Specified-Time Distributed Nash Equilibrium Seeking for Multicoalition Cyber-Physical Systems

This paper studies distributed Nash equilibrium seeking (DNES) for multicoalition cyber-physical systems over weight-unbalanced directed communication networks. Within each coalition, all nodes cooperate to optimize the coalition's objective under a consensus constraint, while different coalitions compete with one another. First, by integrating multistep planning with optimal control techniques, a specifiedtime DNES framework is developed for such multicoalition cyber-physical systems, guaranteeing convergence to the Nash equilibrium (NE) within a specified settling time. Furthermore, to eliminate biases in both the average gradient estimation and the system state that arise from the unbalanced directed communication topology inside each coalition, a specified-time balance compensator is designed for each coalition based on in-neighbor sampling information. Then, by utilizing properties of iteration matrices and constructing discrete Lyapunov functions, the specified-time convergence of the compensator and the overall system is rigorously established. Finally, a simulation result involving the power generation game is presented to demonstrate the effectiveness of the proposed algorithm.