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Observer-based optimal fault detection using pdfs for time-delay stochastic systems. (English) Zbl 1156.93395

Summary: This paper concerns the problem of fault detection (FD) for general stochastic systems with time delays. Different from the classical FD problem, the available information for the FD is the input and the measured output probability density functions (PDFs) of the system. Based on this, firstly, square root B-spline expansions technique is applied to model the PDFs so that the concerned FD problem is transformed into a nonlinear FD problem subject to the weight dynamical systems. Secondly, by using the FD observer as residual generator and guaranteed cost performance index as objective function, design of the FD observer is formulated as an optimization problem. A delay-dependent condition to solve this problem is established in terms of the feasibility of linear matrix inequality (LMI). Moreover, in order to improve FD performance, the guaranteed cost algorithm is applied to optimal observer design. Finally, two examples are given to demonstrate the applicability of the proposed approach.

MSC:

93E10 Estimation and detection in stochastic control theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K20 Stability theory of functional-differential equations
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[1] Boyd, S.; Ghaoui, L. El.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics (1994), SIAM: SIAM Philadelphia, PA · Zbl 0816.93004
[2] Chen, J.; Patton, R., Robust Model-based Fault Diagnosis for Dynamic Systems (1999), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0920.93001
[3] Chen, R. H.; Mingori, D. L.; Speyer, J. L., Optimal stochastic fault detection filter, Automatica, 39, 377-390 (2003) · Zbl 1036.93060
[4] W.T. Chen, M. Saif, Fault detection and isolation based on novel unknown input observer design, Proceedings of American Control Conference Minneapolis, Minnesota, USA, 2006, pp. 5129-5234.; W.T. Chen, M. Saif, Fault detection and isolation based on novel unknown input observer design, Proceedings of American Control Conference Minneapolis, Minnesota, USA, 2006, pp. 5129-5234.
[5] Crowley, T. J.; Meadows, E. S.; Kostoulas, E.; Doyle III, F. J., Control of particle size distribution described by a population balance model of semibatch emulsion polymerization, J. Process. Control, 10, 419-432 (2000)
[6] Frank, P. M., Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: a survey and some new results, Automatica, 26, 459-744 (1990) · Zbl 0713.93052
[7] Fridman, E.; Shaked, U., An improved stabilization method for linear time-delay systems, IEEE Trans. Automat. Control, 47, 1931-1937 (2002) · Zbl 1364.93564
[8] Fridman, E.; Shaked, U., Delay dependent stability and \(H_\infty\) control: constant and time-varying delays, Int. J. Control, 76, 48-60 (2003) · Zbl 1023.93032
[9] Guo, L.; Wang, H., Applying constrained nonlinear generalized PI strategy to PDF tracking control through square root b-spline models, Int. J. Control, 77, 1481-1492 (2004) · Zbl 1076.93018
[10] Guo, L.; Wang, H., PID controller design for output PDFs of stochastic systems using linear matrix inequalities, IEEE Trans. Syst. Man Cybern. B, 35, 65-71 (2005)
[11] Guo, L.; Wang, H., Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filter, IEEE Trans. Circuits Syst. I, 2, 1644-1652 (2005) · Zbl 1374.94963
[12] Guo, L.; Zhang, Y. M.; Wang, H.; Fang, J. C., Observer-based optimal fault detection and diagnosis using conditional probability distributions, IEEE Trans. Signal Process., 54, 3712-3719 (2006) · Zbl 1373.93321
[13] He, Y.; Wang, Q. G.; Lin, C.; Wu, M., Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic type uncertainties, IEEE Trans. Automat. Control, 49, 828-832 (2004) · Zbl 1365.93368
[14] Jiang, B.; Chowdhury, F. N., Fault estimation and accommodation for linear MIMO discrete-time systems, IEEE Trans. Control Syst. Technol., 13, 493-499 (2005)
[15] Jiang, B.; Chowdhury, F. N., Parameter fault detection and estimation of a class of nonlinear systems using observers, J. Franklin Inst., 342, 725-736 (2005) · Zbl 1079.93011
[16] Jiang, B.; Staroswiecki, M.; Cocquempot, V., Fault estimation in nonlinear uncertain systems using robust-sliding-mode observers, IEE Proc. Control Theory Appl., 151, 29-37 (2004)
[17] Jiang, B.; Wang, J. L.; Soh, Y. C., An adaptive technique for robust diagnosis of faults with independent effect on system outputs, Int. J. Control, 75, 792-802 (2002) · Zbl 1038.93016
[18] Karny, M.; Bohm, J.; Guy, T. V.; Nedoma, P., Mixture-based adaptive probabilistic control, Int. J. Adapt. Control Signal Process., 17, 119-132 (2003) · Zbl 1019.93028
[19] Li, P.; Kadirkamanathan, V., Particle filtering based likelihood ratio approach to fault diagnosis in nonlinear stochastic systems, IEEE Trans. Syst. Man Cybern. C, 31, 337-343 (2001)
[20] Liu, J.; Wang, J. L.; Wang, G. H., Residual guaranteed variance filtering against senor failures, IEEE Trans. Signal Process., 51, 1403-1411 (2003) · Zbl 1369.94210
[21] Ren, J. S., LMI-based fault detection filter design for a class of neutral system with time delay in states, (Proceedings of the 6th World Congress on Intelligent Control and Automation (2006), Dalian: Dalian China), 21-23
[22] Wang, H., Bounded Dynamic Stochastic Systems: Modelling and Control (2000), Springer: Springer London · Zbl 0938.93001
[23] H. Wang, Detecting faults in dynamic and bounded stochastic distributions: an observer based technique, in: Proceedings of ACC01, Arlington, VA, 2001, pp. 482-487.; H. Wang, Detecting faults in dynamic and bounded stochastic distributions: an observer based technique, in: Proceedings of ACC01, Arlington, VA, 2001, pp. 482-487.
[24] Wang, H.; Lin, W., Applying observer based FDI techniques to detect faults in dynamic and bounded stochastic distributions, Int. J. Control, 73, 1424-1436 (2000) · Zbl 0992.93089
[25] Zhang, X. M.; Wu, M.; She, J. H.; He, Y., Delay-dependent stabilization of linear systems with time-varying state and input delays, Automatica, 41, 1405-1412 (2005) · Zbl 1093.93024
[26] Zhang, Y. M.; Guo, L.; Wang, H., Filter-based fault detection and diagnosis using output PDFs for stochastic systems with time delays, Int. J. Adapt. Control Signal Process., 20, 175-194 (2006) · Zbl 1282.93281
[27] Zhong, M.; Ye, H.; Shi, P.; Wang, G., Fault detection for markovian jump systems, IEE Proc. Control Theory Appl., 152, 397-402 (2005)
[28] Zhong, M. Y.; Ding, S. X.; Lam, J.; Wang, H. B., An LMI approach to design robust fault detection filter for uncertain LTI systems, Automatica, 39, 543-550 (2003) · Zbl 1036.93061
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