Aggregation Analysis for Competitive Multiagent Systems With Saddle Points via Switching Strategies

This paper addresses the aggregation issues of competitive multiagent systems (CMASs) consisting of competitive agents with multimodes and saddle points. In such CMASs, due to existing mutual competitions, every agent is equipped with finite multimodes, and every mode in any agent is described as a second-order linear time-invariant (LTI) control system. When the origin is the same saddle point of all modes of agents, to investigate aggregation of the CMASs with switching strategies, we first use switched LTI systems with saddle points to formulate such CMASs. Then, two new stability concepts, called initial-state-dependent(ISD) stability and initial-state-independent(ISI) stability, are defined for the CMASs. Based on these new stability concepts, a practical criterion of local/global ISI asymptotic aggregation is proposed for the CMASs. A local/global ISD/ISI asymptotical-stabilizing-control observed as distributed controls of multimodes, stabilizing-switching-paths, and a corresponding algorithm are all designed for local/global aggregation of such CMASs with switching delays. Finally, a numerical example illustrates the effectiveness and practicality of our new results.