Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism

This paper is focused on the stabilization of Takagi–Sugeno fuzzy model-based Markovian jump systems with the aid of a delayed state observer. Due to network-induced constraints in the communication channel, a delay partition method combined with an event-triggered mechanism is proposed to design th...

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Autores principales:	Min Cheng, Chunyang Zhang, Jin Qiu, Zhengtian Wu, Qing Gao
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Markovian jump systems sliding mode control observer design event-triggering scheme Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/e755d97293674d14b31d9cbd30e10aff
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id	oai:doaj.org-article:e755d97293674d14b31d9cbd30e10aff
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spelling	oai:doaj.org-article:e755d97293674d14b31d9cbd30e10aff2021-11-25T18:12:06ZTime-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism10.3390/machines91102592075-1702https://doaj.org/article/e755d97293674d14b31d9cbd30e10aff2021-10-01T00:00:00Zhttps://www.mdpi.com/2075-1702/9/11/259https://doaj.org/toc/2075-1702This paper is focused on the stabilization of Takagi–Sugeno fuzzy model-based Markovian jump systems with the aid of a delayed state observer. Due to network-induced constraints in the communication channel, a delay partition method combined with an event-triggered mechanism is proposed to design the observer. Then, a novel integral sliding surface is designed, based on which sliding mode dynamics is obtained. Further, according to stochastic stability theory, feasible conditions are provided to ensure the sliding mode dynamics and the error dynamics have an <i>H<sub>∞</sub></i> attenuate level γ. The challenge is to deal with the issue that transition rates may be totally unknown. Moreover, an observer-based sliding mode controller is constructed to ensure the finite-time reachability of the predefined sliding surface. Finally, a numerical example based on a robotic manipulator is given to verify the effectiveness of the proposed method.Min ChengChunyang ZhangJin QiuZhengtian WuQing GaoMDPI AGarticleMarkovian jump systemssliding mode controlobserver designevent-triggering schemeMechanical engineering and machineryTJ1-1570ENMachines, Vol 9, Iss 259, p 259 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Markovian jump systems sliding mode control observer design event-triggering scheme Mechanical engineering and machinery TJ1-1570
spellingShingle	Markovian jump systems sliding mode control observer design event-triggering scheme Mechanical engineering and machinery TJ1-1570 Min Cheng Chunyang Zhang Jin Qiu Zhengtian Wu Qing Gao Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism
description	This paper is focused on the stabilization of Takagi–Sugeno fuzzy model-based Markovian jump systems with the aid of a delayed state observer. Due to network-induced constraints in the communication channel, a delay partition method combined with an event-triggered mechanism is proposed to design the observer. Then, a novel integral sliding surface is designed, based on which sliding mode dynamics is obtained. Further, according to stochastic stability theory, feasible conditions are provided to ensure the sliding mode dynamics and the error dynamics have an <i>H<sub>∞</sub></i> attenuate level γ. The challenge is to deal with the issue that transition rates may be totally unknown. Moreover, an observer-based sliding mode controller is constructed to ensure the finite-time reachability of the predefined sliding surface. Finally, a numerical example based on a robotic manipulator is given to verify the effectiveness of the proposed method.
format	article
author	Min Cheng Chunyang Zhang Jin Qiu Zhengtian Wu Qing Gao
author_facet	Min Cheng Chunyang Zhang Jin Qiu Zhengtian Wu Qing Gao
author_sort	Min Cheng
title	Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism
title_short	Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism
title_full	Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism
title_fullStr	Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism
title_full_unstemmed	Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism
title_sort	time-delay luenberger observer design for sliding mode control of nonlinear markovian jump systems via event-triggered mechanism
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/e755d97293674d14b31d9cbd30e10aff
work_keys_str_mv	AT mincheng timedelayluenbergerobserverdesignforslidingmodecontrolofnonlinearmarkovianjumpsystemsviaeventtriggeredmechanism AT chunyangzhang timedelayluenbergerobserverdesignforslidingmodecontrolofnonlinearmarkovianjumpsystemsviaeventtriggeredmechanism AT jinqiu timedelayluenbergerobserverdesignforslidingmodecontrolofnonlinearmarkovianjumpsystemsviaeventtriggeredmechanism AT zhengtianwu timedelayluenbergerobserverdesignforslidingmodecontrolofnonlinearmarkovianjumpsystemsviaeventtriggeredmechanism AT qinggao timedelayluenbergerobserverdesignforslidingmodecontrolofnonlinearmarkovianjumpsystemsviaeventtriggeredmechanism
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Time-Delay Luenberger Observer Design for Sliding Mode Control of Nonlinear Markovian Jump Systems via Event-Triggered Mechanism

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