Abstract:
This paper proposes a new variable gain robust state observer for a class of uncertain nonlinear systems. The variable gain robust state observer proposed in this paper consists of fixed observer gain matrices and nonlinear modification functions which are determined by appropriate updating rules. It is shown that sufficient conditions for the existence of the proposed variable gain robust state observer can be reduced to solvability of Linear Matrix Inequalities (LMIs). Finally, we give a simple numerical example.
Authors:
1. Kazuhiro Hirasawa (Tokyo City University, Japan)
2. Daiki Asada (Tokyo City University, Japan)
3. Shunya Nagai (National Institute of Technology (KOSEN), Niihama College, Japan)
4. Hidetoshi Oya (Tokyo City University, Japan)
References:
1. M. Norton, “Modern Control Engineering,” Pergamon Press, 1972
2. B. D. O. Anderson and J. B. Moore, “Optimal Control : Linear Quadratic
Methods,” Prentice Hall, Englewood Cliffs, NJ, 1990.
3. D. G. Luenberger, “Observing the State of a Linear System,” IEEE
Transactions on Military Electronics, vol. 8, no. 2, pp. 74-80, 1964.
4. D. G. Luenberger, “Observer for Multivariable Systems,” IEEE Transactions on Automatic Control, vol. 11, no. 2, pp. 190-197, 1966.
5. B. Gopinath, “On the Control of Linear Multiple Input-Output Systems,”
The Bell System Technical Journal, vol. 50, no. 3, pp. 1063-1081, 1971.
6. J. O
Reilly, “Observers for Linear Systems,” Academic Press, Newyork,
USA, 1983.
7. M. M. Monahemi, J. B. Barlow and D. P. O'
Leary, “Design of ReducedOrder Observers with Precise Loop Transfer Recovery,” Journal of
Guidance, Control and Dynamics, Vol. 15, No. 6, pp. 1320-1326, 1992.
8. J. C. Doyle and G. Stein, “Robustness with Observers,” IEEE Transactions on Automatic Control, vol. 24, no. 4, pp. 607-611, 1979.
9. A. Fattouh, O. Sename, J.-M. Dion, “Robust observer design for timedelay systems: A Riccati equation approach,” Kybernetika vol. 35, no.
6, pp.753-64, 1999.
10. D. W. Gu and F. W. Poon, “A Robust State Observer Scheme,” IEEE
Transactions on Automatic Control, vol. 46, no. 12, pp. 1958-1963,
December 2001.
11. B. L. Walcott and S. H. Zak, “Observation of Dynamical Systems in
the Presence of Bounded Nonlinearities/Uncertainties,” Proceedings of
the 25th IEEE Conference on Decision and Control, IEEE Press, April
2007.
12. S. D. Wang, T. S. Kuo, and C. F. Hsu, “Optimal-Observer Design for
Linear Dynamical Systems with Uncertain Parameters,” International
Journal of Control, vol. 45, no. 2, pp. 701-711, March 2007.
13. M. Boutayab and M. Darouach, “Comments of “A Robust State Observer
Scheme”,” IEEE Transactions on Automatic Control, vol. 48, no. 7, pp.
1292-1293, 2003.
14. D. W. Gu and F. W. Poon, “Author’s Reply,” IEEE Transactions on
Automatic Control, vol. 48, no. 7, pp. 1293, 2003.
15. Y. H. Chen, “Adaptive Robust Observers for Non-linear Uncertain
Systems,” International Journal of System Sciences, Vol. 21, pp. 803-
814, 1990.
16. H. Wu and T. Tanaka, “Adaptive Robust Asymptotic State Observers for
Uncertain Nonlinear Dynamical Systems,” IEEJ Transactions EIS, vol.
127, no.1, pp. 726-732, 2007.
17. S. Nagai, H. Oya and T. Matsuki, “A Point Memory State Observer with
Adjustable Parameters for a Class of Uncertain Linear Systems with
State Delays,” Proceedings of Engineering and Technology Innovation,
vol. 11, pp. 38-45, 2019.
18. H. Oya and K. Hagino, “Robust Control with Adaptive Compensation
Input for Linear Uncertain Systems,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.
E86-A, no. 6, pp. 1517-1524, 2003.
19. F. R. Gantmacher, “The Theory of Matrices,” vol. 1, Chelsea Publishing
Company, New York, 1960.
20. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix
Inequalities in System and Control Theory,” SIAM, 1994.
21. H. K. Khalil, “Nonlinear Systems, Third Edition”, Prentice Hall, 2002
Page(s): 18-23
Date of Publication: 19 September 2024