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Linear-Quadratic Mean-Field-Type Games-Based Stochastic Model Predictive Control: A Microgrid Energy Storage Application | IEEE Conference Publication | IEEE Xplore

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


Abstract:

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...Show More

Abstract:

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.
Date of Conference: 10-12 July 2019
Date Added to IEEE Xplore: 29 August 2019
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Conference Location: Philadelphia, PA, USA

I. Introduction

Mean-field-type games have been studied in [1]–[4], where the assumption about having a large number of decision makers is not longer required. Mean-field-type games address problems involving both mean and variance of the system state and the control inputs. Indeed, both mean and variance terms might also be involved in the system dynamics. The problem incorporating these mean-variance terms is associated to the paradigm established by H. Markowitz, 1990 Nobel Laureate in Economics, on the mean-variance portfolio selection problem [5]. In addition, mean-field-type control has also been studied in the literature. For instance, discrete-time mean-field-type control problems are addressed using a Lagrange and operator approach for finite and infinite time horizon in [6] and [7], respectively. In contrast, maximum principle is used to solve mean-field-type control problems in [8], [9].

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