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

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  • Shen Zhang
  • Jingmei Liu
  • Juanjuan Xu
  • Huanshui Zhang

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.

Suggested Citation

  • Shen Zhang & Jingmei Liu & Juanjuan Xu & Huanshui Zhang, 2025. "LQ control of system governed by backward stochastic difference equations and applications," International Journal of Systems Science, Taylor & Francis Journals, vol. 56(11), pages 2557-2569, August.
    • Handle: RePEc:taf:tsysxx:v:56:y:2025:i:11:p:2557-2569
    DOI: 10.1080/00207721.2025.2449587
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