Abstract
Based on the theory of positive systems, the goal of interval observers is to compute sets of admissible values of the state vector at each instant of time for systems subject to bounded uncertainties (noises, disturbances and parameters). The size of the estimated sets, which should be minimised, has to be proportional to the model uncertainties. An interval estimation can be seen as a conventional point estimation (the centre of the interval) with an estimation error given by the interval radius. The reliable uncertainties propagation performed in this context can be useful in several fields such as robust control, diagnosis and fault-tolerant control. This paper presents some recent results on interval observers for several dynamical systems classes such as continuous-time and switched systems.
Zusammenfassung
Basierend auf der Theorie der positiven Systeme ist es das Ziel von Intervallbeobachtern, zulässige Wertesätze des Zustandsvektors zu jedem Zeitpunkt für Systeme zu berechnen, die beschränkten Unsicherheiten unterliegen (Geräusche, Störungen und Parameter). Die Größe der geschätzten Mengen, die minimiert werden sollte, muss proportional zu den Modellunsicherheiten sein. Eine Intervallschätzung kann als eine konventionelle Mittelpunktschätzung gesehen werden, deren Schätzfehler durch den Intervallradius gegeben ist. Die in diesem Kontext ausgeführte zuverlässige Ungewissheitspropagierung kann in verschiedenen Bereichen wie Robustheit, Diagnose und fehlertoleranter Kontrolle nützlich sein. Dieser Artikel präsentiert aktuelle Ergebnisse zu Intervallbeobachtern für mehrere dynamische Systemklassen wie beispielsweise zeitkontinuierliche und geschaltete Systeme.
About the authors
Tarek Raïssi received the Engineering degree from École Nationale d’Ingénieurs de Tunis in 2000, the Master in Automatic Control from École Centrale de Lille in 2001, the Ph.D. degree from the University of Paris XII in 2004 and the Accreditation to Supervise/Conduct Research (HDR) from the University of Bordeaux 1 in 2012. From 2005 to 2011 he was an Associate Professor at the University of Bordeaux 1. Currently, he is a Full Professor at the Conservatoire National des Arts et Métiers, Paris, France. He is a member of the IFAC Technical Committee “Modelling, Identification and Signal Processing” and a Senior member of IEEE. His research interests include fault detection and isolation, nonlinear systems estimation and robust control.
Denis Efimov received the Ph.D. degree in Automatic Control from the Saint-Petersburg State Electrical Engineering University (Russia) in 2001, and the Dr.Sc. degree in Automatic control in 2006 from Institute for Problems of Mechanical Engineering RAS (Saint-Petersburg, Russia). From 2000 to 2009 he was research fellow of the Institute for Problems of Mechanical Engineering RAS, Control of Complex Systems Laboratory. From 2006 to 2011 he was working in the LSS (Supelec, France), the Montefiore Institute (University of Liege, Belgium) and the Automatic control group at IMS lab (University of Bordeaux I, France). Since 2011 he joined the Non-A team at Inria Lille center. He is a member of several IFAC TCs and a Senior member of IEEE. His main research interests include nonlinear oscillation analysis, observation and control, switched and nonlinear system stability.
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