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Attainability problems under stochastic perturbations

Attainability problems under stochastic perturbations Differential Equations, Vol. 40, No. 11, 2004, pp. 1573–1578. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 11, 2004, pp. 1494–1499. Original Russian Text Copyright c 2004 by Digailova, Kurzhanskii. ORDINARY DIFFERENTIAL EQUATIONS I. A. Digailova and A. B. Kurzhanskii Moscow State University, Moscow, Russia Received June 8, 2004 INTRODUCTION The attainability problem is one of the key problems in control theory. It is motivated by numerous applied problems in automation, navigation, and related elds. It is of interest to consider the case involving perturbations and readjustment of the system. Under unknown but bounded perturbations, this problem was considered in [1, 2], and attainability in hybrid systems was studied in [3]. The present paper deals with attainability issues for continuous linear systems under stochas- tic perturbations. The noises are assumed to be stochastic Wiener processes de ned via their characteristics, which can depend on a control parameter. In turn, the control parameter can be unbounded or bounded by geometric constraints. In the present paper, attainability domains are introduced as level sets of a solution of a Hamilton{Jacobi{Bellman equation of special form. In the case of an unconstrained control param- eter, the corresponding cost function can be computed directly. But if http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Attainability problems under stochastic perturbations

Differential Equations , Volume 40 (11) – Feb 26, 2005

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References (11)

Publisher
Springer Journals
Copyright
Copyright © 2004 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/s10625-005-0069-6
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 40, No. 11, 2004, pp. 1573–1578. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 11, 2004, pp. 1494–1499. Original Russian Text Copyright c 2004 by Digailova, Kurzhanskii. ORDINARY DIFFERENTIAL EQUATIONS I. A. Digailova and A. B. Kurzhanskii Moscow State University, Moscow, Russia Received June 8, 2004 INTRODUCTION The attainability problem is one of the key problems in control theory. It is motivated by numerous applied problems in automation, navigation, and related elds. It is of interest to consider the case involving perturbations and readjustment of the system. Under unknown but bounded perturbations, this problem was considered in [1, 2], and attainability in hybrid systems was studied in [3]. The present paper deals with attainability issues for continuous linear systems under stochas- tic perturbations. The noises are assumed to be stochastic Wiener processes de ned via their characteristics, which can depend on a control parameter. In turn, the control parameter can be unbounded or bounded by geometric constraints. In the present paper, attainability domains are introduced as level sets of a solution of a Hamilton{Jacobi{Bellman equation of special form. In the case of an unconstrained control param- eter, the corresponding cost function can be computed directly. But if

Journal

Differential EquationsSpringer Journals

Published: Feb 26, 2005

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