We study the problem of identification of an input to a linear finite-dimensional system. We assume that the input has a feedback form, which is related to a problem often encountered in fault detection. The method we use is to embed the identification problem in a class of inverse problems of dynamics for controlled systems. Two algorithms for identification of a feedback matrix based on the method of feedback control with a model are constructed. These algorithms are stable with respect to noise-corrupted observations and computational errors.
@article{bwmeta1.element.bwnjournal-article-amcv11i4p835bwm, author = {Maksimov, Vyacheslav and Pandolfi, Luciano}, title = {Robust identification of parasitic feedback disturbances for linear lumped parameter systems}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {11}, year = {2001}, pages = {835-858}, zbl = {1058.93021}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p835bwm} }
Maksimov, Vyacheslav; Pandolfi, Luciano. Robust identification of parasitic feedback disturbances for linear lumped parameter systems. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 835-858. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p835bwm/
[000] Blizorukova M.S. and Maksimov V.I. (1997): On the reconstruction of an extremal input in a system with hereditary. - Vestnik PGTU. Funct. Diff. Eqns., Vol.4, No.4, pp.51-61 (in Russian).
[001] Fagnani F. and Pandolfi L. (2000): A singular perturbation approach to an input identification problem. - Rapp. Interno n. 4, Dipartimento di Matematica, Politecnico di Torino. | Zbl 1018.93016
[002] Kryazhimskii A.V. (1999): Convex optimization via feedbacks. - SIAM J. Contr. Optim., Vol.37, No.1, pp.278-302. | Zbl 0917.90256
[003] Kryazhimskii A.V. and Osipov Yu.S. (1987): To a regularization of a convex extremal problem within accurately given constraints. An application to an optimal control problem with state constraints. In: Some Methods of Positional and Program Control (A.I. Korotkii and V.I. Maksimiv, Eds.). - Academic Press, Sverdlovsk, pp.34-54 (in Russian).
[004] Kryazhimskii A.V., Maksimov V.I. and Osipov Yu.S. (1997): Reconstruction of extremal perturbations in parabolic equations. - Comp. Math. Math. Phys., Vol.37, No.3, pp.288-298.
[005] Maksimov V.I. (1994): Control reconstruction for nonlinear parabolic equations. - IIASA Working Paper WP-94-04, IIASA, Laxenburg, Austria.
[006] Maksimov V. and Pandolfi L. (1999): Dynamical reconstruction of inputs for contraction semigroup systems: the boundary inputcase. - J. Optim. Theory Applic., Vol.103, No.2, pp.401-420. | Zbl 0956.49020
[007] Osipov Yu.S. and Kryazhimskii A.V. (1995): Inverse Problems for Ordinary Differential Equations: Dynamical Solutions. - London: Gordon and Breach. | Zbl 0884.34015
[008] Unbehauen H. (1990): Continuous time approaches to system identification. - Automatica, Vol.26, No.6, pp.23-35. | Zbl 0714.93007