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Formation-containment control for high-order linear time-invariant multi-agent systems with time delays. (English) Zbl 1395.93011
Summary: Formation-containment analysis and design problems for time-delayed high-order linear time-invariant multi-agent systems with directed interaction topologies are studied. Firstly, protocols with time delays are presented for leaders and followers, where the formation for leaders can be time-varying. Then formation-containment problems for time-delayed multi-agent systems are transformed into asymptotic stability problems of time-delayed systems. Sufficient conditions for multi-agent systems to achieve formation-containment are proposed, which include eight linear matrix inequalities independent of the number of leaders and followers. Furthermore, an explicit expression of the formation reference function for leaders is derived, where the motion modes of formation reference can be specified. An approach to determine the gain matrices in the protocols is given using the method of changing variables. Finally, numerical simulations are provided to demonstrate theoretical results.

MSC:
93A13 Hierarchical systems
68T42 Agent technology and artificial intelligence
93C85 Automated systems (robots, etc.) in control theory
93B51 Design techniques (robust design, computer-aided design, etc.)
93C05 Linear systems in control theory
93D20 Asymptotic stability in control theory
93B17 Transformations
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