Artículos de revistas
H2 Robust Filter Design With Performance Certificate Via Convex Programming
Registro en:
Automatica. , v. 44, n. 4, p. 937 - 948, 2008.
51098
10.1016/j.automatica.2007.08.010
2-s2.0-41049086517
Autor
Geromel J.C.
Korogui R.H.
Institución
Resumen
In this paper a new approach to H2 robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of the most expressive methods available for H2 robust filter design, a new one based on a performance certificate calculation is presented. The performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the H2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear, rational and causal filters. The calculations are performed through convex programming methods developed to deal with linear matrix inequality (LMI). Many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs. © 2007 Elsevier Ltd. All rights reserved. 44 4 937 948 Anderson, B.D.O., Moore, J.B., (1979) Optimal filtering, , Prentice Hall, Englewood Cliffs, NJ Barbosa, K.A., de Souza, C.E., Trofino, A., Robust H2 filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions (2005) Systems & Control Letters, 54 (3), pp. 251-262 Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear matrix inequalities in system and control theory, , SIAM, Philadelphia Colaneri, J., Geromel, C., Locatelli, A., (1997) Control theory and design-An RH2 and RH∞ viewpoint, , Academic Press, New York Geromel, J.C., Convex analysis and global optimization of joint actuator location and control problems (1989) IEEE Transactions on Automatic Control, 34 (7), pp. 711-720 Geromel, J.C., Optimal linear filtering under parameter uncertainty (1999) IEEE Transactions on Signal Processing, 47 (1), pp. 168-175 Geromel, J.C., de Oliveira, M.C., Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions (2002) SIAM Journal on Control Optimization, 41 (3), pp. 700-711 Geromel, J.C., de Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Linear Algebra and Its Applications, 285, pp. 69-80 Geromel, J.C., Regis, L.A.V., H2 Optimal robust filtering (2006) European Journal of Control, 12 (1), pp. 30-39 Hoang, N.T., Tuan, H.D., Apkarian, P., Hosoe, S., Robust filtering for discrete nonlinear fractional transformation systems (2004) IEEE Transactions Circuit and Systems II-Express Briefs, 51, pp. 587-592 Jain, B.N., Guaranteed error estimation in uncertain systems (1975) IEEE Transactions on Automatic Control, 20, pp. 230-232 Li, L., Luo, Z.Q., Davidson, T.N., Wong, K.M., Bossé, E., Robust filtering via semidefinite programming with applications to target tracking (2002) SIAM Journal on Optimization, 12 (3), pp. 740-755 Martin, C.J., Mintz, M., Robust filtering and prediction for linear systems with uncertain dynamics: A game-theoretic approach (1983) IEEE Transactions on Automatic Control, 28 (9), pp. 888-896 Meirovitch, L., Baruh, H., Oz, H., A comparison of control techniques for large flexible systems (1983) J. Guidance, 6 (4), pp. 302-310 de Oliveira, M.C., Geromel, J.C., Hsu, L., LMI characterization of structural and robust stability: The discrete-time case (1999) Linear Algebra and Its Applications, 296, pp. 27-38 Poor, H.V., On robust wiener filtering (1980) IEEE Transactions on Automatic Control, 25 (3), pp. 531-536 Rockafellar, R., (1970) Convex analysis, , Princeton Press Scherer, C. W., Köse, I. E. (2006). Robust H2 estimation with dynamic IQCs: A convex solution. In IEEE Conference on Decision and Control, USAShaked, U., Xie, L., Soh, Y.C., New approaches to robust minimum variance filter design (2001) IEEE Transactions on Signal Processing, 49 (11), pp. 2620-2629 de Souza, C.E., Trofino, A., An LMI approach to the design of robust H2 filters (1999) Recent Advances on linear matrix inequalities methods in control, , El Ghaoui L., and Niculescu S.-I. (Eds), SIAM, Englewood Cliffs, NJ Theodor, Y., Shaked, U., Robust discrete-time minimum variance filtering (1996) IEEE Transactions on Signal Processing, 44, pp. 181-189 Tuan, H.D., Apkarian, P., Nguyen, T.Q., Robust and reduce-order filtering : New LMI-based characterizations and methods (2001) IEEE Transactions on Signal Processing, 49 (12), pp. 2975-2984 Xie, L.H., Soh, Y.C., Robust Kalman filtering for uncertain systems (1994) Systems Control Letters, 22, pp. 123-129 Xie, L.H., Soh, Y.C., de Souza, C.E., Robust Kalman filtering for uncertain discrete-time systems (1994) IEEE Transactions on Automatic Control, 39, pp. 1310-1314 Xie, L. H., Soh, Y. C., Du, C. (1999). RobustH2 estimation and control. School of Electrical and Electronic Engineering Nanyang Technological University, Singapore, Technical Report