Game-theoretic demand-side management and closed-loop control for a class of networked smart grid

A new systematic scheme is proposed for demand-side management and control of a class of networked smart grid. The networked smart grid is modelled into an evolutionary game, and the theory of semi-tensor product is applied to analyse its dynamic behaviours. By using a newly defined stacked form of structural matrix, a closed-loop feedback control is designed to shape the structural matrix of the evolutionary game, such that the Nash equilibrium (with respect to minimum total cost) can be reached and maintained. Based on the proposed feedback control, a robust control can be designed for the smart grid to reach the Nash equilibrium in case of model uncertainties resulted from fake behaviours of some users. Examples are provided to illustrate the theoretical results.