This chapter studies output containment control problems for high-order linear time-invariant (LTI) swarm systems and state containment problems for high-order LTI singular swarm systems with time delays. First, a dynamic output containment protocol is presented. Necessary and sufficient conditions for swarm systems to achieve output containment are proposed. To ensure the scalability of the criteria, a sufficient condition which only includes two linear matrix inequality constraints independent of the number of agents is further presented. An approach independent of the number of agents is proposed to determine the gain matrices in the dynamic output containment protocols by solving an algebraic Riccati equation. Second, to eliminate impulse terms in singular swarm systems and ensure that the singular swarm systems can achieve containment, time-delayed protocols are presented for leaders and followers, respectively. By model transformation, containment problems of singular swarm systems are converted into stability problems of multiple low-dimensional time-delayed systems. In terms of linear matrix inequality, sufficient conditions are presented for time-delayed singular swarm systems to achieve state containment, which are independent of the number of agents. By using the method of changing variables, an approach is provided to determine the gain matrices in the protocols. Finally, numerical simulations are presented to demonstrate theoretical results.
Swarm Systems Containment Control Problem Output Container Containment Protocols State Containment
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