Deterministic optimal control for discrete-time systems with multiplicative noises and random coefficients. (April 2023)

• Record Type: Journal Article
• Authors: Li, Hongdan; Li, Xun; Fu, Minyue; Zhang, Huanshui
• Is Part Of: Automatica. Volume 150(2023)
• Publication Date: 2023-04
• Subjects: Deterministic optimal -- Stochastic linear quadratic control -- Forward and backward stochastic difference equations -- Coupled Riccati-type difference equations; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2023.110852
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper studies a linear-quadratic optimal control problem for discrete-time systems with multiplicative noise and random coefficients. Motivated by fiscal policy planning problems, where deterministic policies are required, this paper aims to find a deterministic optimal controller. The challenge is to seek a solution to forward and backward stochastic difference equations with structural inconsistency caused by random and deterministic terms. We derive necessary and sufficient conditions to solve this optimal control problem by employing a decoupling method. We also present an explicit expression of the optimal controller based on coupled stochastic Riccati-type difference equations.