Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control
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Publication:4630691
DOI10.1137/18M119121XzbMATH Open1412.49045arXiv1805.11990OpenAlexW2806594861WikidataQ128013926 ScholiaQ128013926MaRDI QIDQ4630691
Author name not available (Why is that?)
Publication date: 23 April 2019
Published in: (Search for Journal in Brave)
Abstract: Consider a general nonlinear optimal control problem in finite dimension, with constant state and/or control delays. By the Pontryagin Maximum Principle, any optimal trajectory is the projection of a Pontryagin extremal. We establish that, under appropriate assumptions, Pontryagin extremals depend continuously on the parameter delays, for adequate topologies. The proof of the continuity of the trajectory and of the control is quite easy, however, for the adjoint vector, the proof requires a much finer analysis. The continuity property of the adjoint with respect to the parameter delay opens a new perspective for the numerical implementation of indirect methods, such as the shooting method. We also discuss the sharpness of our assumptions.
Full work available at URL: https://arxiv.org/abs/1805.11990
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