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Control synthesis in a class of higher-order distributions

Control synthesis in a class of higher-order distributions ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 11, pp. 1479–1489.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c A.N. Dar’in, A.B. Kurzhanskii, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 11, pp. 1443–1453. ORDINARY DIFFERENTIAL EQUATIONS Control Synthesis in a Class of Higher-Order Distributions A. N. Dar’in and A. B. Kurzhanskii Moscow State University, Moscow, Russia Received July 4, 2007 DOI: 10.1134/S0012266107110018 The present paper deals with impulse control. Unlike other papers, here the controls are chosen in the class of functions that admit first-order impulses (delta functions) as well as finitely many higher derivatives of these functions (generalized impulses or higher-order impulses). In addition, the control is sought in the form of positional strategies rather than open-loop solutions. The latter leads to the use of a modified version of dynamic programming theory, which is adjusted for such problems and based on the reduction of the original problem to another one problem considered in the class of only first-order impulses. In this modification, instead of the Hamilton–Jacobi–Bellman (HJB) equation, one uses variational inequalities of similar structure. However, solutions in the class of higher-order distributions do not necessarily admit physical realization. In order to make http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Control synthesis in a class of higher-order distributions

Dar’in, A.; Kurzhanskii, A.
Differential Equations , Volume 43 (11) – Mar 24, 2007
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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266107110018
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 11, pp. 1479–1489.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c A.N. Dar’in, A.B. Kurzhanskii, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 11, pp. 1443–1453. ORDINARY DIFFERENTIAL EQUATIONS Control Synthesis in a Class of Higher-Order Distributions A. N. Dar’in and A. B. Kurzhanskii Moscow State University, Moscow, Russia Received July 4, 2007 DOI: 10.1134/S0012266107110018 The present paper deals with impulse control. Unlike other papers, here the controls are chosen in the class of functions that admit first-order impulses (delta functions) as well as finitely many higher derivatives of these functions (generalized impulses or higher-order impulses). In addition, the control is sought in the form of positional strategies rather than open-loop solutions. The latter leads to the use of a modified version of dynamic programming theory, which is adjusted for such problems and based on the reduction of the original problem to another one problem considered in the class of only first-order impulses. In this modification, instead of the Hamilton–Jacobi–Bellman (HJB) equation, one uses variational inequalities of similar structure. However, solutions in the class of higher-order distributions do not necessarily admit physical realization. In order to make

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Differential Equations – Springer Journals

Published: Mar 24, 2007

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