Sufficient conditions for relative minima of broken extremals in optimal control theory
type: Item
instance of: scholarly article
title: Sufficient conditions for relative minima of broken extremals in optimal control theory
zbMATH Open document ID: 1012.49023
DOI: 10.1016/S0022-247X(02)00008-2
author: John Noble
author: Heinz Schättler
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-08T00:00:00Z
review text: In this paper the authors consider smoothly parametrized families of broken extremals related to optimal control problems. Roughly speaking, these are families of controlled trajectories parametrized by some parameter \(p\) with the controls being piecewise continuous and depending smoothly on \(p\), such that each trajectory satisfies necessary optimality conditions. For such families the authors derive sufficient conditions under which the values associated with these parameterized trajectories (given by the optimal control problem under consideration) solve the related Hamilton-Jacobi-Bellman equation. Based on this result, the authors conclude conditions under which the given family of trajectories is relatively optimal, i.e., optimal with respect to all other trajectories lying in some given set.
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 49K15
zbMATH DE Number: 1764673
zbMATH Keywords: nonlinear optimal control
zbMATH Keywords: Hamilton-Jacobi-Bellman equation
zbMATH Keywords: sufficient conditions for optimality
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1764673