This paper focuses on the problem of fault estimation for a class of interconnected nonlinear systems with time varying delays. In contrast to the common assumption imposed on the problem in most literature, here, there is no need for the delay rate to be less than one. Both actuator and component faults are considered within the general fault model invoked as multiplicative faults in this study. Robust adaptive observers are used to detect and estimate simultaneously the states and the parameter faults in each subsystem. The designed observers ensure a prescribed H ∞ performance level for the fault estimation error, irrespective of the uncertainties which are assumed here to be the unknown interconnections between the subsystems. With the aid of H ∞ performance index, the common assumption regarding the observer matching condition is no longer required. Sufficient conditions for asymptotic stability of the observers are derived via a matrix inequality approach with the aid of LyapunovKrasovskii function. Finally, a simulation example is presented to show the validity and feasibility of the proposed method.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
R. Isermann, Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer, 2006. [click]
L. H. Chiang, E. L. Russell, and R. D. Braatz, Fault Detection and Diagnosis in Industrial Systems, Springer, 2001. [click]
V. Venkatasubramanian, R. Rengaswamy, K. Yin, and S. N. Kavuri, “A review of process fault detection and diagnosis part i: quantitative model-based methods,” Computers and Chemical Engineering, vol. 27, no. 3, pp. 293–311, 2003. [click]
R. Isermann, “Model-based fault-detection and diagnosis-status and applications,” Annual Reviews in Control, vol. 29, no. 1, pp. 71–85, 2005. [click]
X. G. Yan and C. Edwards, “Nonlinear robust fault reconstruction and estimation using a sliding mode observer,” Automatica, vol. 43, no. 9, pp. 1605–1614, 2007. [click]
X. Zhang, M. M. Polycarpou, and T. Parisini, “Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation,” Automatica, vol. 46, no. 2, pp. 290–299, 2010. [click]
H. J. Ma, G. H. Yang, and W. Lin, “Adaptive observerbased fault diagnosis for a class of MIMO nonlinear uncertain systems,” Proc. of 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pp. 1044–1049, 2009. [click]
M. Van, H. J. Kang, Y. S. Suh, and K. S. Shin, “A robust fault diagnosis and accommodation scheme for robot manipulators,” International Journal of Control, Automation, and Systems, vol. 11, no. 2, pp. 377–388, 2013. [click]
R. Sakthivel, S. Selvi, and K. Mathiyalagan, “Fault-tolerant sampled-data control of flexible spacecraft with probabilistic time delays,” Nonlinear Dynamics, vol. 79, no. 3, pp. 1835–1846, 2015. [click]
C. Gao and G. Duan, “Robust adaptive fault estimation for a class of nonlinear systems subject to multiplicative faults,” Circuits, Systems, and Signal Processing, vol. 31, no. 6, pp. 2035–2046, 2012. [click]
C. P. Tan and C. Edwards, “Multiplicative fault reconstruction using sliding mode observers,” Proc. of 5th Asian Control Conference, pp. 957–96, 2004. [click]
M. Hou and P. C. Muller, “Design of observers for linear systems with unknown inputs,” IEEE Transaction on Automatic Control, vol.37, pp.871–875, 1992. [click]
P. T. Nam, P. N. Pathirana, and H. Trinh, “e -bounded state estimation for time-delay systems with bounded disturbances,” International Journal of Control, vol. 87, no. 9, pp. 1747–1756, 2014.
W. Chen and M. Saif, “An iterative learning observer for fault detection and accommodation in nonlinear time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 16, no.1, pp.1–19, 2006. [click]
R. Sakthivel, P. Vadivel, K. Mathiyalagan, and A. Arunkumar, “Fault-distribution dependent reliable H ∞ control for takagi-sugeno fuzzy systems,” Journal of Dynamic Systems, Measurement, and Control, vol.136, no.2, 2014. [click]
Z. Gao and B. Jiang, “Delay-dependent robust fault detection for a class of nonlinear time-delay systems,” Int. Conference on Systems and Control in Aerospace and Astronautics, pp. 1–6, 2008. [click]
L. Bai, Z. Tian, and S. Shi, “Robust fault detection for a class of nonlinear time-delay systems,” Journal of The Franklin Institute, vol. 344, no. 6, pp. 873–888, 2007. [click]
L. Chen, M. Y. Zhong, and M. Y. Zhang, “H ∞ fault detection for linear singular systems with time-varying delay,” International Journal of Control, Automation and Systems, vol. 9, no.1, pp. 9–14, 2011. [click]
X. Zhang, “Decentralized fault detection for a class of large-scale nonlinear uncertain systems,” Proc. of American Control Conference, pp. 5650–5655, 2010. [click]
K. Zhang, B. Jiang and V. Cocquempot, “Fast adaptive fault estimation and accommodation for nonlinear timevarying delay systems,” Asian Journal of Control, vol.11, no. 6, pp. 643–652, 2009. [click]
W. Chen, A. Chen, Q. M. Abid, and S. X. Ding, “Integrated design of observer based fault detection for a class of uncertain nonlinear systems,” International Journal of Applied Mathematics and Computer Science, vol. 21, no. 3, pp. 423–430, 2011. [click]
K. Gu, “An integral inequality in the stability problem of time-delay systems,” Proc. IEEE Conf. Decision Control, Sydney, Australia, pp. 2805–2810, 2000. [click]
M. Grant and S. Boyd, CVX: Matlab Software for Disciplined Convex Programming, version 2.0 beta, http://cvxr.com/cvx, 2013.
M. Ghanes, J. De Leon, and J. P. Barbot, “Observer design for nonlinear systems under unknown time-varying delays,” IEEE Transactions on Automatic Control, vol. 58, no. 6, pp. 1529–1534, 2013. [click]
S. S. Delshad and T. Gustafsson, “Nonlinear observer design for a class of Lipschitz time-delay systems with unknown inputs: LMI approach,” Proceedings of the XXIII International Symposium on Information, Communication and Automation Technologies, Sarajevo, Bosnia and Herzegovina, pp. 1–5, 2011. [click]
J. T. Spooner and K. M. Passino, “Decentralized adaptive control of nonlinear systems using radial basis neural networks,” IEEE Transactions on Automatic Control, vol. 44, no. 11, pp. 2050–2057, 1999. [click]
M. Dehghani and S. K. Y. Nikravesh, “Robust tuning of pss parameters using the linear matrix inequalities approach,” Power Tech, 2007 IEEE Lausanne, pp. 322–326, 2007. [click]
S. Mondal and W. K. Chung, “Adaptive observer for a class of nonlinear systems with time-varying delays,” International Journal of Adaptive Control and Signal Processing, vol. 27, no. 7, pp. 610–619, 2013. [click]
Recommended by Associate Editor Nam H. Jo under the direction of Editor Duk-Sun Shim.
Maryam Kazerooni received the M.Sc. degree from Shiraz University, Iran, in 2010. Since 2010, she is a Ph.D. candidate in Shiraz University of Iran. Her research interests include fault diagnosis and fault tolerant control for linear and nonlinear systems.
Alireza Khayatian received his Ph.D. degree in the Control Engineering from Georgia Institute of Technology 1993. He has been a faculty member with department of electrical engineering, since 1993. His research interests include Nonlinear Control, Estimation and Navigation.
Ali Akbar Safavi received his Ph.D. in Process Systems Engineering from Sydney University in 1995. His research interests are model predictive control, wavelets, neural networks, system identification, networked based Control, and information technology.
About this article
Cite this article
Kazerooni, M., Khayatian, A. & Safavi, A.A. Robust delay dependent fault estimation for a class of interconnected nonlinear time delay systems. Int. J. Control Autom. Syst. 14, 569–578 (2016). https://doi.org/10.1007/s12555-014-0455-z
- Fault estimation
- interconnected nonlinear systems
- Lyapunov-Krasovskii approach
- time delay