Group Consensus Tracking Problem For Second-order Multi-agent Systems

The theory of multi-agent systems is a hot topic in the field of system and control in recent years,which has attracted more and more attention and research from relevant scholars.In the practical problems of national economic and social development,the theory of cooperative control of multi-agent systems has broad application prospects,such as formation control of underwater vehicles,autonomous configuration of sensor networks,cooperative control of unmanned vehicles,attitude control of artificial satellites,etc.Consensus behavior is the basic problem of cooperative control for multi-agent sys-tems.The focus of the study on consensus is to design state evolution protocols for each agent,which has simple dynamic system,by using the state information of neighboring agents and its own.Under these protocols,some key quantities of all the agents converge to the same state.The ideas of these state evolution protocols are usually based on the self-organizing or external incentive cooperation mechanism of swarming phenomenons in nature.The research on consensus can improve the developments of modern technol-ogy and swarm intelligence.It has received extensive attention in the field of system and control and has obtained a lot of theoretic results,such as asynchronous consensus,finite-time consensus,leader-following consensus and group consensus,etc.In engineering applications,sometimes agents are required to perform multiple tasks,monitor several targets or station in different geographic locations.Thus the group of multi-agent system needs to be divided into different subgroups.In the term of consensus,the key quantities of agents in different subgroup converge to different state.It motivates the researchers to propose and study the problem of group consensus.At present,two situations of group consensus are mainly considered.One is the case without leaders.The state evolution of each agent depends on the information exchange of the internal neighbors of its subgroup and the neighboring information obtained from other subgroups.Another is the case with leaders.Each subgroup is equipped with different leader.In addition to the influence of the above mentioned information,the state evolution of each agent is directly or indirectly influenced by the leader's state of the subgroup in which it is located.The goal of this situation is to make the agents' states of different subgroup converge to their own leaders.Also it is called the problem of group consensus tracking.The relevant theoretical analysis is more complicated than the consensus theory.In this dissertation,the problems of group consensus tracking are studied for two kinds of second-order multi-agent systems.The main results and contributions are listed as follows:1.The group consensus tracking which is based on the leader's velocity observer,is considered for some second-order linear multi-agent systems.Iems.It is assumed that each agent only obtains the position information of its neighbors,its own position and ve-locity information.By using these position information,an observer is established to estimate the leader's velocity,the estimated value of which is transmitted to the agent's controller to design the protocol.For the case without measurement time-delays,a neces-sary and sufficient condition for the multi-agent system to solve group consensus tracking is established,by applying algebraic graph theory,matrix theory and stability theory of polynomials.The design of protocol parameters is given.For the case with measurement time-delays,it is proved the system can tolerate certain measurement delays under the given protocol parameters,on the basis of stability theory of time-delay systems is used to prove that.It is shown that the whole group can also achieve group consensus track-ing.Finally,two simulation examples are given to illustrate the effectiveness of the main results.2.For double-integrator multi-agent systems,the problem of group consensus track-ing is considered under the case of impulsive control.It is assumed that the agent periodi-cally samples its neighbors' position information,its own position and velocity information at discrete times.By using these sampled information,an impulsive protocol with an ob-server of leader velocity is proposed.According to the theory of impulsive differential equations and Schur stability theory of complex polynomials,the necessary and sufficient condition for the system to achieve group consensus tracking is established.The algebraic conditions for protocol parameters and sampling period are also given.An example of numerical simulation shows the applicability of these conditions.