Document Zbl 1334.93082

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J. Robust Nonlinear Control</a> <a href="/?q=in%3A354161" title="Articles in this Issue">26, No. 7, 1530-1548 (2016)</a>. </div> <div class="abstract">Summary: The paper presents a robust fault estimation approach for a class of nonlinear discrete-time systems. In particular, two sources of uncertainty are present in the considered class of systems, that is, an unknown input and an exogenous external disturbance. Thus, apart from simultaneous state and fault estimation, the objective is to decouple the effect of an unknown input while minimizing the influence of the exogenous external disturbance within the $\mathcal{H}_\infty$ framework. The resulting design procedure guarantees that a prescribed disturbance attenuation level is achieved with respect to the state and fault estimation error while assuring the convergence of the observer. The core advantage of the proposed approach is its simplicity by reducing the fault estimation problem to matrix inequalities formulation. In addition, the design conditions ensure the convergence of the observer with guaranteed $\mathcal{H}_\infty$ performance. The effectiveness of the proposed approach is demonstrated by its application to a twin rotor multiple-input multiple-output system.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6569560">Cited in <strong>36</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E10" title="MSC2020">93E10</a> </td> <td class="space"> Estimation and detection in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B35" title="MSC2020">93B35</a> </td> <td class="space"> Sensitivity (robustness) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C35" title="MSC2020">93C35</a> </td> <td class="space"> Multivariable systems, multidimensional control systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afault+diagnosis">fault diagnosis</a>; <a href="/?q=ut%3Afault+identification">fault identification</a>; <a href="/?q=ut%3Arobust+estimation">robust estimation</a>; <a href="/?q=ut%3Anonlinear+systems">nonlinear systems</a>; <a href="/?q=ut%3Aobservers">observers</a>; <a href="/?q=ut%3Alinear+matrix+inequalities">linear matrix inequalities</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1334.93082" data-ciurl="/ci/06569560" data-biburl="/bibtex/06569560.bib" data-amsurl="/amsrefs/06569560.bib" data-xmlurl="/xml/06569560.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06569560.pdf" title="Zbl 1334.93082 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1002/rnc.3365" aria-label="DOI for “An LMI approach to robust fault estimation for a class of nonlinear systems”" title="10.1002/rnc.3365">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://hdl.handle.net/2117/82598" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Blanke, M.; Kinnaert, M.; Lunze, J.; Staroswiecki, M., Diagnosis and Fault‐tolerant Control, 2006, Springer‐Verlag: Berlin, Heidelberg · <a href="/1126.93004" class="nowrap">Zbl 1126.93004</a></td> </tr><tr> <td>[2]</td> <td class="space">Gertler, J., Fault Detection and Diagnosis in Engineering Systems, 1998, Marcel Dekker: New York</td> </tr><tr> <td>[3]</td> <td class="space">Chen, J.; Patton, RJ, Robust Model‐based Fault Diagnosis for Dynamic Systems, 1999, Kluwer Academic Publishers: Boston · <a href="/0920.93001" class="nowrap">Zbl 0920.93001</a></td> </tr><tr> <td>[4]</td> <td class="space">Isermann, R., Fault Diagnosis Systems. An Introduction from Fault Detection to Fault Tolerance, 2006, Springer‐Verlag: New York</td> </tr><tr> <td>[5]</td> <td class="space">Ding, SX, Model‐based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools, 2008, Springer‐Verlag: Berlin, Heidelberg</td> </tr><tr> <td>[6]</td> <td class="space">Korbicz, J.; Kościelny, J.; Kowalczuk, Z.; Cholewa, W., Fault Diagnosis. Models, Artificial Intelligence, Applications, 2004, Springer‐Verlag: Berlin · <a href="/1074.93004" class="nowrap">Zbl 1074.93004</a></td> </tr><tr> <td>[7]</td> <td class="space">Witczak, M., Modelling and Estimation Strategies for Fault Diagnosis of Non‐linear Systems, 2007, Springer‐Verlag: Berlin · <a href="/1192.93003" class="nowrap">Zbl 1192.93003</a></td> </tr><tr> <td>[8]</td> <td class="space">Isermann, R., Fault Diagnosis Applications: Model Based Condition Monitoring, Actuators, Drives, Machinery, Plants, Sensors, and Fault‐tolerant Systems, 2011, Springer‐Verlag: Berlin · <a href="/1304.94001" class="nowrap">Zbl 1304.94001</a></td> </tr><tr> <td>[9]</td> <td class="space">Mahmoud, M.; Jiang, J.; Zhang, Y., Active Fault Tolerant Control Systems: Stochastic Analysis and Synthesis, 2003, Springer‐Verlag: Berlin · <a href="/1036.93002" class="nowrap">Zbl 1036.93002</a></td> </tr><tr> <td>[10]</td> <td class="space">Noura, H.; Theilliol, D.; Ponsart, J.; Chamseddine, A., Fault‐tolerant Control Systems: Design and Practical Applications, 2003, Springer‐Verlag: Berlin</td> </tr><tr> <td>[11]</td> <td class="space">Keller, JY; Darouach, M., Two‐stage Kalman estimator with unknown exogenous inputs, Automatica, 35, 2, 339-342, 1999 · <a href="/0937.93049" class="nowrap">Zbl 0937.93049</a></td> </tr><tr> <td>[12]</td> <td class="space">Gillijns, S.; De Moor, B., Unbiased minimum‐variance input and state estimation for linear discrete‐time systems, Automatica, 43, 111-116, 2007 · <a href="/1140.93480" class="nowrap">Zbl 1140.93480</a></td> </tr><tr> <td>[13]</td> <td class="space">Kemir, K.; Ben Hmida, F.; Ragot, J.; Gossa, M., Novel optimal recursive filter for state and fault estimation of linear systems with unknown disturbances, International Journal of Applied Mathematics and Computer Science, 21, 4, 629-638, 2011 · <a href="/1283.93282" class="nowrap">Zbl 1283.93282</a></td> </tr><tr> <td>[14]</td> <td class="space">Zhang, X.; Polycarpou, MM; Prisini, T., Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation, Automatica, 46, 2, 290-299, 2010 · <a href="/1205.93066" class="nowrap">Zbl 1205.93066</a></td> </tr><tr> <td>[15]</td> <td class="space">Veluvolu, KC; Kim, M. Y.; Lee, D., Nonlinear sliding mode high‐gain observers for fault estimation, International Journal of Systems Science, 42, 7, 1065-1074, 2011 · <a href="/1230.93014" class="nowrap">Zbl 1230.93014</a></td> </tr><tr> <td>[16]</td> <td class="space">Nobrega, EG; Abdalla, MO; Grigoriadis, KM, Robust fault estimation of unceratain systems using an LMI‐based approach, International Journal of Robust and Nonlinear Control, 18, 7, 1657-1680, 2008 · <a href="/1169.93323" class="nowrap">Zbl 1169.93323</a></td> </tr><tr> <td>[17]</td> <td class="space">Rotondo, D.; Nejjari, F.; Puig, V., A virtual actuator and sensor approach for fault tolerant control of LPV systems, Journal of Process Control, 24, 3, 203-222, 2014</td> </tr><tr> <td>[18]</td> <td class="space">Ichalal, D.; Marx, B.; Ragot, J.; Maquin, D., Fault detection, isolation and estimation for Takagi-Sugeno nonlinear systems, Journal of The Franklin Institute, 351, 7, 3651-3676, 2014 · <a href="/1290.93107" class="nowrap">Zbl 1290.93107</a></td> </tr><tr> <td>[19]</td> <td class="space">Seron, MM.; De Doná, JA, Robust fault estimation and compensation for {LPV} systems under actuator and sensor faults, Automatica, 52, 0, 294-301, 2015 · <a href="/1309.93116" class="nowrap">Zbl 1309.93116</a></td> </tr><tr> <td>[20]</td> <td class="space">Tabatabaeipour, SM; Bak, T., Robust observer‐based fault estimation and accommodation of discrete‐time piecewise linear systems, Journal of the Franklin Institute, 351, 1, 277-295, 2014 · <a href="/1293.93725" class="nowrap">Zbl 1293.93725</a></td> </tr><tr> <td>[21]</td> <td class="space">De Persis, C.; De Santis, R.; Isidori, A., Nonlinear actuator fault detection and isolation for a VTOL aircraft, 4449-4454, 2001, Arlington, VA</td> </tr><tr> <td>[22]</td> <td class="space">Amato, F.; Cosentino, C.; Mattei, M.; Paviglianiti, G., A mixed direct/functional redundancy scheme for the FDI on a small commercial aircraft, 331-339, 2003</td> </tr><tr> <td>[23]</td> <td class="space">Hammouri, H.; Kabore, P.; Othman, S.; Biston, J., Observer‐based approach to fault detection and isolation for nonlinear systems, IEEE Transactions on Automatic Control, 44, 10, 1879-1884, 1999 · <a href="/0956.93005" class="nowrap">Zbl 0956.93005</a></td> </tr><tr> <td>[24]</td> <td class="space">De Persis, C.; De Santis, R.; Isidori, A., An $\mathcal{\mathcal{H}}_\infty $‐suboptimal fault detection filter for bilinear systems, 331-339, 2000 · <a href="/1239.93034" class="nowrap">Zbl 1239.93034</a></td> </tr><tr> <td>[25]</td> <td class="space">Hammouri, H.; Kinnaert, M.; El Yaagoubi, EH, Observer‐based approach to fault detection and isolation for nonlinear systems, IEEE Transactions on Automatic Control, 44, 1879-1884, 1999 · <a href="/0956.93005" class="nowrap">Zbl 0956.93005</a></td> </tr><tr> <td>[26]</td> <td class="space">De Persis, C.; Isidori, A., A geometric approach to nonlinear fault detection and isolation, IEEE Transactions on Automatic Control, 46, 6, 853-865, 2001 · <a href="/1009.93003" class="nowrap">Zbl 1009.93003</a></td> </tr><tr> <td>[27]</td> <td class="space">Mattei, M.; Paviglianiti, G.; Scordamaglia, V., Nonlinear observers with $\mathcal{\mathcal{H}}_\infty$ performance for sensor fault detection and isolation: a linear matrix inequality design procedure, Control Engineering Practice, 13, 1271-1281, 2006</td> </tr><tr> <td>[28]</td> <td class="space">Mrugalski, M., An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection, International Journal of Applied Mathematics and Computer Science, 23, 1, 157-169, 2013 · <a href="/1293.93743" class="nowrap">Zbl 1293.93743</a></td> </tr><tr> <td>[29]</td> <td class="space">Frank, PM; Marcu, T.; TeodorescuHN (ed.); MlynekD (ed.); KandelA (ed.); ZimmermannHJ (ed.), Diagnosis strategies and systems. Principles, fuzzy and neural approaches, Intelligent Systems and Interfaces, 307-350, 2000, Kluwer Academic Publishers: Boston</td> </tr><tr> <td>[30]</td> <td class="space">Hammouri, H.; Kabore, P.; Othman, S.; Biston, J., Failure diagnosis and nonlinear observer. Application to a hydraulic process, Journal of The Franklin Institute, 339, 4-5, 455-478, 2002 · <a href="/1021.93011" class="nowrap">Zbl 1021.93011</a></td> </tr><tr> <td>[31]</td> <td class="space">Kabore, R.; Wang, H., Design of fault diagnosis filters and fault tolerant control for a class of nonlinear systems, IEEE Transactions on Automatic Control, 46, 11, 1805-1809, 2001 · <a href="/1006.93068" class="nowrap">Zbl 1006.93068</a></td> </tr><tr> <td>[32]</td> <td class="space">Hammouri, H.; Kabore, P.; Kinnaert, M., A geometric approach to fault detection and isolation for bilinear systems, IEEE Transactions on Automatic Control, 46, 9, 1451-1455, 2001 · <a href="/1006.93014" class="nowrap">Zbl 1006.93014</a></td> </tr><tr> <td>[33]</td> <td class="space">Sami, M.; Patton, RJ, A multiple‐model approach to fault tolerant tracking control for non‐linear systems, 498-503, 2012, Barcelona, Spain, IEEE</td> </tr><tr> <td>[34]</td> <td class="space">Patton, RJ; Klinkhieo, S., Actuator fault estimation and compensation based on an augmented state observer approach, 8482-8487, 2009, Shanghai, China, IEEE</td> </tr><tr> <td>[35]</td> <td class="space">Patton, RJ; Chen, L.; Klinkhieo, S., LPV approach to friction estimation as a fault diagnosis problem, 296-301, 2010, Miedzyzdroje, Poland, IEEE</td> </tr><tr> <td>[36]</td> <td class="space">Sun, X.; Patton, RJ, Robust actuator multiplicative fault estimation with unknown input decoupling for a wind turbine system, 263-268, 2013, Nice, France, IEEE</td> </tr><tr> <td>[37]</td> <td class="space">Sun, X.; Patton, RJ; Goupil, P., Robust adaptive fault estimation for a commercial aircraft oscillatory fault scenario, 595-600, 2012, Cardif, United Kingdom, IEEE</td> </tr><tr> <td>[38]</td> <td class="space">Stipanovic, DM; Siljak, DD, Robust stability and stabilization of discrete‐time non‐linear: the LMI approach, International Journal of Control, 74, 5, 873-879, 2001 · <a href="/1022.93034" class="nowrap">Zbl 1022.93034</a></td> </tr><tr> <td>[39]</td> <td class="space">Zemouche, A.; Boutayeb, M.; Iulia Bara, G., Observer for a class of Lipschitz systems with extension to $\mathcal{\mathcal{H}}_\infty$ performance analysis, Systems and Control Letters, 57, 1, 18-27, 2008 · <a href="/1129.93006" class="nowrap">Zbl 1129.93006</a></td> </tr><tr> <td>[40]</td> <td class="space">Abbaszadeh, M.; Marquez, HJ, LMI optimization approach to robust $\mathcal{\mathcal{H}}_\infty$ observer design and static output feedback stabilization for non‐linear uncertain systems, International Journal of Robust and Nonlinear Control, 19, 3, 313-340, 2008 · <a href="/1163.93027" class="nowrap">Zbl 1163.93027</a></td> </tr><tr> <td>[41]</td> <td class="space">Marquez, HJ, Nonlinear Control Systems. Analysis and Design, 2003, Wiley: New Jersey · <a href="/1037.93003" class="nowrap">Zbl 1037.93003</a></td> </tr><tr> <td>[42]</td> <td class="space">Rajamani, R., Observers for Lipschitz non‐linear systems., IEEE Transactions on Automatic Control, 43, 3, 397-401, 1998 · <a href="/0905.93009" class="nowrap">Zbl 0905.93009</a></td> </tr><tr> <td>[43]</td> <td class="space">Pertew, AM; Marquez, HJ; Zhao, Q., $ \mathcal{\mathcal{H}}_\infty$ synthesis of unknown input observers for non‐linear Lipschitz systems, International Journal of Control, 78, 15, 1155-1165, 2005 · <a href="/1077.93018" class="nowrap">Zbl 1077.93018</a></td> </tr><tr> <td>[44]</td> <td class="space">Montes de Oca, S.; Puig, V.; Witczak, M.; Dziekan, L., Fault‐tolerant control strategy for actuator faults using LPV techniques: application to a two degree of freedom helicopter, International Journal of Applied Mathematics and Computer Science, 22, 1, 161-171, 2012 · <a href="/1273.93049" class="nowrap">Zbl 1273.93049</a></td> </tr><tr> <td>[45]</td> <td class="space">Dziekan, L.; Witczak, M.; Korbicz, J., Active fault‐tolerant control design for Takagi-Sugeno fuzzy systems, Bulletin of the Polish Academy of Sciences: Technical Sciences, 59, 1, 93-102, 2011 · <a href="/1291.93176" class="nowrap">Zbl 1291.93176</a></td> </tr><tr> <td>[46]</td> <td class="space">Witczak, M.; Puig, V.; de Oca, S., A fault‐tolerant control strategy for non‐linear discrete‐time systems: application to the twin‐rotor system, International Journal of Control, 86, 10, 1788-1799, 2013 · <a href="/1312.93037" class="nowrap">Zbl 1312.93037</a></td> </tr><tr> <td>[47]</td> <td class="space">Zhao, Y.; Tao, J.; Shi, N., A note on observer design for one‐sided lipschitz nonlinear systems, Systems and Control Letters, 59, 1, 66-71, 2010 · <a href="/1186.93017" class="nowrap">Zbl 1186.93017</a></td> </tr><tr> <td>[48]</td> <td class="space">Chadli, M.; Karimi, HR, Robust observer design for unknown inputs Takagi-Sugeno models, IEEE Transactions on Fuzzy Systems, 21, 1, 158-164, 2013</td> </tr><tr> <td>[49]</td> <td class="space">Zemouche, A.; Boutayeb, M., Observer design for Lipschitz non‐linear systems: the discrete time case, IEEE Transactions on Circuits and Systems ‐ II:Express Briefs, 53, 8, 777-781, 2006</td> </tr><tr> <td>[50]</td> <td class="space">Li, H.; Fu, M., A linear matrix inequality approach to robust $\mathcal{\mathcal{H}}_\infty$ filtering, IEEE Transactions on Signal Processing, 45, 9, 2338-2350, 1997</td> </tr><tr> <td>[51]</td> <td class="space">Witczak, M., Fault Diagnosis and Fault‐tolerant Control Strategies for Non‐linear Systems: Analytical and Soft Computing Approaches, 2014, Springer International Publishing: Heidelberg, Germany · <a href="/1321.93003" class="nowrap">Zbl 1321.93003</a></td> </tr><tr> <td>[52]</td> <td class="space">de Oliveira, MC; Bernussou, J.; Geromel, JC, A new discrete‐time robust stability condition, Systems and Control Letters, 37, 4, 261-265, 1999 · <a href="/0948.93058" class="nowrap">Zbl 0948.93058</a></td> </tr><tr> <td>[53]</td> <td class="space">Rotondo, D.; Fatiha Nejjari, F.; Puig, V., Quasi‐LPV modeling, identification and control of a twin rotor MIMO system, Control Engineering Practice, 21, 6, 829-846, 2013</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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