Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances

Khémiri, Karim; Hmida, Fayçal; Ragot, José; Gossa, Moncef

doi:10.2478/v10006-011-0049-3

Abstract

This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.

References

Ben Hmida, F., Khémiri, K., Ragot, J. and Gossa, M. (2010). Unbiased minimum-variance filter for state and fault estimation of linear time-varying systems with unknown disturbances, Mathematical Problems in Engineering, Vol. 2010, Article ID 343586, 17 pages.
Search in Google Scholar
Blanke, M., Kinnaert, M., Lunze, J. and Staroswiecki, M. (2006). Diagnosis and Fault-Tolerant Control, Springer-Verlag, Berlin/Heidelberg.
Search in Google Scholar
Chen, J. and Patton, R. (1996). Optimal filtering and robust fault diagnosis of stochastic system with unknown disturbances, IEE Proceedings: Control Theory Application 143(1): 31-36.10.1049/ip-cta:19960059
Search in Google Scholar
Chen, J. and Patton, R. (1999). Robust Model-based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Norwell, MA.10.1007/978-1-4615-5149-2
Search in Google Scholar
Cheng, Y., Ye, H., Wang, Y. and Zhou, D. (2009). Unbiased minimum-variance state estimation for linear systems with unknown input, Automatica 45(2): 485-491.10.1016/j.automatica.2008.08.009
Search in Google Scholar
Darouach, M. and Zasadzinski, M. (1997). Unbiased minimum variance estimation for system with unknown exogenous inputs, Automatica 33(4): 717-719.10.1016/S0005-1098(96)00217-8
Search in Google Scholar
Darouach, M., Zasadzinski, M. and Boutayeb, M. (2003). Extension of minimum variance estimation for systems with unknown inputs, Automatica 39(5): 867-876.10.1016/S0005-1098(03)00006-2
Search in Google Scholar
Gillijns, S. and Moor, B. (2007a). Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough, Automatica 43(5): 934-937.10.1016/j.automatica.2006.11.016
Search in Google Scholar
Gillijns, S. and Moor, B. (2007b). Unbiased minimum-variance input and state estimation for linear discrete-time systems, Automatica 43(1): 111-116.10.1016/j.automatica.2006.08.002
Search in Google Scholar
Hou, M. and Patton, R. J. (1998). Optimal filtering for system with unknown inputs, IEEE Transactions on Automatic Control 43(3): 445-449.10.1109/9.661621
Search in Google Scholar
Hsieh, C. (2009). Extension of unbiased minimum-variance input and state estimation for systems with unknown inputs, Automatica 45(9): 2149-2153.10.1016/j.automatica.2009.05.004
Search in Google Scholar
Hsieh, C. S. (2000). Robust two-stage Kalman filters for systems with unknown inputs, IEEE Transactions on Automatic Control 45(12): 2374-2378.10.1109/9.895577
Search in Google Scholar
Jamouli, H., Keller, J. and Sauter, D. (2003). Fault isolation filter with unknown inputs in stochastic systems, Proceedings of Safeprocess, Washington, DC, USA, pp. 531-536.
Search in Google Scholar
Kailath, T., Sayed, A. and Hassibi, B. (2000). Linear Estimation, Prentice Hall, Englewood Cliffs, NJ.
Search in Google Scholar
Keller, J. (1998). Fault isolation filter design for linear stochastic systems with unknown inputs, 37th IEEE Conference on Decision and Control, Tampa, FL, USA, pp. 598-603.
Search in Google Scholar
Keller, J. (1999). Fault isolation filter design for linear stochastic systems, Automatica 35(10): 1701-1706.10.1016/S0005-1098(99)00079-5
Search in Google Scholar
Keller, J. and Sauter, D. (2011). Restricted diagonal detection filter and updating strategy for multiple fault detection and isolation, International Journal of Adaptive Control and Signal Processing 25(1): 68-87.10.1002/acs.1210
Search in Google Scholar
Kitanidis, P. (1987). Unbiased minimum-variance linear state estimation, Automatica 23(6): 775-778.10.1016/0005-1098(87)90037-9
Search in Google Scholar
Nikoukhah, R. (1994). Innovation generation in the presence of unknown inputs: Application to robust failure detection, Automatica 30(12): 1851-1867.10.1016/0005-1098(94)90047-7
Search in Google Scholar

Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances

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