability or interference of the communication. In the light of the characteristics of jointly-connected topologies, by using the characteristics of the Laplacian matrix of the communication topology, the Laplacian matrix can be decomposed into block diagonal matrix, so the non strongly connected system can be decomposed into several connected subsystems, then according to the characteristics of the eigenvalues of the communication topology matrix of each subsystem is greater than 0, determining the Lyapunov function,analyzing the convergence of tracking error, which solves the problem that the conventional method can not effectively analyze this kind of variable structure system.Further, when the communication between agents is unidirectional (communication topology is directed graph), it is proved that when the leader's information is globally reachable in the sub-connected structure, various intelligent agents' tracking of the leader could be realized. Through numerical simulation, the effectiveness of the proposed method in undirected graphs and directed graphs is proved.On this basis, it is concluded from further studies that the upper bound of the tracking error and the relationship between tracking error and some parameters, under the condition that the communication structure is unstable and the leader information is not completely known. According to the characteristic that the Laplacian matrix of the jointly-connected topology can be decomposed into a block diagonal matrix, the non-strongly connected system can be decomposed into several sub-connected subsystems. And through using the Lyapunov method, the relationship between the changing structure of each subsystem and tracking error is studied, with the inequality of tracking error estimation being obtained. The inequality defines the relationship between the upper bound of the tracking error and some parameters, such as the communication topology, the target acceleration and the time delay. Through studying the connected variable structure system based on tracking error estimation, the upper bound of tracking error could be obtained, which has a good application value. Through numerical simulation, the results show that the proposed method can achieve the leader-tracking and estimate the upper bound of the tracking error,with and without time delay.Then the rotating tracking control problem of the multi-agent system is studied,with the methods and conditions of rotation tracking control being obtained. Besides, a method of target velocity error estimation method based on position information is proposed, which solves the rotating tracking control problem with unknown velocity.First, the control strategies of rotating tracking based on velocity and position information with and without time-delay have been put forward, and by analyzing the convergence of tracking error, the validity of the method has been proved. On this basis,to solve the uncertainty information problem that the velocity of the rotating leader cannot be measured, a velocity error estimation method based on position information is proposed. Through setting the inputting of a knowable variable, and using the relationship between the variable and the velocity error, the error estimation and design of control protocol have been achieved. The numerical simulation shows that the proposed method can solve the rotating tracking control in the corresponding conditions.Finally, the adaptive control problem of variable structure system and rotating tracking system is studied. An adaptive control method for variable structure systems is proposed, and based on the adaptive error estimation method of relative position, the tracking control conditions for variable structure systems with multiple uncertainties are obtained, with the method and condition of rotating tracking control without acceleration measurement being established. In the study of adaptive control of variable structure systems, using the characteristics that the Laplacian matrix of the jointly-connected topology can be decomposed into a block diagonal matrix, the non strongly connected system is decomposed into several connected subsystems. Through combining with the analysis method of variable structure system and adaptive control method, the adaptive control problem of multi-agent system with jointly-conntcted topology is solved. Simultaneous,different from the traditional method of error estimating that is base on the velocity or position error between the leader and the follower, the method for estimating based on the relative velocity and position information among agents is applied to estimate the unknown information and the external disturbance. Then the adaptive control protocol is designed by using the relative velocity and position information, which is applied to the tracking control of active and rotating target,realizing the adaptive tracking control in two cases. Through the numerical simulation, it is respectively testified in the two kinds of systems that the proposed methods could achieve leader-following and estimation of unknown variables.