The integral estimations for ordinary differential equations and its application to the non-smooth optimal control problems
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2010
- DOI:
- 10.48550/arXiv.1010.6123
- arXiv:
- arXiv:1010.6123
- Bibcode:
- 2010arXiv1010.6123D
- Keywords:
-
- Mathematics - Optimization and Control;
- Mathematics - Classical Analysis and ODEs;
- 49K45;
- 49K15;
- 49K15;
- 34A99
- E-Print:
- Differential Equations V.27 (1991), N 10. 1181-1191