Robust receding-horizon state estimation for uncertain discrete-time linear systems. (English) Zbl 1129.93528

Summary: An approach to robust receding-horizon state estimation for discrete-time linear systems is presented. Estimates of the state variables can be obtained by minimizing a worst-case quadratic cost function according to a sliding-window strategy. This leads to state the estimation problem in the form of a regularized least-squares one with uncertain data. The optimal solution (involving on-line scalar minimization) together with a suitable closed-form approximation are given. The stability properties of the estimation error for both the optimal filter and the approximate one have been studied and conditions to select the design parameters are proposed. Simulation results are reported to show the effectiveness of the proposed approach.


93E10 Estimation and detection in stochastic control theory
93C55 Discrete-time control/observation systems
Full Text: DOI


[1] Alessandri, A.; Baglietto, M.; Battistelli, G., Receding-horizon estimation for discrete-time linear systems, IEEE Trans. on Automatic Control, 48, 3, 473-478 (2003) · Zbl 1364.93758
[2] Alessandri, A.; Baglietto, M.; Parisini, T.; Zoppoli, R., A neural state estimator with bounded errors for nonlinear systems, IEEE Trans. on Automatic Control, 44, 11, 2028-2042 (1999) · Zbl 0955.93050
[3] Bierman, G. J., Fixed-memory least squares filtering, IEEE Trans. on Inf. Theory, 21, 6, 690-692 (1975) · Zbl 0319.93056
[5] Dussy, S.; El Ghaoui, L., Measurement-scheduled control for the RTAC probleman LMI approach, Internat. J. Robust and Nonlinear Control, 8, 377-400 (1998) · Zbl 0925.93854
[6] El Ghaoui, L.; Lebret, H., Robust solutions to least-squares problems with uncertain data, SIAM J. Matrix Anal. Appl., 18, 4, 1035-1064 (1997) · Zbl 0891.65039
[7] Ferrari-Trecate, G.; Mignani, D.; Morari, M., Moving horizon estimation for hybrid systems, IEEE Trans. on Automatic Control, 47, 10, 1663-1676 (2002) · Zbl 1364.93768
[8] Jazwinski, A. H., Limited memory optimal filtering, IEEE Trans. on Automatic Control, 13, 5, 558-563 (1968) · Zbl 0186.23501
[9] Jazwinski, A. H., Stochastic Processes and Filtering Theory (1970), Academic Press: Academic Press New York · Zbl 0203.50101
[10] Li, H.; Fu, M., A linear matrix inequality approach to \(H_\infty\) filtering, IEEE Trans. on Signal Processing, 45, 9, 2338-2350 (1997)
[11] Ling, K. V.; Lim, K. W., Receding horizon recursive state estimation, IEEE Trans. on Automatic Control, 44, 9, 1750-1753 (1999) · Zbl 0958.93014
[12] Mareels, I. M.Y., Recovering state trajectories from output measurements and dynamic modelsa computational complexity point of view, Internat. J. Bifurcation and Chaos, 12, 5, 1079-1095 (2002) · Zbl 1051.93503
[13] Medvedev, A., Continuous least-squares observers with applications, IEEE Trans. on Automatic Control, 41, 10, 1530-1537 (1996) · Zbl 0858.93016
[14] Moraal, P. E.; Grizzle, J. W., Observer design for nonlinear systems with discrete-time measurements, IEEE Trans. on Automatic Control, 40, 3, 395-404 (1995) · Zbl 0821.93014
[15] Primbs, J. A.; Nevistic, V., A framework for robustness analysis of constrained finite receding horizon control, IEEE Trans. on Automatic Control, 45, 10, 1828-1838 (2000) · Zbl 0990.93024
[16] Rao, C. V.; Rawlings, J. B.; Lee, J. H., Constrained linear estimation—a moving horizon approach, Automatica, 37, 10, 1619-1628 (2001) · Zbl 0998.93039
[17] Rauch, H. E.; Tung, F.; Striebel, C. T., Maximum likelihood estimates of linear dynamic systems, AIAA J., 3, 1445-1450 (1965)
[18] Sayed, A. H., A framework for state-space estimation with uncertain models, IEEE Trans. on Automatic Control, 46, 7, 998-1013 (2001) · Zbl 1009.93075
[19] Sayed, A. H.; Nascimento, V. H.; Cipparrone, F. A.M., A regularized robust design criterion for uncertain data, SIAM J. Matrix Anal. and Appl., 23, 4, 1120-1142 (2002) · Zbl 1058.15002
[20] Schweppe, F. C., Uncertain Dynamic Systems (1973), Prentice-Hall: Prentice-Hall Englewood Cliffs, New Jersey
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