LQ control of system governed by backward stochastic difference equations and applications

Shen Zhang, Jingmei Liu, Juanjuan Xu and Huanshui Zhang

International Journal of Systems Science, 2025, vol. 56, issue 11, 2557-2569

Abstract: This paper investigates the linear quadratic (LQ) optimal control of system governed by backward stochastic difference equations. In particular, multiple multiplicative noises are involved in the stochastic system, which leads to the situation that the controller uses partial information to complete optimisation. The main contribution is to give the explicitly optimal controller based on introduced Riccati equation. The key technique is to solve the corresponding forward–backward stochastic difference equations by establishing the non-homogeneous relationship, which is completely different from the homogeneous relationship in standard optimal control of system governed by forward stochastic difference equations. Moreover, the derived results are applied to stochastic optimal control problem with terminal constraints as applications.

Date: 2025
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DOI: 10.1080/00207721.2025.2449587

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