This work investigates the demand-side management of smart grids via the semi-tensor product of matrices. Firstly, based on the criterion of potential games, the potential game is used to model the demand-side management of smart grids and the corresponding potential function can be constructed. Secondly, when the cascading myopic best response adjustment is used as the strategy updating rule, a pinning control is designed to make the potential game converge to the optimal Nash equilibrium. During the process of designing the pinning control, in order to reduce the control cost, an algorithm is constructed to get as few control players as possible. Finally, an example is provided to verify the theoretical results.