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http://dx.doi.org/10.3795/KSME-A.2004.28.5.503

Design of the Well-Conditioned Observer - A Linear Matrix Inequality Approach -  

Jung, Jong-Chul (한양대학교 대학원 정밀기계공학과)
Huh, Kun-Soo (한양대학교 기계공학부)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.28, no.5, 2004 , pp. 503-510 More about this Journal
Abstract
In this paper, the well-conditioned observer for a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic uncertainties such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic uncertainties such as disturbance and sensor noise. In deterministic perspectives, a small value in the L$_{2}$ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic uncertainties. In stochastic viewpoints, the estimation variance represents the robustness to the stochastic uncertainties and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.
Keywords
Condition Number, Eigenvector Matrix; LMI(Linear Matrix Inequality); Well-Conditioned; Observer;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Luenberger, D. G., 1966, 'Observers for Multivariable Systems,' IEEE Trans. on Automatic Control, Vol. 11, pp. 190-197   DOI
2 Bhattacharyya, S. P., 1976, 'The Structure of Robust Observers,' IEEE Trans. on Automatic Control, Vol. 21, pp. 581-588   DOI
3 Shen, L. C. and Hsu, P. L., 1998, 'Robust Design of Fault Isolation Observers,' Automatica, Vol. 34, No. 11, pp. 1421-1429   DOI   ScienceOn
4 Kim, J.-S. and Oh, J.-H., 1996, 'A Robust Disturbance Observer for Uncertain Linear Systems,' Trans. of the KSME, A, Vol. 20, No. 9, pp. 2731-2743   과학기술학회마을
5 Kalman, R. E. and Bucy, R. S., 1969, 'New Results in Linear Filtering and Prediction Theory,' Trans. of the ASME Series D: J. of Basic Engineering, Vol. 83, No. 3, pp. 95-108
6 Huh, K. and Stein, J. L., 1994, 'A Quantitative Performance Index for Observer-Based Monitoring Systems,' Trans. of the ASME J. of Dynamic Systems, Measurement, and Control, Vol. 116, pp. 487-497   DOI   ScienceOn
7 Patton, R. J. and Chen, J., 1997, 'Observer-Based Fault Detection and Isolation: Robustness and Applications,' Control Engineering Practice, Vol. 5, No. 5, pp. 671-682   DOI   ScienceOn
8 Huh, K. and Stein, J. L., 1995, 'Well-Conditioned Observer Design for Observer-Based Monitoring Systems,' Trans. of the ASME J. of Dynamic Systems, Measurement, and Control, Vol. 117, pp. 592-599   DOI
9 Shafai, B. and Carrol, R. L., 1985, 'Design of Proportional-Integral Observer for Linear Time-Varying Multivariable Systems,' Proc. of the IEEE Conference on Decision and Control, pp. 597-599   DOI
10 Sasa, S., 1998, 'Robustness of a Kalman Filter Against Uncertainties of Noise Covariances,' Proc. of the American Control Conference, pp. 2344-2348   DOI
11 Xia, L. and Soh, Y. C., 1994, 'Robust Kalman filtering for uncertain systems,' Systems and Control Letters, Vol. 22, pp. 123-129   DOI   ScienceOn
12 Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory, SIAM
13 Kwak, B. K. and Huh, K., 1997, 'Discrete-time Robust Observer Design for Two-output Systems,' Trans. of the KSME, A, Vol. 21, No. 4, pp. 625-633
14 Bernstein, D. S. and Haddad, W. M., 1989, 'Steady-state Kalman filtering with an $H_{\infty}$ error bound,' Systems and Control Letters, Vol. 12, pp. 9-16   DOI   ScienceOn
15 Chen, X. and Zhou, K., 2002, '$H_{\infty}$ Gaussian Filter on Infinite Time Horizon,' IEEE Trans. on Circuits and Systems I, Vol. 49, No. 5, pp. 674-679   DOI   ScienceOn
16 Shaked, U., Xie, L. and Soh, Y. C., 2001, 'New Approaches to Robust Minimum Variance Filter Design,' IEEE Trans. on Signal Processing, Vol. 49, No. 11, pp. 2620-2629   DOI   ScienceOn
17 Howell, A. and Hedrick, J. K., 2002, 'Nonlinear Observer Design via Convex Optimization,' Proc. of the American Control Conference, pp. 2088-2093   DOI
18 Slotine, J. J. E. and Li, W., 1991, Applied Nonlinear Control, Prentice Hall, Inc.
19 Golub, G. H. and Van Loan, C. F., 1996, Matrix Computations, 3rd Ed., The Johns Hopkins University Press
20 El Ghaoui, L., Delebeque, F. and Nikoukhah, R., 1999, LMITOOL Ver.2.1, available via anonymous ftp to ftp.ensta.fr,directory pub/elghaoui/lmitool2.1