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arXiv · 2203.03070

Goh conditions for minima of nonsmooth problems with unbounded controls

Francesca Angrisani·Franco Rampazzo
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Abstract

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.

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Francesca Angrisani, Franco Rampazzo. 2022-03-06. Goh conditions for minima of nonsmooth problems with unbounded controls. https://arxiv.org/abs/2203.03070

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