Successive approximations to the optimal control of stochastic systems with after-effect. I

Successive approximations to the optimal control of stochastic systems with after-effect. I Random Oper. & Stock. Eqs., Vol. 1, No. 3, pp. 245-258 (1993) © VSP 1993 V. B. KOLMANOVSKIJ1 and L. E. SHAIKHET2 Moscow Institute of Electronic Industry, 109028 Moscow, Russia Research Institute of Mining Mechanics, 340055 Donetsk, Ukraine Received for ROSE 11 May 1991 Abstract--The method of successive approximations to the optimal control of stochastic differential equations is considered. Some examples are given. In this review a method of successive approximations to the optimal control of stochastic differential equations with after-effect is described. This method is based on the following reasoning. First, the class of functionals which integrally depends on the past history and is sufficiently smooth with respect to a current state of a system. Second, every successive approximation to the optimal control is the optimal control for some auxiliary problem of control which is built in a special way. The reader is referred to [1-4]. In [5] an application of modification of this method to the problems of optimal control in non-full data is shown. 1. A PROBLEM OF SYNTHESIS OF AN OPTIMAL CONTROL In this section a formulation of the problem of synthesis of optimal control of stochastic systems with after-effect is given. The Bellman http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Random Operators and Stochastic Equations de Gruyter

Successive approximations to the optimal control of stochastic systems with after-effect. I

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0926-6364
eISSN
1569-397X
DOI
10.1515/rose.1993.1.3.245
Publisher site
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Abstract

Random Oper. & Stock. Eqs., Vol. 1, No. 3, pp. 245-258 (1993) © VSP 1993 V. B. KOLMANOVSKIJ1 and L. E. SHAIKHET2 Moscow Institute of Electronic Industry, 109028 Moscow, Russia Research Institute of Mining Mechanics, 340055 Donetsk, Ukraine Received for ROSE 11 May 1991 Abstract--The method of successive approximations to the optimal control of stochastic differential equations is considered. Some examples are given. In this review a method of successive approximations to the optimal control of stochastic differential equations with after-effect is described. This method is based on the following reasoning. First, the class of functionals which integrally depends on the past history and is sufficiently smooth with respect to a current state of a system. Second, every successive approximation to the optimal control is the optimal control for some auxiliary problem of control which is built in a special way. The reader is referred to [1-4]. In [5] an application of modification of this method to the problems of optimal control in non-full data is shown. 1. A PROBLEM OF SYNTHESIS OF AN OPTIMAL CONTROL In this section a formulation of the problem of synthesis of optimal control of stochastic systems with after-effect is given. The Bellman

Journal

Random Operators and Stochastic Equationsde Gruyter

Published: Jan 1, 1993

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