Properties of the Bellman function in time-optimal control problems
type: Item
instance of: scholarly article
title: Properties of the Bellman function in time-optimal control problems
zbMATH Open document ID: 0909.49012
DOI: 10.1023/A:1022615921015
author: Bernhard Rupp
published in: Journal of Optimization Theory and Applications
publication date: 1998-05-27T00:00:00Z
review text: The author considers a nonautonomous, nonlinear time-optimal control problem and addresses the question of Hölder and Lipschitz continuity of the optimal value function. Under usual regularity conditions, and for arbitrary closed targets a condition on a lower Dini derivative at the boundary of the target is established which guarantees Hölder continuity of the solution, allowing also an estimate for the Hölder coefficient. This condition is then modified using the exterior normal cone at each boundary point of the target. The modified condition derived this way is shown to be equivalent to the Lipschitz continuity of the value function.
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 1069776
zbMATH Keywords: time-optimal control
zbMATH Keywords: optimal value function
zbMATH Keywords: regularity
zbMATH Keywords: continuity properties
zbMATH Keywords: Bellman functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1069776