Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32771
Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems

Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061784

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2550

References:


[1] O. G. Bastin and M. R. Gevers, Stable adaptive observers for nonlinear time-varying systems, IEEE Trans. on Automatic Control, 33 (1988) pp. 650-658.
[2] R. Marino, Adaptive observers for single output nonlinear systems, IEEE Trans. on Automatic Control, 35 (1990) 1054-1058.
[3] R. Marino and P. Tomei, Global adaptive observers for nonlinear systems via filtered transformations, IEEE Trans. on Automatic Control, 37 (1992) 1239-1245.
[4] R. Marino, and P. Tomei, Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems, IEEE Trans. Automatic Control, 40 (1995) 1300-1304.
[5] R. Rajamani and J. K. Hedrick, Adaptive observers for active automotive suspensions: Theory and experiment, IEEE Trans. on Control Systems Technology, 3 (1995) 86-93.
[6] Y. M. Cho, R. Rajamani, A systematic approach to adaptive observer synthesis for nonlinear systems, IEEE Trans. Autom. Control. 42 (1997) 534-537.
[7] R. Marino, G. L. Santosuosso, and P. Tomei, Robust adaptive observers for nonlinear systems with bounded disturbances, IEEE Trans. on Automatic Control, 46 (2001) 967-972.
[8] J. Jung, K. Hul, H.K. Fathy and J.L. Srein, Optimal robust adaptive observer design for a class of nonlinear systems via an H-infinity approach, American Control Conf., 2006, 3637-3642.
[9] M. Hasegawa, Robust adaptive observer design based on ╬│-Positive real problem for sensorless Induction-Motor drives, IEEE Trans. on Industrial Electronics, 53 (2006) 76-85.
[10] A. Zemouche, M. Boutayeb, G. I. Bara, Observers for a class of Lipschitz systems with extension to performance analysis, Systems & Control Letters, 57 (2008) 18-27.
[11] C. S. Jeong, E. E. Yaz, A. Bahakeem, Y. I. Yaz, Resilient design of observers with general criteria using LMIs, Proc. of ACC, 2006, 111- 116.
[12] L.H., Keel, and S.P. Bhattacharyya, Robust, fragile, or optimal?, IEEE - Trans. Autom. Control, 42 (1997) 1098-1105.
[13] P. Dorato., non-fragile contoller design: an overview, Proc. ofACC, 1998, 2829-2831.
[14] D. Famulara, C. T. Abdallah, A. Jadbabaie, P. Domto, and W. H. Haddad, Robust non-fragile LQ controllers: the statis feekback case", Proc. of ACC, 1998, 1109-1113.
[15] G.H. yang, J.L. Wang, Robust nonfragile Kalman filtering for uncertain linear systems, IEEE Trans. on Automatic Control, 46 (2001) 343-348.
[16] C. S. Jeong, E. E. Yaz, and Y. I. Yaz, Lyapunov-Based design of resilient observers for a class of nonlinear systems and general performance criteria, IEEE Multi-conference on Systems and Control, 2008, 942-947.
[17] C. S. Jeong, E. E. Yaz, and Y. I. Yaz , Stochastically resilient design of H∞ observers for discrete-time nonlinear systems, IEEE Conf. CDC, 2007, 1227- 1232.
[18] F. Chen and W. Zhang, LMI criteria for robust chaos synchronization of a class of chaotic systems, Nonlinear Analysis, 67 (2007) 3384-3393.
[19] M. Krstic, I. Kanellakopoulos, P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley and Sons, 1995.
[20] J. Lofberg, YALMIP: A toolbox for modeling and optimization in MATLAB, IEEE Int. Symp. Computer Aided Contol Syst. Design Conf., 2004, 284-289.
[21] P. Gahinet, A. Nemirovski, A. Laub, M. Chilai, LMI control toolbox user-s guide, Massachusetts: The Mathworks, 1995.