Solving Potential Games With Dynamical Constraint

We solve N -player potential games with dynamical constraint in this paper. Potential games with stable dynamics are first considered followed by one type of potential games without inherently stable dynamics. Different from most of the existing Nash seeking methods, we provide an extremum seeking-based method that does not require explicit information on the game dynamics or the payoff functions. Only measurements of the payoff functions are needed in the game strategy synthesis. Lie bracket approximation is used for the analysis of the proposed Nash seeking scheme. A singularly semi-globally practically uniformly asymptotically stable result is presented for potential games with stable dynamics and an ultimately bounded result is provided for potential games without inherently stable dynamics. For first-order perturbed integrator-type dynamics, we employ an extended-state observer to deal with the disturbance such that better convergence is achievable. Stability of the closed-loop system is proven and the ultimate bound is quantified. Numerical examples are presented to verify the effectiveness of the proposed methods.