Formation-Containment Control of Swarm Systems
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This chapter studies state and output formation-containment control problems for high-order linear time-invariant (LTI) swarm systems. First, protocols are presented for leaders and followers, respectively, to drive the states of leaders to realize the predefined time-varying state formation and propel the states of followers, to converge to the convex hull formed by states of leaders. State formation-containment problems of swarm systems are transformed into asymptotic stability problems, and an explicit expression of the formation reference function is derived. Sufficient conditions for swarm systems to achieve state formation-containment are proposed. Necessary and sufficient conditions for swarm systems to achieve state containment and time-varying state formation are presented respectively as special cases. An approach to determine the gain matrices in the state formation-containment protocols is given. Then, output formation-containment control problems for high-order LTI swarm systems are dealt with. Sufficient conditions for swarm systems to achieve output formation-containment are proposed. An approach to determine the gain matrices in the output formation-containment protocols for swarm systems to achieve output formation-containment is given. It is revealed that state formation-containment, state/output containment, state/output formation control, state/output consensus, and state/output consensus tracking problems can be unified in the framework of output formation-containment problems. Finally, numerical simulations are provided to demonstrate theoretical results.
KeywordsSwarm Systems Consensus Tracking Problem State Containment Asymptotic Stability Problem Reference Formulation
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