Controllability and extremality in nonconvex differential inclusions
type: Item
instance of: scholarly article
title: Controllability and extremality in nonconvex differential inclusions
zbMATH Open document ID: 0824.49021
DOI: 10.1007/BF02192236
published in: Journal of Optimization Theory and Applications
publication date: 1995-11-13T00:00:00Z
review text: Let \(F: [0, T]\times \mathbb{R}^ n\to 2^{\mathbb{R}^ n}\) be a set-valued map with compact values; let \(\eta: \mathbb{R}^ n\to \mathbb{R}^ m\) be a locally Lipschitzian map, \(z(t)\) a given trajectory, and \(\mathcal R\) the reachable set at \(T\) of the differential inclusion \(\dot x(t)\in F(t, x(t))\). We prove sufficient conditions for \(\eta(z(T))\in \text{int }\eta({\mathcal R})\) and establish necessary conditions in maximum principle form for \(\eta(z(T))\in \partial\eta({\mathcal R})\). As a consequence of these results, we show that every boundary trajectory is simultaneously a Pontryagin extremal, Lagrangian extremal, and relaxed Lagrangian extremal.
Mathematics Subject Classification ID: 49K24
zbMATH DE Number: 790575
zbMATH Keywords: Kaskosz maximum principle
zbMATH Keywords: differential inclusion
zbMATH Keywords: Pontryagin extremal
zbMATH Keywords: relaxed Lagrangian extremal
author: Hoang Duong Tuan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 790575