Linear-Quadratic Mean-Field-Type Games-Based Stochastic Model Predictive Control: A Microgrid Energy Storage Application

In this paper, we study the design of a stochastic predictive controller based on discrete-time mean-field-type games (MFTG-SPC) involving an arbitrary number of decision makers. We consider a dynamical system described by a stochastic difference equation that includes mean-field terms, e.g., the expected value for both the system state and control inputs. In addition, the cost function incorporates the mean and variance of both system state and control inputs. We provide a semi-explicit solution for the optimization problem that is behind the predictive controller. Finally, we present some simulations over a microgrid application consisting of the energy storage problem.