Design games to solve distributed optimization problem with application in electric vehicle charge management

In this paper, we investigate the distributed optimization problem based on state-based potential game. We propose a method using lagrange multiplier as state in the design of state-based potential game. We employ a continuous-time dynamic to design the state dynamic and learning algorithms of the state-based potential game. We show that the stationary state Nash equilibrium of the designed game contains the optimal solution of the optimization problem. In addition, we prove the convergence and stability of the learning algorithms for both undirected and directed communication graph under some mild assumptions. Then we propose a model to use our method in Plug-in Electric Vehicle charge management.