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Noticing that physical limitations are ubiquitous in practical engineeringsystems, this paper considers Nash equilibrium seeking for games in systemswhere the control inputs are bounded. More specifically, first-orderintegrator-type systems with bounded control inputs are firstly considered andtwo saturated control strategies are designed to seek for the Nash equilibriumof the game. Then, we further consider the Nash equilibrium seeking problem forgames in second-order integrator-type systems. As this problem has rarely beeninvestigated, we firstly propose a centralized seeking strategy withoutconsidering the boundedness of the control inputs, followed by a distributedcounterpart. By further adapting a saturation function into the Nashequilibrium seeking strategy, a new seeking strategy is then designed for theconsidered second-order systems with bounded controls. In the proposeddistributed strategies, consensus protocols are included for informationsharing and the saturation functions are utilized to construct bounded controlinputs. The convergence results are established through conducting Lyapunovstability analysis. Lastly, by considering the connectivity control of mobilesensor networks, the proposed methods are numerically verified.

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