Dontchev, A. L., Krastanov, M. I., & Veliov, V. M. (2019). On the Existence of Lipschitz Continuous Optimal Feedback Control. Vietnam Journal of Mathematics, 47, 579–597. https://doi.org/10.1007/s10013-019-00347-5
E105 - Institut für Stochastik und Wirtschaftsmathematik
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Journal:
Vietnam Journal of Mathematics
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ISSN:
2305-221X
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Date (published):
2019
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Number of Pages:
19
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Publisher:
Springer New York LLC
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Peer reviewed:
Yes
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Keywords:
Optimal control; Optimal feedback control; Lipschitz continuity; Value function
en
Abstract:
We consider an optimal control problem involving a nonlinear ODE with control, an integral cost functional, and a control constraint. Our main assumptions include a coercivity condition and the condition that the optimal control is an isolated solution of the variational inequality appearing in the first-order optimality condition. We show that 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. Then, we establish the existence of a Lipschitz continuous optimal feedback control. As an application, we study regularity properties of the optimal value function. A main tool for obtaining these results is the property of uniform strong metric regularity.