The integral estimations for ordinary differential equations and its application to the non-smooth optimal control problems

Details The integral estimations for ordinary differential equations and its application to the non-smooth optimal control problems The integral estimations for ordinary differential equations and its application to the non-smooth optimal control problems

2010-10-29

arxiv.org/abs/1010.6123v1

Differential Equations V.27 (1991), N 10. 1181-1191

Mathematics

Optimization and Control

Scientific paper

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.

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