Mode-dependent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities

Zhang, Lixian; Boukas, El‐Kébir

doi:10.1016/j.automatica.2009.02.002

Cited by 375 publications

(219 citation statements)

References 15 publications

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“…It is a fact that transition probability plays an important role in the performance of such systems, under the assumption that the transition probabilities of MJSs are time invariant, some problems have been studied, such as system analysis [2,3], stochastic stability and stabilization [4], control [5][6][7][8][9][10][11][12], fault detection and filtering [13][14][15][16][17], fault tolerant and estimation [18,19] etc. Some work has also been done on systems with partially known or uncertain transition probability (see, e.g., [20][21][22][23][24] and the references therein). However, in many practical systems, the transition probability is not a constant matrix, but a time-varying and time-depended matrix.…”

Section: Introductionmentioning

confidence: 99%

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Yin

Shi

Liu

et al. 2013

Int. J. Robust Nonlinear Control

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SUMMARYThis paper considers the problem of observer‐based H ∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H ∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Yin

Shi

Liu

et al. 2013

Int. J. Robust Nonlinear Control

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“…(Zhang e Boukas, 2009b). Além disso, as probabilidades de transição com incertezas politópi-cas ou limitadas em norma exigem o conhecimento de limites ou da estrutura das incertezas.…”

Section: Slsm E Resultados Básicosunclassified

Controle tolerante a falhas para sistemas lineares com saltos markovianos via atuadores virtuais

Néspoli¹,

Takamoto²

2013

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract-In this paper a Fault Tolerant Control (FTC) strategy using a virtual actuator is developed for Markovian Jump Linear Systems (MJLS) with partly unknown transition probabilities. The main idea of the virtual actuator approach is to reconfigure the control loop such that the nominal controller in use can be kept in the loop at all times even after actuator failures occur. Instead of adapting the controller to the faulty plant this FTC method adapts the faulty plant to the nominal controller. The MJL virtual actuator is designed using Linear Matrix Inequalities (LMIs). One such scheme using virtual actuator for MJLS was still not proposed to the best of the author 0 s knowledge.Keywords-Fault Tolerant Control, Markov Jump Linear System, Virtual Actuator.Resumo-Neste trabalho uma estratégia de Controle Tolerante a Falhas (CTF) baseada no uso de atuadores virtuaisé estendida para uma classe de Sistemas Lineares com Saltos Markovianos (SLSM) com probabilidades de transição parcialmente desconhecidas. A principal ideia do esquema de CTF usando atuadores virtuais consiste em reconfigurar o sistema de controle de modo a manter o controlador nominal em uso mesmo em caso de falhas nos atuadores. O problema de reconfiguração proposto consiste em determinar um controlador reconfigurado que garante a estabilidade estocástica do sistema e o desempenho H1. Neste sentido, o atuador virtual LSMé obtido através de um problema de otimização envolvendo Inequações Lineares Matriciais. Palavras-chave-Controle Tolerante a Falhas, Sistema Linear com Salto Markoviano, Atuador Virtual IntroduçãoO avanço tecnológico testemunhado nasúltimas décadas permitiu a integração de sensores, atuadores, controladores e microprocessadores inteligentes nos sistemas de controle automático, contribuindo para a aplicação de modernos sistemas de controle integrados em um número considerá-vel de setores industriais. Em contrapartida, a demanda por eficiência e confiabilidade destes sistemas de controle automático aumentou, estimulada pelo crescimento econômico assim como pelos requisitos ecológicos, de qualidade e segurança que envolvem a indústria moderna. Por sua vez, a ampla interconexão presente entre os componentes nos sistemas de controle integrados faz com que uma falha em um deles possa levar todo o processo de operação a um colapso. Dessa forma, a rápida detecção do mau funcionamento do sistema e o correto diagnóstico de sua causaé fundamental para que se tomem medidas eficazes no sentido de acomodar ou reconfigurar o sistema, buscando adaptá-lo a sua nova situação. Os sistemas de controle tolerantes a falhas (CTF) combinam de forma integrada diagnóstico e identificacão de falhas (DIF), e reconfiguração de controle de modo a evitar, ou minimizar, a degradação do sistema. De acordo com Blanke et al. (2006), o objetivo do sistema CTF consiste em manter desejávelíndice de performance e preservar as condições de estabilidade na presença de falhas. A capacidade de acomodação de um sistema de controle depende de fatores tais como severidade da ...

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“…However, due to the cross coupling of matrices in (18), it is difficult to directly design the desired filter by Theorem 3.1. To eliminate the coupling terms, similar to Zhang and Boukas (2009), the slack matrix variables will be introduced and the corresponding result is shown in Theorem 3.2. (14) …”

Section: Analysis Of H ∞ Performancesmentioning

confidence: 99%

“…For instance, in Chen et al (2013), the adaptive sliding mode control problem has been investigated for a class of Markovian jump systems with actuator degradation. The modedependent H ∞ filter design problem has been solved in Zhang and Boukas (2009) for Markovian jump linear systems with partly unknown transition probabilities.…”

Section: Introductionmentioning

confidence: 99%

Robust finite-horizon filtering for nonlinear time-delay Markovian jump systems with weighted try-once-discard protocol

Liu

Wang

et al. 2018

Systems Science & Control Engineering

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In this paper, the network-based robust H ∞ filtering problem is investigated for a class of nonlinear delayed Markovian jump systems subject to packet dropouts. To regulate the transmission order of multiple sensor nodes, the Weighted Try-Once-Discard (WTOD) protocol is adopted to avoid data collision and improve transmission accuracy and efficiency. Via the scheduling of WTOD protocol, only one sensor node is allowed to get access to the shared communication network at each step to send data. The purpose of the addressed problem is to design a network-based filter such that, the prespecified H ∞ disturbance attenuation level is guaranteed with the help of scheduling of WTOD protocol. Sufficient conditions are established for the existence of desired filter where the filter parameters are obtained by solving the proposed series of recursive linear matrix inequalities (RLMIs). Finally, an illustrative example is given to demonstrate the effectiveness of the presented filter design method. ARTICLE HISTORY

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Mode-dependent H∞ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities

Cited by 375 publications

References 15 publications

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Controle tolerante a falhas para sistemas lineares com saltos markovianos via atuadores virtuais

Robust finite-horizon filtering for nonlinear time-delay Markovian jump systems with weighted try-once-discard protocol

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Mode-dependent H∞ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities

Cited by 375 publications

References 15 publications

Observer-basedH ∞ control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH ∞ control on nonhomogeneous Markov jump systems with nonlinear input

Controle tolerante a falhas para sistemas lineares com saltos markovianos via atuadores virtuais

Robust finite-horizon filtering for nonlinear time-delay Markovian jump systems with weighted try-once-discard protocol

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Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input