Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints

A. V. Arutyunov; D. Yu. Karamzin; F. L. Pereira

doi:10.1134/S0081543816020036

Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints

Authors: Arutyunov A.V.¹, Karamzin D.Y.², Pereira F.L.³
Affiliations:
1. People’s Friendship University of Russia
2. Computing Center of the Russian Academy of Sciences
3. University of Porto
Issue: Vol 292, No Suppl 1 (2016)
Pages: 27-35
Section: Article
URL: https://journals.rcsi.science/0081-5438/article/view/173281
DOI: https://doi.org/10.1134/S0081543816020036
ID: 173281

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Abstract

Properties of Lagrange multipliers from the Pontryagin maximum principle for problems with state constraints are investigated. Sufficient conditions for the continuity of the solution of the adjoint equation depending on how the extremal trajectory approaches the state constraint boundary are obtained. The proof uses the notion of closure with respect to measure of a Lebesgue measurable function and the Carathéodory theorem.