Distributed Nash equilibrium seeking for integrated game and control of multi-agent systems with input delay

This paper aims to investigate integrated game and control (IGC) problems for networked multi-agent systems (MASs) subjected to input delay. To be specific, single-integrator systems with input delay are firstly considered, and both centralized and distributed Nash equilibrium (NE) seeking algorithms are designed to accommodate the considered IGC problem. Then, the results are extended to seek the NE for second-order nonlinear systems with the consideration of disturbance rejection and output measurements. In the proposed strategies, predictive observers and distributed observers are adapted to tackle input delays and share information among agents, respectively. Finally, the effectiveness of the proposed algorithms are demonstrated through theoretical analysis and numerical experiments.

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