Volume 29, 2023
|Number of page(s)||31|
|Published online||27 February 2023|
GOH Conditions for Minima of Nonsmooth Problems with Unbounded Controls
1 Department of Information Engineering, Computer Science and Mathematics (DISIM), University of L’Aquila, L’Aquila, Italy
2 Department of Mathematics “T. Levi-Civita”, University of Padova, Padova, Italy
* Corresponding author: email@example.com
Accepted: 28 December 2022
Higher order necessary conditions for a minimizer of an optimal control problem are generally obtained for systems whose dynamics is continuously differentiable in the state variable. Here, by making use of the notion of set-valued Lie bracket, we obtain a Goh-type condition for a control affine system with Lipschitz continuous dynamics and unbounded controls. In order to manage the simultaneous lack of smoothness of the adjoint equation and of the Lie bracket-like variations we make use of the notion of Quasi Differential Quotient. We conclude the paper with a worked out example where the established higher order condition is capable to rule out the optimality of a control verifying the standard maximum principle.
Mathematics Subject Classification: 49K15 / 49N25 / 49K99
Key words: Goh conditions / nonsmooth optimal control / set-valued Lie brackets / unbounded controls
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.