Publications in Scientific Journals:
A.L. Dontchev, M. Krastanov, V.M. Veliov:
"On the existence of Lipschitz continuous optimal feedback control";
Vietnam Journal of Mathematics,
47
(2019),
3;
579
- 597.
English abstract:
We consider an optimal control problem governed by a nonlinear ODE with an integral cost functional and a control constraint. We give conditions under which the optimal open-loop control is Lipschitz continuous in time; moreover, we identify the dependence of the Lipschitz constant of the optimal control on the data of the problem.
Our main assumptions include a coercivity condition and that the optimal control is an isolated solution of the variational inequality appearing in the first-order optimality system. Then we show the existence of a Lipschitz continuous optimal feedback control.
As an application, we establish regularity properties of the optimal value function. A main tool for obtaining these results is the theory around Robinsonīs strong regularity.
Keywords:
optimal control, optimal feedback control, Lipschitz continuity, value function
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1007/s10013-019-00347-5
Electronic version of the publication:
https://publik.tuwien.ac.at/files/publik_281413.pdf
Created from the Publication Database of the Vienna University of Technology.