A distributed strategy for games in Euler–Lagrange systems with actuator dead zone

Abstract

This paper explores a distributed Nash equilibrium (NE) seeking problem for games in which the involved players are of Euler–Lagrange (EL) dynamics with actuator dead zone. To find NE of such games, a novel distributed algorithm with a dynamical dead-zone compensator is proposed. The compensating module in this new strategy is regarded as a fast dynamics that rapidly addresses the effect caused by actuator dead-zone characteristic. The other module of this algorithm is a slow optimizer that enables the actions of EL players to approach the NE. Since the designed strategy is a two-time-scale model, semi-global practical asymptotic stability of this strategy can be obtained by utilizing the generalized singular perturbation method. Finally, an electricity market game with six turbine-generator dynamics is utilized to validate the theoretical result of the proposed method.