Stochastic LQ Optimal Control With Initial and Terminal Constraints

• Published in: IEEE transactions on automatic control Vol. 69; no. 9; pp. 6261 - 6268
• Main Authors: Liu, Jingmei, Xu, Juanjuan, Zhang, Huanshui, Fu, Minyue
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Backward stochastic difference equation; Control systems; Cost function; Difference equations; initial and terminal constraints; Maximum principle; Optimal control; Riccati equation; Riccati equations; stochastic linear quadratic (LQ) optimal control; Stochastic systems; Terminal constraints; Transforms; White noise
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3376422

In this article, we consider the discrete-time stochastic linear quadratic (LQ) optimal control with both initial and terminal constraints. The main contribution includes two aspects: one is to provide a necessary and sufficient condition for the exact reachability of stochastic systems; the other is to characterize the solvability condition of the constrained stochastic LQ optimal control problem based on the exact reachability of the stochastic systems and obtain the explicitly optimal controller. The key technique is to innovatively transform the stochastic system governed by a forward stochastic difference equation into one governed by a backward stochastic difference equation. This way, we are able to solve the forward and backward stochastic difference equations derived from the stochastic maximum principle.