Indefinite LQ optimal control for mean-field stochastic systems with information asymmetry

Abstract

This paper addresses the indefinite linear quadratic (LQ) optimal control problem within mean-field stochastic systems characterized by asymmetric information. In such models, multiple controllers operate, each with a unique information structure. Notably, the introduction of mean-field terms disrupts the adaptiveness of control inputs, thereby making the control problem under consideration distinct from the standard LQ formulations. Employing the maximum principle, we propose necessary and sufficient conditions for the indefinite LQ control problem by considering forward and backward stochastic difference equations (FBSDEs). Specifically, through an orthogonal decomposition method, we introduce a novel technique to decouple the FBSDEs, facilitating the derivation of optimal controllers via non-symmetric Riccati equations. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed approach.