Distributed Nash Equilibrium Seeking of $N$-Coalition Noncooperative Games With Application to UAV Swarms

Abstract

Nash equilibrium seeking problems for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -coalition noncooperative games are studied in this paper, where the players in the game possess second-order fully-actuated dynamics with disturbances and uncertainties. The players in one coalition focus on the minimization of the coalition cost instead of individual costs. Moreover, only measurements of the cost functions can be accessed in consideration that their explicit expressions cannot be available in complex application environments. An extremum seeking-based approach is proposed to estimate the gradients of the cost functions that are obtained by dynamic average consensus protocols. Sinusoid signals, required to have different frequencies, are used as perturbations in the strategy while the dynamic disturbances and uncertainties are compensated by introducing an extended state observer. Convergence results are proved via averaging and singular perturbation analysis. Then confrontation of two unmanned aerial vehicle (UAV) swarms in territory-defense scenario is introduced and tasks for UAVs are designed. Countermeasures for the UAVs are obtained by utilizing the Nash equilibrium seeking strategy in the two-coalition noncooperative game. Numerical examples are provided and the effectiveness of the proposed strategy is verified.