Quantised control of delayed Markovian jump systems with partly known transition probabilities
Abstract This paper is devoted to solve the quantised control problem of the continuous‐time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities. For the Markov chain, the transition rates are assumed to be partly known. The involved mixed time delays co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-02-01
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| Series: | IET Control Theory & Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/cth2.12049 |
| _version_ | 1818041123313025024 |
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| author | Ning Yang Dongyan Chen Jun Hu |
| author_facet | Ning Yang Dongyan Chen Jun Hu |
| author_sort | Ning Yang |
| collection | DOAJ |
| description | Abstract This paper is devoted to solve the quantised control problem of the continuous‐time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities. For the Markov chain, the transition rates are assumed to be partly known. The involved mixed time delays comprise both time‐varying delays and distributed delays. The logarithmic quantiser is introduced in the design of the state feedback controller and the uncertainty is entered into the quantization error matrix represented by an interval matrix. Based on the generalised Itô's formula, the free‐connection weighting matrix method and the stochastic analysis theory, several novel sufficient conditions are derived to guarantee that the trivial solution of the closed‐loop system is robustly exponentially stable in the mean square. Then, the concrete expression form of the desired controller gain is obtained via the solutions to a set of linear matrix inequalities. In addition, the corresponding stability criteria are given for three special situations of Markovian jump systems. Finally, a numerical example and a practical example (the wheeled mobile manipulator) are provided to show the feasibility and availability of the proposed theoretical results. |
| first_indexed | 2024-12-10T08:25:25Z |
| format | Article |
| id | doaj.art-22662c7986db430a989a556cb8aba48f |
| institution | Directory Open Access Journal |
| issn | 1751-8644 1751-8652 |
| language | English |
| last_indexed | 2024-12-10T08:25:25Z |
| publishDate | 2021-02-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Control Theory & Applications |
| spelling | doaj.art-22662c7986db430a989a556cb8aba48f2022-12-22T01:56:14ZengWileyIET Control Theory & Applications1751-86441751-86522021-02-0115337238910.1049/cth2.12049Quantised control of delayed Markovian jump systems with partly known transition probabilitiesNing Yang0Dongyan Chen1Jun Hu2Department of Mathematics Harbin University of Science and Technology Harbin ChinaDepartment of Mathematics Harbin University of Science and Technology Harbin ChinaDepartment of Mathematics Harbin University of Science and Technology Harbin ChinaAbstract This paper is devoted to solve the quantised control problem of the continuous‐time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities. For the Markov chain, the transition rates are assumed to be partly known. The involved mixed time delays comprise both time‐varying delays and distributed delays. The logarithmic quantiser is introduced in the design of the state feedback controller and the uncertainty is entered into the quantization error matrix represented by an interval matrix. Based on the generalised Itô's formula, the free‐connection weighting matrix method and the stochastic analysis theory, several novel sufficient conditions are derived to guarantee that the trivial solution of the closed‐loop system is robustly exponentially stable in the mean square. Then, the concrete expression form of the desired controller gain is obtained via the solutions to a set of linear matrix inequalities. In addition, the corresponding stability criteria are given for three special situations of Markovian jump systems. Finally, a numerical example and a practical example (the wheeled mobile manipulator) are provided to show the feasibility and availability of the proposed theoretical results.https://doi.org/10.1049/cth2.12049AlgebraMarkov processesOther topics in statisticsLinear control systemsControl system analysis and synthesis methodsStability in control theory |
| spellingShingle | Ning Yang Dongyan Chen Jun Hu Quantised control of delayed Markovian jump systems with partly known transition probabilities IET Control Theory & Applications Algebra Markov processes Other topics in statistics Linear control systems Control system analysis and synthesis methods Stability in control theory |
| title | Quantised control of delayed Markovian jump systems with partly known transition probabilities |
| title_full | Quantised control of delayed Markovian jump systems with partly known transition probabilities |
| title_fullStr | Quantised control of delayed Markovian jump systems with partly known transition probabilities |
| title_full_unstemmed | Quantised control of delayed Markovian jump systems with partly known transition probabilities |
| title_short | Quantised control of delayed Markovian jump systems with partly known transition probabilities |
| title_sort | quantised control of delayed markovian jump systems with partly known transition probabilities |
| topic | Algebra Markov processes Other topics in statistics Linear control systems Control system analysis and synthesis methods Stability in control theory |
| url | https://doi.org/10.1049/cth2.12049 |
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