Distributed Nash Equilibrium Seeking for Games in Systems With Non-Symmetric Dead-Zone Inputs

The paper investigates the distributed Nash equilibrium seeking problem for games with players having unknown non-symmetric dead-zone inputs. First-order and second-order integrator-type systems without the knowledge of dead-zone slopes and widths are considered, respectively. By embedding the adaptive compensation algorithm into the gradient-like optimization method and consensus-based protocols, the control strategies are developed. To be specific, we transform the player's dynamic, which involves dead-zone inputs, into an uncertain nonlinear system that is influenced by a linear input with a non-smooth input coefficient that varies over time, as well as an external perturbation. Then, an adaptive compensation algorithm is adopted to estimate the unknown bounds associated with the time-varying input coefficient and perturbations. With the aid of Lyapunov stability analysis, it has been proven that the actions of the players can globally and asymptotically converge to the Nash equilibrium. The effectiveness of the developed algorithms is validated through a numerical example.