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

Jing Xie, Bowen Zhang, Tianliang Zhang () and Xiangtong Kong
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Jing Xie: School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, China
Bowen Zhang: School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, China
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

Mathematics, 2025, vol. 13, issue 4, 1-20

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.

Keywords: stochastic singular system; discrete-time Markovian chain; LQ optimal control problem; output feedback control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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