Fault detection for LPV systems using Set-Valued Observers: A coprime factorization approach

This paper addresses the problem of fault detection for linear parameter-varying systems in the presence of measurement noise and exogenous disturbances using Set-Valued Observers (SVOs). The applicability of current methods is limited in the sense that, to increase accuracy, the detection requires a large number of past measurements and the boundedness of the set-valued estimates is only guaranteed for stable systems. In order to widen the class of systems to be modeled and also to reduce the associated computational cost, the aforementioned issues must be addressed. A solution involving left-coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of SVOs for fault detection of unstable systems by using the resulting coprime factorization stable subsystems. The algorithm is shown to produce bounded set-valued estimates and an example is provided. Performance is assessed through simulations, illustrating, in particular that small-magnitude faults (compared to exogenous disturbances) can be detected under mild assumptions. ∗Corresponding author Email addresses: [email protected] (Daniel Silvestre), [email protected] (Paulo Rosa), [email protected] (João P. Hespanha), [email protected] (Carlos Silvestre) 1This work was supported by grant SFRH//BD/71206/2010, from Fundação para a Ciência e a Tecnologia. 2J. Hespanha was supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under grants No. W911NF-09-1-0553 and W911NF-09-D-0001. 3This work was supported in part by the University of Macau, Macao, China, under Project MYRG2015-00126-FST, in part by the Fundação para a Ciência e a Tecnologia under Project FCT [UID/EEA/50009/2013] and in part by ONRg GRANT N62909-15-1-V177. Preprint submitted to Systems and Control Letters June 17, 2016