Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov Chain
In a networked control system scenario, the packet dropout is usually modeled by a time-invariant (homogeneous) Markov chain (MC) process. However, from a practical point of view, the probabilities of packet loss can vary in time and/or probability parameter dependency. Therefore, to design a fault...
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MDPI AG
2023-04-01
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| author | Leonardo Carvalho Jonathan M. Palma Cecília F. Morais Bayu Jayawardhana Oswaldo L. V. Costa |
| author_facet | Leonardo Carvalho Jonathan M. Palma Cecília F. Morais Bayu Jayawardhana Oswaldo L. V. Costa |
| author_sort | Leonardo Carvalho |
| collection | DOAJ |
| description | In a networked control system scenario, the packet dropout is usually modeled by a time-invariant (homogeneous) Markov chain (MC) process. However, from a practical point of view, the probabilities of packet loss can vary in time and/or probability parameter dependency. Therefore, to design a fault detection filter (FDF) implemented in a semi-reliable communication network, it is important to consider the variation in time of the network parameters, by assuming the more accurate scenario provided by a nonhomogeneous jump system. Such a premise can be properly taken into account within the linear parameter varying (LPV) framework. In this sense, this paper proposes a new design method of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> gain-scheduled FDF for Markov jump linear systems under the assumption of a nonhomogeneous MC. To illustrate the applicability of the theoretical solution, a numerical simulation is presented. |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T05:30:39Z |
| publishDate | 2023-04-01 |
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| spelling | doaj.art-5f79a80d2d544318adfa493cc401f2f12023-11-17T17:09:38ZengMDPI AGMathematics2227-73902023-04-01117171310.3390/math11071713Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov ChainLeonardo Carvalho0Jonathan M. Palma1Cecília F. Morais2Bayu Jayawardhana3Oswaldo L. V. Costa4Departamento de Engenharia de Telecomunicacções e Controle, Escola Politécnica na Universidade de São Paulo, São Paulo 05508-010, SP, BrazilFacultad de Ingeniería, Universidad de Talca, Curico 3340000, Maule, ChilePontifical Catholic University of Campinas (PUC-Campinas), Center for Exact, Environmental and Technological Sciences (CEATEC), Postgraduate Program in Telecommunication Networks Management, Campinas 13086-900, SP, BrazilEngineering and Technology Institute Groningen, Faculty of Science and Engineering, Rijksuniversiteit Groningen, 9747 AG Groningen, The NetherlandsDepartamento de Engenharia de Telecomunicacções e Controle, Escola Politécnica na Universidade de São Paulo, São Paulo 05508-010, SP, BrazilIn a networked control system scenario, the packet dropout is usually modeled by a time-invariant (homogeneous) Markov chain (MC) process. However, from a practical point of view, the probabilities of packet loss can vary in time and/or probability parameter dependency. Therefore, to design a fault detection filter (FDF) implemented in a semi-reliable communication network, it is important to consider the variation in time of the network parameters, by assuming the more accurate scenario provided by a nonhomogeneous jump system. Such a premise can be properly taken into account within the linear parameter varying (LPV) framework. In this sense, this paper proposes a new design method of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> gain-scheduled FDF for Markov jump linear systems under the assumption of a nonhomogeneous MC. To illustrate the applicability of the theoretical solution, a numerical simulation is presented.https://www.mdpi.com/2227-7390/11/7/1713fault-detection filterMarkovian jump linear system<named-content content-type="inline-formula"><inline-formula><mml:math id="mm1111"><mml:semantics><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mo>∞</mml:mo></mml:msub></mml:semantics></mml:math></inline-formula></named-content> normLMI relaxationsnonhomogeneous Markov chains |
| spellingShingle | Leonardo Carvalho Jonathan M. Palma Cecília F. Morais Bayu Jayawardhana Oswaldo L. V. Costa Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov Chain Mathematics fault-detection filter Markovian jump linear system <named-content content-type="inline-formula"><inline-formula><mml:math id="mm1111"><mml:semantics><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mo>∞</mml:mo></mml:msub></mml:semantics></mml:math></inline-formula></named-content> norm LMI relaxations nonhomogeneous Markov chains |
| title | Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov Chain |
| title_full | Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov Chain |
| title_fullStr | Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov Chain |
| title_full_unstemmed | Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov Chain |
| title_short | Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov Chain |
| title_sort | gain scheduled fault detection filter for markovian jump linear system with nonhomogeneous markov chain |
| topic | fault-detection filter Markovian jump linear system <named-content content-type="inline-formula"><inline-formula><mml:math id="mm1111"><mml:semantics><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mo>∞</mml:mo></mml:msub></mml:semantics></mml:math></inline-formula></named-content> norm LMI relaxations nonhomogeneous Markov chains |
| url | https://www.mdpi.com/2227-7390/11/7/1713 |
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