  Noticing that physical limitations are ubiquitous in practical engineering
systems, this paper 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 firstly considered and
two saturated control strategies are designed to seek for the Nash equilibrium
of the game. Then, we further consider the Nash equilibrium seeking problem for
games in second-order integrator-type systems. As this problem has rarely been
investigated, we firstly propose a centralized seeking strategy without
considering the boundedness of the control inputs, followed by a distributed
counterpart. 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.
