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Optimal control for both forward and backward discrete-time systems

Author

Listed:
  • Chen, Xin
  • Yuan, Yue
  • Yuan, Dongmei
  • Ge, Xiao

Abstract

Forward discrete-time systems use past information to update the current state, while backward discrete-time systems use future information to update the current state. This study focuses on optimal control problems within the context of forward and backward discrete-time systems. We begin by investigating a general optimal control problem for both forward and backward discrete-time systems. Leveraging the inherent properties of these systems and the Bellman optimality principle, we derive recursive equations as a means to solve such optimal control problems. Using these recursive equations, we obtain analytical expressions for both the optimal controls and optimal values of bang–bang and linear quadratic optimal control problems. Finally, we present a numerical example and an industrial wastewater treatment problem to illustrate and demonstrate our findings.

Suggested Citation

  • Chen, Xin & Yuan, Yue & Yuan, Dongmei & Ge, Xiao, 2024. "Optimal control for both forward and backward discrete-time systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 298-314.
    • Handle: RePEc:eee:matcom:v:221:y:2024:i:c:p:298-314
    DOI: 10.1016/j.matcom.2024.03.009
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