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


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.


Download Citation

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


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

zbMATH: 0879.49003
MathSciNet: MR1424801

Primary: 49J15
Secondary: 49J45

Rights: Copyright © 1997 Khayyam Publishing, Inc.


Vol.10 • No. 1 • 1997
Back to Top