A New Interval Observer Design Method with Application to Fault Detection
This chapter proposes a novel interval observer for continuous-time linear systems with unknown disturbance. Based on the stability criterion of a Metzler matrix, the interval observer design problem is converted into a series of nonlinear inequalities. To attenuate the effect of unknown disturbance on estimation error, an interval observer design method based on constrained optimization is proposed. The proposed interval observer is able to estimate upper and lower bounds of the states in the general assumption that disturbance is unknown but bounded. Thus it is particularly suitable for fault detection for uncertain linear systems. Therefore, the proposed method is further used to generate dynamic thresholds to achieve fault detection. Finally, a flight control system is simulated to demonstrate the effectiveness of the proposed method.
KeywordsInterval observer Metzler matrix Constrained optimization Fault detection
- 2.Chambon, E., Apkarian, P., Burlion, L.: Metzler matrix transform determination using a non-smooth optimization technique with an application to interval observers. SIAM Conf. Control Appl. 205–211 (2015)Google Scholar
- 11.Narendra, K.S., Shorten, R.: A characterization of the Hurwitz stability of Metzler matrices. In: Proceedings of the American Control Conference, pp. 1833–1837. IEEE Press, New York (2009)Google Scholar
- 13.Rami, M.A., Cheng, C.H., Prada, C.De.: Tight robust interval observers: an LP approach. In: Proceedings of the 47th IEEE Conference on Decision and Control, pp. 2967–2972. IEEE Press, New York (2008)Google Scholar
- 15.Smith, J.L.: Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Math. Surv. Monogr. 41 (1995)Google Scholar