Lyapunov-Krotov inequality and sufficient conditions in optimal control
type: Item
instance of: scholarly article
title: Lyapunov-Krotov inequality and sufficient conditions in optimal control
zbMATH Open document ID: 1088.49021
DOI: 10.1023/B:JOTH.0000023085.65837.49
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-05-23T00:00:00Z
review text: The paper is devoted to the analysis of the canonical theory based on the use of a family of solutions of the Lyapunov-Krotov inequality. Classical smooth optimal control with terminal constraints is studied and it is established that if the sufficient conditions with the family of solutions of the Lyapunov-Krotov inequality hold, then the gradients of ``essential'' functions of the family along the optimal trajectory coincide with the adjoint components of the Pontryagin extremals in the sense of Milyutin. There are presented some examples with singularities that are characteristic for the non-existence of the smooth Bellman and Krotov functions, namely, the presence of invariant sets and abnormal Pontryagin extremals and extremals with the set of normed Lagrange multipliers consisting of more than one point. The examples show that the application of the canonical theory can be efficient in these situations, while the smooth versions of the Bellman and Krotov functions cannot be applied here in principle.
reviewed by: Gheorghe Aniculăesei
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 2170237
zbMATH Keywords: Bellman functions
zbMATH Keywords: Krotov functions
zbMATH Keywords: smooth optimal control
author: Vladimir Dykhta
MaRDI profile type: Publication
full work available at URL: b:joth.0000023085.65837.49
OpenAlex ID: W2028495088
description: scientific article; zbMATH DE number 2170237