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1997 Optimal control problems in spaces of functions of bounded variation
J. P. Raymond
Differential Integral Equations 10(1): 105-136 (1997).

Abstract

We study optimal control problems governed by differential systems involving measures as controls and where the state vector is a function of bounded variation. Such problems are defined as extensions to $BV$-spaces of classical problems which do not admit solutions in the class of absolutely continuous functions. We give a definition of generalized solutions for differential systems with measures, for which we prove a stability result for the weak-star topology of measures. We next prove existence of $BV$-solutions for control problems. A relaxation theorem is given: the classical control problem defined for $AC$-functions and the control problem extended to $BV$-spaces have the same value and the solutions of extended problem are cluster points of minimizing sequences for the initial problem. We finally characterize $BV$-solutions of control problems by means of Lipschitz solutions of an auxiliary control problem.

Citation

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J. P. Raymond. "Optimal control problems in spaces of functions of bounded variation." Differential Integral Equations 10 (1) 105 - 136, 1997.

Information

Published: 1997
First available in Project Euclid: 6 May 2013

zbMATH: 0879.49003
MathSciNet: MR1424801

Subjects:
Primary: 49J15
Secondary: 49J45

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.10 • No. 1 • 1997
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