Potential game design for a class of distributed optimisation problems
Peng Yi, Yanqiong Zhang, Yiguang Hong · Journal of Control and Decision · 2014
The state-based potential game is discussed and a game-based approach is proposed for distributed optimisation problem in this paper. A continuous-time model is employed to design the state dynamics and learning algorithms of the state-based potential game with Lagrangian multipliers as the states. It is shown that the stationary state Nash equilibrium of the designed game contains the optimal solution of the optimisation problem. Moreover, the convergence and stability of the learning algorithms are obtained for both undirected and directed communication graph. Additionally, the application to plug-in electric vehicle management is also discussed.