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A.L. Dontchev, M. Krastanov, V.M. Veliov:
"On the existence of Lipschitz continuous optimal feedback control";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2018-04 (2018), 4; 20 pages.

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 Robinson´s strong regularity.

optimal control, optimal feedback control, Lipschitz continuity, value function

https://publik.tuwien.ac.at/files/publik_272772.pdf