Distributed Strategy Design for Solving Games in Systems with Bounded Control Inputs

Noticing that physical limitations are ubiquitous in practical engineering systems, this paper deals with Nash equilibrium seeking strategy design for games in systems where the control inputs are bounded. More specifically, first-order integrator-type systems with bounded control inputs are firstly considered and a saturated control strategy is designed to seek for the Nash equilibrium of the game. Then, we further consider the problem for games in second-order integrator-type systems. As this problem has rarely been investigated, we firstly propose a distributed seeking strategy without considering the boundedness of the control inputs. By further adapting a saturation function into the Nash equilibrium seeking strategy, a new seeking strategy is then designed for the considered second-order systems with bounded controls. 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 established through conducting Lyapunov stability analysis. Lastly, by considering the connectivity control of mobile sensor networks, the proposed methods are numerically verified.