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Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains

Author

Listed:
  • Jing Xie

    (School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, China
    These authors contributed equally to this work.)

  • Bowen Zhang

    (School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, China
    These authors contributed equally to this work.)

  • Tianliang Zhang

    (School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, China)

  • Xiangtong Kong

    (School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, China)

Abstract

This paper delves into the exploration of the indefinite linear quadratic optimal control (LQOC) problem for discrete-time stochastic singular systems driven by discrete-time Markov chains. Initially, the conversion of the indefinite LQOC problem mentioned above for stochastic singular systems into an equivalent problem of normal stochastic systems is executed through a sequence of transformations. Following this, the paper furnishes sufficient and necessary conditions for resolving the transformed LQOC problem with indefinite matrix parameters, alongside optimal control strategies ensuring system regularity and causality, thereby establishing the solvability of the optimal controller. Additionally, conditions are derived to verify the definiteness of the transformed LQOC problem and the uniqueness of solutions for the generalized Markov jumping algebraic Riccati equation (GMJARE). The study attains optimal controls and nonnegative cost values, guaranteeing system admissibility. The results of the finite horizon are extended to the infinite horizon. Furthermore, it introduces the design of an output feedback controller using the LMI method. Finally, a demonstrative example demonstrates the validity of the main findings.

Suggested Citation

  • Jing Xie & Bowen Zhang & Tianliang Zhang & Xiangtong Kong, 2025. "Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains," Mathematics, MDPI, vol. 13(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:634-:d:1591625
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    References listed on IDEAS

    as
    1. Mahmoud Elsisi & Hatim G. Zaini & Karar Mahmoud & Shimaa Bergies & Sherif S. M. Ghoneim, 2021. "Improvement of Trajectory Tracking by Robot Manipulator Based on a New Co-Operative Optimization Algorithm," Mathematics, MDPI, vol. 9(24), pages 1-21, December.
    2. Lu, Qinyun & Zhu, Yuanguo, 2021. "LQ optimal control of fractional-order discrete-time uncertain systems," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
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