Coordination Control Of Fractional-order Multi-agent Systems

Distributed coordination control of multiagent systems has been studied extensively due to its wide applications,such as attitude control of multi-mobile robots,formation control of unmanned aerial vehicles,collective motion of bacteria and so on.Some fundamental problems in coordination control of multiagent systems has attracted a lot of attention,such as consensus problem,group consensus problem,containment control problem,formation control problem.In this thesis,we mainly research consensus prob-lem,group consensus problem and containment control problem.The main works have been given below.1.In the first part,consensus of fractional-order multiagent systems via sampled-data event-triggered control is discussed.Firstly,an event-triggered algorithm is defined using sampled states.Thus,Zeno behaviors can be naturally avoided.Then,a distributed con-trol protocol is proposed to ensure the consensus of fractional-order multiagent systems,where each agent updates its current state based on its neighbors' states at event-triggered instants.Furthermore,the pinning control technology is taken into account to ensure all agents in multiagent systems reach the specified reference state.With the aid of linear ma-trix inequalities(LMI),some sufficient conditions are obtained to guarantee the consensus of fractional-order multiagent system.2.In the second part,group consensus problem for fractional-order multiagent sys-tems is investigated.With the help of double-tree-form transformations,the group con-sensus problem of fractional-order multiagent systems is proved to be equivalent to the asymptotical stability problem of reduced-order error systems.A class of distributed con-trol protocols and some simple LMI sufficient conditions as well as necessary and suffi-cient conditions are proposed to solve the group consensus problem for fractional mul-tiagent systems.Moreover,pinning control strategy has been taken into consideration.It is shown that the system converges more rapidly when the designed pinning protocols are adopted.In addition,the case of fractional system with switching topologies is also discussed and some corresponding sufficient conditions are obtained.3.Containment control for fractional-order heterogeneous multiagent systems with general linear dynamics is investigated.First,the containment control problem is trans-formed into an asymptotical stability problem by a designed error vector related to leaders and followers.Second,a distributed dynamic observer and a Luenberger observer are de-signed for each follower to estimate its state and the convex hull formed by the leaders respectively.With the aid of matrix theory and stability theory of fractional-order system,some simpler sufficient conditions for containment of fractional-order heterogeneous lin-ear MASs are obtained.It is shown that if each follower is fractionally stabilizable and fractionally detectable,meanwhile,each leader is detectable,then a suitable observer-based control protocol can be designed such that the containment is achieved.Moreover,it is only required for interaction topology that there exists a directed path from at least one leader to the isolated followers and to the followers whose in-degree are less than out-degree.