On the operator formalization of the separation property in ensured control problems / Kruglikov S.V. // ECC 1997 - European Control Conference. - 1997. - V. , l. . - P. 3222-3227.

ISSN:
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Type:
Conference Paper
Abstract:
The separation principle and the certainty equivalence property in ensured problems of control/estimation optimal are considered. Problems under discussion are stated for linear uncertain systems with unknown in advance parameters. Indeces of performance are given by extremal values of a convex functional. A priori procedures of control and estimation are supposed to be determined by the choice of causal (nonanticipative) operators. Investigation is based on a symmetrical representation of extremal problems in Hilbert spaces. Formalized definitions of the separation and certainty equivalence properties are given. Conditions on elements of a problem structure sufficient for the properties to hold are presented.
Author keywords:
Estimation; Linear uncertain systems; Nonanticipative control
Index keywords:
Estimation; Uncertain systems; Uncertainty analysis; Certainty equivalence; Control problems; Extremal; Extremal problems; Linear uncertain systems; Problem structure; Separation principle; Separation
DOI:
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84949093883&partnerID=40&md5=e83116416c1cb2942ee399745f7e2e04
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Art. No. 7082607
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84949093883&partnerID=40&md5=e83116416c1cb2942ee399745f7e2e04
Affiliations Institute for Mathematics and Mechanics, Urals Branch, Russian Academy of Sciences, S. Kovalevskoi 16, Ekaterinburg, Russian Federation
Author Keywords Estimation; Linear uncertain systems; Nonanticipative control
References Gusev, M.L., On the stability of solutions of the inverse problems in control system dynamics (1988) Problems of Control & Inform. Theory, 17, pp. 297-310; Kruglikov, S.V., On the duality principle in a priory problems of ensured control and estimation (1994) Doklady Akademii Nauk, 335, pp. 570-572. , in Russian; Kurzanskii, A.B., (1977) Control and Observation Under Conditions of Uncertainty, p. 365c. , Moskow: Nauka, in Russian; Fliriart-Urruty, J.-B., Lemarecal, C., (1993) Convex Analysis and Minimization Algoritms, , Springer-Verlag; Başar, T., Bernhard, P., (1991) H∞ Optimal Control and Related Minmax Design Problems. A Dynamic Game Approach, , Boston etc.: Birkhauser; Kruglikov, S.V., On the separation principle in guaranteed control (1991) Modeling, Estimation and Control of Systems with Uncertainty., 335, pp. 570-572. , Boston etc.: Birkhauser; Rishel, R., A strong separation principle for stochastic control systems driven by a hidden Markov model (1994) SIAM J. Control and Optimiz., 32, pp. 1008-1020; Rockafeilar, R.T., Linear-quadratic programming and optimal control (1987) SIAM J. Control and Optimiz., 25, pp. 781-814; Saeks, R., Causality in Ftilbert space (1970) SIAM Review, 12, pp. 357-383; Wonham, W.M., On the separation theorem of stochastic control (1968) SIAM J. Control, 8, pp. 312-326
Correspondence Address Kruglikov, S.V.; Institute for Mathematics and Mechanics, Urals Branch, Russian Academy of Sciences, S. Kovalevskoi 16, Russian Federation
Sponsors Communaute Francaise de Belgique;et al.;European Union (DGXII);Fonds National de la Recherche Scientifique (FNRS);IBRA - BIRA;Region Wallonne
Publisher Institute of Electrical and Electronics Engineers Inc.
Conference name 4th European Control Conference, ECC 1997
Conference date 1 July 1997 through 4 July 1997
Conference code 111881
ISBN 9783952426906
Language of Original Document English
Abbreviated Source Title ECC - Eur. Control Conf.
Source Scopus