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: firstname.lastname@example.org
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
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