Distributed Nash Equilibrium Seeking Under Input Dead Zone

This article investigates the Nash equilibrium (NE) seeking problem for games in the presence of input dead-zone nonlinearity. The purpose of each player is to minimize its own cost function, which depends not only on its own decision variable, but also on decision variables of the other players. To obtain an NE, a novel two-time-scale distributed algorithm is designed. This new strategy consists of two parts: one is the fast compensating dynamics, which can rapidly compensate the effect of input dead zone; the other is the optimization dynamics that can distributively drive the players’ decision variables to achieve the NE. Since the proposed algorithm has a two-time-scale structure, singular perturbation techniques are used to prove that the players’ actions semiglobally practically asymptotically converge to the NE. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed strategy.