Distributed Nash Equilibrium Seeking for Games in Systems With Bounded Control Inputs

Noticing that actuator limitations are ubiquitous in practical engineering systems, this article considers Nash equilibrium seeking for games in systems where the control inputs are bounded. More specifically, first-order integrator-type systems with bounded control inputs are first considered and two saturated control strategies are designed to seek the Nash equilibrium of the game. Then, second-order integrator-type systems are further considered. In this case, a centralized seeking strategy is first proposed without considering the boundedness of the control inputs, followed by a distributed counterpart. By further adapting a saturation function into the distributed Nash equilibrium seeking strategy, the boundedness of the control input is addressed. In the proposed distributed strategies, consensus protocols are included for information sharing and the saturation functions are utilized to construct bounded control inputs. The convergence results are analytically studied by Lyapunov stability analysis. Finally, by considering the connectivity control of mobile sensor networks, the proposed methods are numerically verified.