Coordinated Control Problem Of Stochastic Multi-agent System

Coherence in collective motion of interacting multi-individual particles or swarming systems are omnipresent in nature and man-made systems of very different kinds,from foraging ant colonies to marching locusts,from schooling fish or prawns to flocking birds,and from coordinated robots to synchronized spacecrafts.A distinctive feature of these behaviors is that a large number of individuals only rely solely on local information but they have collective behaviors.If each individual is regarded as an agent,the moving group can be regarded as a multi-agent system.The coordination control problem of multi-agent system is to design suitable control protocols to realize the consensus of the positions or velocities of individuals and to derive conditions for the coordination of the whole group.The research of the collective behavior of the multi-agent system has a long history and has been attracting an increasing attention across many fields,including biology,physics,mathematics,and engineering.Due to its broad applications in emergency evacuation,robot formation,and prevention of locusts and other pests,many authors have been trying to uncover the mechanisms leading to the collective behavior.Noise is ubiquitous in nature as well as in manmade systems.The collective motion of self-propelled particles is inevitably affected by intrinsic or environmental noise.Previous studies have confirmed that the influence of noise in real systems are twofold.On the one hand,noise can easily cause disorder of the group motion.On the other hand,noise may have constructive role on the collective motion.The main sources of noise in multi-agent systems include the internal forces and the random perturbation of the external environment.Interactions among moving agents are not necessarily instantaneous,because the information transmission and processing times are finite.Therefore,the influence of noise and time delays should be taken into account when investigating more realistic multi-agent systems,which will be a challenge problem.This thesis studies the coordinated control of stochastic multi-agent systems.Different from previous studies,we focus on the constructive effect of noise and time delays on the collective motion of multi-agent systems.The main content of the thesis can be summarized as follows:In chapter 1,the research background and progress on coordinated control of multi-agent systems and synchronization of complex networks are introduced.Moreover,some preliminaries and the structure of this thesis are given.In Chapter 2,the finite-time and fixed-time pinning consensus problems of stochastic multi-agent systems are presented.Combining finite-time control technology and pinning control method,new consensus protocols are proposed.Different from the existing linear protocol based on the linear graph Laplacian,the proposed protocols based on the graph p-Laplacian only need to control a small number of individuals,so that the multi-agent systems can achieve the consensus in finite time,which is more practical.The results show that,as the nonlinear generalization of the graph Laplacian,the graph p-Laplacian can be used as a unified framework for the study of the finite-time consensus and the asymptotic consensus problems.Combining the advantages of finite-time control technology and pinning control method,several pinning protocols are proposed.Compared with the consensus protocols without pinning control,the proposed finite-time and fixed-time protocols need to control only a small fraction of agents,which is practical and has advantages from the physical viewpoint of energy consumption.More specifically,we analytically show that the graph p-Laplacian,a nonlinear generalization of the standard graph Laplacian,has important role in solving the finite-time as well as the fixed-time consensus problems.In Chapter 3,the noise-induced flocking of a stochastic version of Cucker-Smale system is considered.Assuming that the individual cannot accurately measure the state of other individuals in a noisy environment,noise is introduced into the original Cucker-Smale model.Using the stability theory of stochastic differential equations,sufficient conditions for noise-induced flocking of Cucker-Smale system is obtained.Theoretical and numerical simulation results show that the flocking of stochastic Cucker-Smale system depends on communication rate,group size,noise intensity and initial state errors.Different from the results that noise suppresses the flocking,the results that noise can accelerate the emergence of flocking of Cucker-Smale system.In Chapter 4,the directional switches of multi-agent system with time-delayed interactions is investigated.We focus on the influence of both the information processing and transmission delays on the mean switching time between different moving directions.Theoretical estimation of the mean switching time is obtained.Our results show that as the group density increases,in spite of the delayed interactions,disordered movement of individuals within the group can transit to high aligned collective motion.We show that time delays can induce the directional switching both analytically and numerically.Specifically,increasing the transmission delay can increase the mean switching time if the information processing delay is sufficient small.However,large transmission delay may destroy the ordered directional switching when the information processing delay is large enough.In Chapter 5,the synchronization problem of two complex networks with random adaptive coupling is investigated.Combining the advantages of adaptive control technology and random coupling method,a new stochastic adaptive coupling is proposed.Compared with deterministic adaptive coupling,the stochastic adaptive coupling can more quickly adjust to the appropriate coupling strength,so it can reduce the time and energy cost of synchronization.The conclusions in this chapter not only expand the application of adaptive control technology,but also can better understand the constructive role of noise in network synchronization.At the end of this thesis,the conclusions and some topics for future work are given.There are totaly 26 figures and 125 references in this dissertation.