Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains
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...
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MDPI AG
2025-02-01
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| author | Jing Xie Bowen Zhang Tianliang Zhang Xiangtong Kong |
| author_facet | Jing Xie Bowen Zhang Tianliang Zhang Xiangtong Kong |
| author_sort | Jing Xie |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a8223208564243fa85e166cea3cdb3dd |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a8223208564243fa85e166cea3cdb3dd2025-08-20T02:03:31ZengMDPI AGMathematics2227-73902025-02-0113463410.3390/math13040634Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov ChainsJing Xie0Bowen Zhang1Tianliang Zhang2Xiangtong Kong3School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, ChinaSchool of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, ChinaSchool of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, ChinaSchool of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, ChinaThis 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.https://www.mdpi.com/2227-7390/13/4/634stochastic singular systemdiscrete-time Markovian chainLQ optimal control problemoutput feedback control |
| spellingShingle | Jing Xie Bowen Zhang Tianliang Zhang Xiangtong Kong Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains Mathematics stochastic singular system discrete-time Markovian chain LQ optimal control problem output feedback control |
| title | Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains |
| title_full | Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains |
| title_fullStr | Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains |
| title_full_unstemmed | Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains |
| title_short | Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains |
| title_sort | output feedback optimal control for discrete time singular systems driven by stochastic disturbances and markov chains |
| topic | stochastic singular system discrete-time Markovian chain LQ optimal control problem output feedback control |
| url | https://www.mdpi.com/2227-7390/13/4/634 |
| work_keys_str_mv | AT jingxie outputfeedbackoptimalcontrolfordiscretetimesingularsystemsdrivenbystochasticdisturbancesandmarkovchains AT bowenzhang outputfeedbackoptimalcontrolfordiscretetimesingularsystemsdrivenbystochasticdisturbancesandmarkovchains AT tianliangzhang outputfeedbackoptimalcontrolfordiscretetimesingularsystemsdrivenbystochasticdisturbancesandmarkovchains AT xiangtongkong outputfeedbackoptimalcontrolfordiscretetimesingularsystemsdrivenbystochasticdisturbancesandmarkovchains |