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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
Differential Equations – Springer Journals
Published: Feb 26, 2005
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