Pontryagin maximum principle for finite dimensional nonlinear optimal control problems on time scales

DOI10.1137/130912219zbMATH Open1282.49016arXiv1302.3513OpenAlexW2075327077MaRDI QIDQ2873854

Author name not available (Why is that?)

Publication date: 27 January 2014

Published in: (Search for Journal in Brave)

Abstract: In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary conditions we derive the corresponding transversality conditions. Our proof is based on Ekeland's variational principle. Our statement and comments clearly show the distinction between right-dense points and right-scattered points. At right-dense points a maximization condition of the Hamiltonian is derived, similarly to the continuous-time case. At right-scattered points a weaker condition is derived, in terms of so-called stable $Omega$-dense directions. We do not make any specific restrictive assumption on the dynamics or on the set $Omega$ of control constraints. Our statement encompasses the classical continuous-time and discrete-time versions of the Pontryagin Maximum Principle, and holds on any general time scale, that is any closed subset of $R$.

Full work available at URL: https://arxiv.org/abs/1302.3513

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Pontryagin maximum principle for finite dimensional nonlinear optimal control problems on time scales

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2873854)