Robust fault detection for networked systems with communication delay and data missing. (English) Zbl 1180.93101

He, Xiao; Wang, Zidong; Zhou, D. H.

Automatica 45, No. 11, 2634-2639 (2009).

Summary: The robust fault detection problem is investigated for a class of discrete-time networked systems with unknown input and multiple state delays. A novel measurement model is utilized to represent both the random measurement delays and the stochastic data missing phenomenon, which typically result from the limited capacity of the communication networks. The network status is assumed to vary in a Markovian fashion and its transition probability matrix is uncertain but resides in a known convex set of a polytopic type. The main purpose of this paper is to design a robust fault detection filter such that, for all unknown inputs, possible parameter uncertainties and incomplete measurements, the error between the residual signal and the fault signal is made as small as possible. By casting the addressed robust fault detection problem into an auxiliary robust \(H_\infty \) filtering problem of a certain Markovian jumping system, a sufficient condition for the existence of the desired robust fault detection filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique.

MSC:

93E11	Filtering in stochastic control theory
93C41	Control/observation systems with incomplete information
60J75	Jump processes (MSC2010)

Keywords:

fault detection; networked systems; parameter uncertainty; random measurement delay; data missing; Markovian jumping system

References:

[1]	Boyd, S., Ghaoui, L. E., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. SIAM Studies in Applied Mathematics. Philadelphia · Zbl 0816.93004
[2]	de Souza, C.E., Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems, IEEE transactions on automatic control, 51, 5, 836-841, (2006) · Zbl 1366.93479
[3]	Fang, H., Ye, H., & Zhong, M. (2006). Fault diagnosis of networked control systems. In Proceedings of IFAC SAFEPROCESS (pp. 1-12)
[4]	Frank, P. M., Ding, S. X., & Koppen-Seliger, B. (2000). Current developments in the theory of FDI. In Proceedings of IFAC SAFEPROCESS (pp.16-27)
[5]	Gao, H.; Wang, C., A delay-dependent approach to robust \(H_\infty\) filtering for uncertain discrete-time state-delayed systems, IEEE transactions on signal processing, 52, 6, 1631-1640, (2004) · Zbl 1369.93175
[6]	He, X.; Wang, Z.; Zhou, D., Robust \(H_\infty\) filtering for networked systems with multiple state-delays, International journal of control, 80, 8, 1217-1232, (2007) · Zbl 1133.93314
[7]	Lam, J.; Shu, Z.; Xu, S.; Boukas, E.K., Robust \(H_\infty\) control of descriptor discrete-time Markovian jump systems, International journal of control, 80, 3, 374-385, (2007) · Zbl 1120.93057
[8]	Liu, G.P.; Mu, J.X.; Rees, D.; Chai, S.C., Design and stability analysis of networked control systems with random communication time delay using the modified MPC, International journal of control, 79, 4, 288-297, (2006) · Zbl 1140.93394
[9]	Mao, Z.; Jiang, B.; Shi, P., \(H_\infty\) fault detection filter design for networked control systems modelled by discrete Markovian jump systems, IET control theory and applications, 5, 1336-1343, (2007)
[10]	Montestruque, L.A.; Antsaklis, P., Stability of model-based networked control systems with time-varying transmission times, IEEE transactions on automatic control, 49, 9, 1562-1572, (2004) · Zbl 1365.90039
[11]	Schenato, L.; Sinopoli, B.; Franceschetti, M.; Poolla, K.; Sastry, S.S., Foundations of control and estimation over lossy networks, Proceedings of IEEE, 49, 9, 163-187, (2007)
[12]	Wang, Z.; Ho, D.W.C.; Liu, X., Variance-constrained filtering for uncertain stochastic systems with missing measurements, IEEE transactions on automatic control, 48, 7, 1254-1258, (2003) · Zbl 1364.93814
[13]	Wang, Z.; Yang, F.; Ho, D.W.C.; Liu, X., Robust \(H_\infty\) control for networked systems with random packet losses, IEEE transactions on systems, man, and cybernetics — part B, 37, 4, 916-924, (2007)
[14]	Xiong, J.; Lam, J., Stabilization of linear systems over networks with bounded packet loss, Automatica, 43, 1, 80-87, (2007) · Zbl 1140.93383
[15]	Xiong, J.; Lam, J., Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers, Automatica, 42, 5, 747-753, (2006) · Zbl 1137.93421
[16]	Yang, F.; Wang, Z.; Hung, Y.S.; Gani, M., \(H_\infty\) control for networked systems with random communication delays, IEEE transactions on automatic control, 51, 3, 511-518, (2006) · Zbl 1366.93167
[17]	Yue, D.; Han, Q.; Lam, J., Network-based robust \(H_\infty\) control of systems with uncertainty, Automatica, 41, 6, 999-1007, (2005) · Zbl 1091.93007
[18]	Zhang, P., Ding, S.X., Frank, P.M., & Sader, M. (2004). Fault detection of networked control systems with missing measurements. In Proceedings of Asian Control Conference (pp. 1258-1263)
[19]	Zhang, P.; Ding, S.X.; Wang, G.Z.; Zhou, D.H., Fault detection of linear discrete-time periodic systems, IEEE transactions on automatic control, 50, 2, 239-244, (2005) · Zbl 1365.93494
[20]	Zhang, L.; Shi, Y.; Chen, T.; Huang, B., A new method for stabilization of networked control systems with random delays, IEEE transactions on automatic control, 50, 8, 1177-1181, (2005) · Zbl 1365.93421
[21]	Zhong, M.; Ding, S.X.; Lam, J.; Wang, H., An LMI approach to design robust fault detection filter for uncertain LTI systems, Automatica, 39, 3, 543-550, (2003) · Zbl 1036.93061