The integral estimations for ordinary differential equations and its application to the non-smooth optimal control problems
Optimization and Control
2010-11-01 v1 Classical Analysis and ODEs
Abstract
The paper studies integral functionals with non-smooth functions from L_2 defined on solutions of ODEs. Some regularity is obtained in the form of estimates of L_2-norm for these functionals. This result is used for regularization of optimal control problems for ODEs with non-smooth functionals: it is suggested to replace the initial vector by a random vector with density. Necessary conditions of optimality and sufficient conditions of existence of optimal control are obtained.
Cite
@article{arxiv.1010.6123,
title = {The integral estimations for ordinary differential equations and its application to the non-smooth optimal control problems},
author = {Nikolai Dokuchaev},
journal= {arXiv preprint arXiv:1010.6123},
year = {2010}
}