Research On Consensus And Containment For Uncertain Nonlinear Multi-Agent Systems

Over the past two decades,multi-agent systems and their distributed control have received much attention because of their broad applications in many areas including formation of unmanned air vehicles,mobile sensor networks and smart grid.Consensus is the basic problem of(distributed)control of multi-agent sys-tems,which implies that all the states of agents reach agreement.Consensus problem can be classified into leaderless consensus and leader-following consen-sus.When multiple leaders exist,the corresponding consensus problem is also called containment problem.On one hand,practical systems are almost nonlin-ear systems.Linear systems by linearization and other methods can only reflect the local and partial characteristics of nonlinear systems.On the other hand,it is impossible to model the actual plants accurately due to the insufficient un-derstanding of the mechanism of the practical systems and their environments,and the inaccuracy of the measurement tools.Hence,the system models are inevitably subjected to various uncertainties/unknowns and disturbances.Non-linearities,uncertainties/unknowns and disturbances bring great challenges to the existing control theories and methods of multi-agent systems,and also promote the emergence of new theories and new methods.This thesis investigates the consensus and containment for several classes of un-certain nonlinear multi-agent systems.The uncertainties mainly include unknown control coefficients,unknown parameters,unknown nonlinearities,unknown input disturbances,random noises and so on.These uncertainties make the problems in question more challenging,especially the establishment of feedback compensation mechanisms and the performance analysis of the closed-loop systems.For sev-eral classes of uncertain nonlinear multi-agent systems,time-varying consensus protocols,time-varying containment protocols and adaptive consensus protocols have been developed to achieve consensus and containment,finite-time consensus and finite-time containment by time-varying method,sliding mode method and adaptive method.The main contents of this thesis include the following four parts:(I)Leader-following consensus for uncertain nonlinear multi-agent systemsThis part(Chapter 3)investigates the leader-following consensus for a class of uncertain nonlinear multi-agent systems.The uncertainties are reflected in the unknown and time-varying growth rate of nonlinearities,serious unknowns of control coefficients and unknown upper bound of input disturbances.These unknowns and time-variations render the existing compensation strategies in-applicable.To deal with these unknowns and time-variations,a time-varying feedback compensation strategy is developed to achieve the leader-following con-sensus.The key idea of this strategy is to introduce a suitable function of time such that these unknowns and time-variations can be overtaken as time increases.(II)Finite-time leader-following consensus and finite-time contain-ment for uncertain nonlinear multi-agent systemsThis part(Chapter 4)studies the finite-time leader-following consensus and finite-time containment for a class of uncertain nonlinear multi-agent systems.The uncertainties are reflected in the unknown and time-varying nonlinearities and control coefficients,and unknown upper bound of input disturbances.These unknowns and time-variations make the problem in question essentially different from those in the existing literature.The distributed finite-time consensus pro-tocol and distributed finite-time containment protocol are given by integrating time-varying method and sliding mode method to achieve the finite-time leader-following consensus and the finite-time containment,respectively.(III)Consensus and containment for uncertain stochastic nonlinear multi-agent systemsThis part(Chapter 5 and Chapter 6)investigates the consensus and contain-ment for a class of uncertain stochastic nonlinear multi-agent systems.A remark-able feature is that the nonlineaxities are unknown and time-varying.Moreover,there exists no known constant interval to restrict the unknown control coeffi-cients.This part shows that the time-varying feedback compensation strategy of Part I is still valid for stochastic nonlinear multi-agent systems.Based on the proposed strategy,the distributed time-varying consensus protocol and the dis-tributed time-varying containment protocol are given to achieve the almost sure consensus and almost sure containment.(IV)Adaptive leader-following consensus for uncertain nonlinear multi-agent systemsThis part(Chapter 7)studies the leader-following consensus for first-order and second-order uncertain nonlinear multi-agent systems,respectively.Remarkably,it is essentially different from those in the related literature that the control coeffi-cients of the followers can not be restricted by any known finite constant interval,that the nonlinearities of the followers have parameterized unknowns,and that the control input of the leader is unknown.To compensate these unknowns,the adaptive leader-following consensus protocols are given by employing adaptive method to achieve the leader-following consensus.In conclusion,the developed time-varying feedback compensation strategy and adaptive feedback compensation strategy not only effectively capture the influ-ence of nonlinearities and uncertainties,achieve the consensus and containment of systems,enrich the design methods of distributed protocols,but also motivate the study of other distributed control problems for uncertain nonlinear multi-agent systems.