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

arXiv: https://arxiv.org/abs/1901.09333 · HTML: https://mlsanity.com/paper/1901.09333/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2019.

## Built on by (most cited first, 1 of 1)

- [Distributed Semi-supervised Fuzzy Regression with Interpolation Consistency Regularization](https://mlsanity.com/paper/2209.09240/) (2022)

## Abstract (arXiv)

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.