Time-varying Formation Tracking Control For Linear Multi-agent Systems With External Disturbances

In recent years,with the development of computer and communication technologies becoming more and more mature,cooperative control of multiagent systems has potential applications in military,industrial manufacturing and civil fields,which has received attentions in the research field of control theory.Formation control,as an important branch of cooperative control of multi-agent systems,refers to that the multi-agent group can maintain the desired formation motion under the designed control algorithm.However,external disturbances are prevalent in practical applications and have an impact on the performance and even the stability of multi-agent systems,control algorithms for multi-agent systems affected by external disturbances.The leader or target to be tracked is usually dynamic and its input or velocity information is difficult to measure in real time,or even each follower agent can only obtain partial output information of the leader or target due to limitations of sensor hardware or environmental restrictions.Therefore,considering these cases,this paper investigates the design of cooperative formation control algorithms for multi-agent systems,with the objective to achieve time-varying formation tracking of a leader or target with unknown dynamic information and reject external disturbances simultaneously,which can be applied to a wider range of practical applications of cooperative control.First,time-varying formation tracking control of a linear multi-agent system with a leader of bounded unknown input under directed graphs is investigated,provided that the external disturbance model is known.To eliminate the disturbances,extended state observers are designed for each agent to estimate states and disturbances.Based on the estimated information and formation information,a fully distributed time-varying formation tracking control protocol is designed for each agent,which does not require the global information of Laplace matrix eigenvalues.Through Lyapunov stability analysis,the multi-agent system is shown to asymptotically tracking the leader with time-varying formations and meanwhile reject the disturbance if the desired formation shape satisfies the feasible conditions.Second,the case where the parameter matrices of the external disturbances are heterogeneous and completely unknown is considered based on the previous chapter.The proposed distributed time-varying formation tracking control protocol can track the nonautonomous leader with the desired formation by means of an adaptive disturbance observer designed to estimate the parameter matrix.Furthermore,as the introduction of discontinuous functions in the controller to compensate the unknown bounded input of the leader may lead to chattering phenomenon,the formation tracking control protocol is modified to continuous.It is finally shown that the formation tracking error can converge asymptotically to a controllable region.Finally,a time-varying formation tracking control protocol based on a distributed observer approach is designed for each agent considering the case where each agent has access to only part of the leader’s output information.Under the designed distributed observer,each agent can asymptotically estimate the leader state information using a portion of the leader’s output information that can be measured and local interaction information with its neighboring agents.Based on the distributed observer information of the leader state,the state and disturbance observer information and the formation compensation input of each agent,a cooperative formation tracking protocol is designed.Under the condition that the communication graph of the multiagent system is strongly connected,it is demonstrated that the designed control protocol can drive the agents to achieve globally asymptotical tracking of the leader with time-varying formations and reject external disturbances.