Abstract
A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization. The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.
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References
C. E. de Souza, L. Xie, Y. Wang. H∞ filtering for a class of uncertain nonlinear systems. Systems & Control Letters, 1993, 20(6): 419–426.
Y. Wang, L. Xie, C. E. de Souza. Robust control of a class of uncertain nonlinear systems. Systems & Control Letters, 1992, 19(2): 139–149.
S. K. Nguang, M. Fu. Robust nonlinear H∞ filtering. Automatica, 1996, 32(8): 1195–1199.
W. M. McEneaney. Robust H∞ filtering for nonlinear systems. Systems & Control Letters, 1998, 33(5): 315–325.
X. Chen, T. Fukuda, K. D. Young. A new nonlinear robust disturbance observer. Systems & Control Letters, 2000, 41(3): 189–199.
C. Yung, Y. Li, H. Sheu. H∞ filtering and solution bound for nonlinear systems. International Journal of Control, 2001, 74(6): 565–570.
M. Abbaszadeh, H. J. Marquez. A robust H∞ observer design method for continuous-time Lipschitz nonlinear systems. Proceedings of the 45th IEEE Conference on Decision and Control. Piscataway: IEEE, 2006: 3895–3900.
M. Abbaszadeh, H. J. Marquez. Robust H∞ observer design for sampled-data Lipschitz nonlinear systems with exact and Euler approximate models. Automatica, 2008, 44(3): 799–806.
A. M. Pertew, H. J. Marquez, Q. Zhao. H∞ observer design for Lipschitz nonlinear systems. IEEE Transactions on Automatic Control, 2006, 51(7): 1211–1216.
M. Abbaszadeh, H. J. Marquez. LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete-time nonlinear uncertain systems. International Journal of Robust and Nonlinear Control, 2009, 19(3): 313–340.
S. Xu, P. V. Dooren. Robust H∞ filtering for a class of non-linear systems with state delay and parameter uncertainty. International Journal of Control, 2002, 75(10): 766–774.
G. Lu, D. W. C. Ho. Robust H∞ observer for nonlinear discrete systems with time delay and parameter uncertainties. IET Control Theory and Applications, 2004, 151(4): 439–444.
P. P. Khargonekar, I. R. Petersen, K. Zhou. Robust stabilization of uncertain linear systems: quadratic stabilizability and H∞ control theory. IEEE Transactions on Automatic Control, 1990, 35(3): 356–361.
S. Xu. Robust H∞ filtering for a class of discrete-time uncertain nonlinear systems with state delay. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2002, 49(12): 1853–1859.
S. Boyd, L. El Ghaoui, E. Feron, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
H. J. Marquez. Nonlinear Control Systems: Analysis and Design. New York: Wiley, 2003.
R. A. Horn, C. R. Johnson. Matrix Analysis. Cambrige: Cambrige University Press, 1985.
R. A. Horn, C. R. Johnson. Topics in Matrix Analysis. Cambrige: Cambrige University Press, 1991.
S. Boyd, L. Vandenberghe. Convex Optimization. Cambrige: Cambrige University Press, 2004.
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This work was partly supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.
Masoud ABBASZADEH reveived his B.S., M.S. and Ph.D. degrees in Electrical Engineering from Amirkabir University of Technology, Tehran, Iran, Sharif University of Technology, Tehran, Iran, and University of Alberta, Edmonton, AB, Canada, in 2000, 2002 and 2008, respectively. From 2001 to 2004, he was working as a control and automation engineer in automotive manufacturing and oil industries. From 2008 to 2011, he was with the Department of Research and Development, Maplesoft, Waterloo, ON, Canada. He was the developer of MapleSim Control Design Toolbox and was a member of a research team working on the Maplesoft-Toyota Joint Model Simplification Project, performing research on modeling, simplification and simulation of complex dynamical systems for powertrain control applications. Since 2011, he has been with the United Technologies Research Center (UTRC), East Hartford, CT, U.S.A., as a senior research engineer.
His current research interests include nonlinear control and observer design, robust and optimal filtering, estimation theory, convex optimization, model simplification, and symbolic-numeric computations for control analysis and design.
Horacio J. MARQUEZ reveived his B.S. degree from the Instituto Tecnologico de Buenos Aires (Argentina), and M.S.E and Ph.D. degrees in Electrical Engineering from the University of New Brunswick, Fredericton, Canada, in 1987, 1990 and 1993, respectively. From 1993 to 1996, he held visiting appointments at the Royal Roads Military College, and the University of Victoria, Victoria, British Columbia. Since 1996 he has been with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada, where he is currently Professor and Department Chair. In 2008, he was a guest research professor at Nancy University — University Henri Poincare, France.
Dr. Marquez is a fellow of IET and is currently an area editor for the International Journal of Robust and Nonlinear Control. He is the author of ‘Nonlinear Control Systems: Analysis and Design’ (Wiley, 2003). He was the recipient of the 2003–2004 McCalla Research Professorship awarded by the University of Alberta. His current research interests include nonlinear dynamical systems and control, nonlinear observer design, robust control, and applications.
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Abbaszadeh, M., Marquez, H.J. Nonlinear robust H-infinity filtering for a class of uncertain systems via convex optimization. J. Control Theory Appl. 10, 152–158 (2012). https://doi.org/10.1007/s11768-012-0290-9
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DOI: https://doi.org/10.1007/s11768-012-0290-9