×

zbMATH — the first resource for mathematics

Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems. (English) Zbl 1309.93155
Summary: This paper is concerned with the finite-horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time-varying. The faults are assumed to occur in a random way governed by two sets of Bernoulli distributed white sequences. The stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well-studied nonlinearities. The aim of the problem is to estimate the random faults, over a finite horizon, such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an \(H_\infty\)-norm in the mean square sense. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are established for the existence of the desired finite-horizon \(H_\infty\) fault estimator whose parameters are then obtained by solving coupled backward recursive Riccati Difference Equations (RDEs). A simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method.

MSC:
93E10 Estimation and detection in stochastic control theory
93E03 Stochastic systems in control theory (general)
93C10 Nonlinear systems in control theory
93B36 \(H^\infty\)-control
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aitrami, M.; Chen, X.; Zhou, X., Discrete-time indefinite LQ control with state and control dependent noises, Journal of Global Optimization, 23, 3-4, 245-265, (2002) · Zbl 1035.49024
[2] Basin, M. V.; Pinsky, M. A., Stability impulse control of faulted nonlinear systems, IEEE Transactions on Automatic Control, 43, 11, 1604-1608, (1998) · Zbl 0957.93069
[3] Ding, S. X.; Jeinsch, T.; Frank, P. M.; Ding, E. L., A unified approach to the optimization of fault detection systems, International Journal of Adaptive Control and Signal Processing, 14, 7, 725-745, (2000) · Zbl 0983.93016
[4] Dong, H.; Wang, Z.; Gao, H., Filtering, control and fault detection with randomly occurring incomplete information, (2013), Wiley Chichester, UK · Zbl 1285.93002
[5] Dong, H.; Wang, Z.; Gao, H., Distributed \(H_\infty\) filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks, IEEE Transactions on Industrial Electronics, 60, 10, 4665-4672, (2013)
[6] Gao, Z.; Ding, S. X., Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems, Automatica, 43, 5, 912-920, (2007) · Zbl 1117.93019
[7] He, X.; Wang, Z.; Zhou, D., Robust fault detection for networked systems with communication delay and data missing, Automatica, 45, 11, 2634-2639, (2009) · Zbl 1180.93101
[8] Hernandez-Gonzalez, M.; Basin, M. V., Discrete-time optimal control for stochastic nonlinear polynomial systems, International Journal of General Systems, 43, 3-4, 359-371, (2014) · Zbl 1302.93241
[9] Hernandez-Gonzalez, M.; Basin, M. V., Discrete-time filtering for nonlinear polynomial systems over linear observations, International Journal of Systems Science, 45, 7, 1461-1472, (2014) · Zbl 1290.93185
[10] Hu, J.; Wang, Z.; Gao, H.; Stergioulas, L. K., Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities, IEEE Transactions on Industrial Electronics, 59, 7, 3008-3016, (2012)
[11] Jiang, B.; Shi, P.; Mao, Z., Sliding mode observer-based fault estimation for nonlinear networked control systems, Circuits, Systems, and Signal Processing, 30, 1-16, (2011) · Zbl 1205.93143
[12] Jiang, B.; Staroswiecki, M.; Cocquempot, V., Fault accommodation for nonlinear dynamic systems, IEEE Transactions on Automatic Control, 51, 9, 1578-1583, (2006) · Zbl 1366.93694
[13] Jiang, B.; Zhang, K.; Shi, P., Integrated fault estimation and accommodation design for discrete-time Takagi-sugeno fuzzy systems with actuator faults, IEEE Transactions on Fuzzy Systems, 20, 1, 192-200, (2011)
[14] Karimi, H. R., Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations, International Journal of Control, Automation, and Systems, 9, 4, 671-680, (2011)
[15] Keliris, C.; Polycarpou, M. M.; Parisini, T., A distributed fault detection filtering approach for a class of interconnected continuous-time nonlinear systems, IEEE Transactions on Automatic Control, 58, 8, 2032-2047, (2013)
[16] Kulcsar, B.; Verhaegen, M., Robust inversion based fault estimation for discrete-time LPV systems, IEEE Transactions on Automatic Control, 57, 6, 1581-1586, (2012) · Zbl 1369.93597
[17] Lancaster, P.; Rodman, L., (Algebraic Riccati equations, Series: Oxford science publications, (1995), Oxford University Press)
[18] NaNacara, W.; Yaz, E. E., Recursive estimator for linear and nonlinear systems with uncertain observations, Signal Processing, 62, 2, 215-228, (1997) · Zbl 0908.93061
[19] Shen, B.; Ding, S. X.; Wang, Z., Finite-horizon fault estimation for linear discrete time-varying systems with delayed measurements, Automatica, 49, 1, 293-296, (2013) · Zbl 1257.93093
[20] Shen, B.; Wang, Z.; Shu, H.; Wei, G., \(H_\infty\) filtering for uncertain time-varying systems with multiple randomly occurred nonlinearities and successive packet dropouts, International Journal of Robust and Nonlinear Control, 21, 14, 1693-1709, (2011) · Zbl 1227.93115
[21] Wang, Y.; Ding, S. X.; Ye, H.; Wang, G., A new fault detection scheme for networked control systems subject to uncertain time-varying delay, IEEE Transactions on Signal Processing, 56, 10, 2558-2568, (2008)
[22] Wang, Z.; Dong, H.; Shen, B.; Gao, H., Finite-horizon \(H_\infty\) filtering with missing measurements and quantization effects, IEEE Transactions on Automatic Control, 58, 7, 1707-1718, (2013) · Zbl 1369.93660
[23] Wang, Z.; Shen, B.; Liu, X., \(H_\infty\) filtering with randomly occurring sensor saturations and missing measurements, Automatica, 48, 3, 556-562, (2012) · Zbl 1244.93162
[24] Wu, L.; Yao, X.; Zheng, W. X., Generalized \(H_2\) fault detection for two-dimensional Markovian jump systems, Automatica, 48, 8, 1741-1750, (2013) · Zbl 1268.93096
[25] Yan, X.; Edwards, C., Nonlinear robust fault reconstruction and estimation using a sliding mode observer, Automatica, 43, 9, 1605-1614, (2007) · Zbl 1128.93389
[26] Yao, X.; Guo, L., Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer, Automatica, 49, 8, 2538-2545, (2013) · Zbl 1364.93102
[27] Yaz, Y. I.; Yaz, E. E., On LMI formulations of some problems arising in nonlinear stochastic system analysis, IEEE Transactions on Automatic Control, 44, 4, 813-816, (1999) · Zbl 0957.93088
[28] Xu, D.; Jiang, B.; Shi, P., Nonlinear actuator fault estimation observer: an inverse system approach via a T-S fuzzy model, Applied Mathematics and Computer Science, 22, 1, 183-196, (2012) · Zbl 1273.93105
[29] Zhang, P.; Ding, S. X.; Liu, P., A lifting based approach to observer based fault detection of linear periodic systems, IEEE Transactions on Automatic Control, 57, 2, 457-462, (2012) · Zbl 1369.93145
[30] Zhang, K.; Jiang, B.; Cocquempot, V., Adaptive observer-based fast fault estimation, International Journal of Control, Automation, and Systems, 6, 3, 320-326, (2008)
[31] Zhong, M.; Ding, S. X.; Han, Q.; Ding, Q., Parity space-based fault estimation for linear discrete time-varying systems, IEEE Transactions on Automatic Control, 55, 7, 1726-1731, (2010) · Zbl 1368.93353
[32] Zhong, M.; Zhou, D.; Ding, S. X., On designing \(H_\infty\) fault detection filter for linear discrete time-varying systems, IEEE Transactions on Automatic Control, 55, 7, 1689-1695, (2010) · Zbl 1368.93738
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.