Dynamic programming for free-time problems with endpoint constraints
type: Item
instance of: scholarly article
title: Dynamic programming for free-time problems with endpoint constraints
zbMATH Open document ID: 0793.49010
DOI: 10.1007/BF01211747
author: J. Kotsiopoulos
author: Richard B. Vinter
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1994-08-03T00:00:00Z
review text: The paper considers optimal control problems with free end-time and endpoint constraints aiming at providing necessary and sufficient conditions for local optimality based on a solution to the Hamilton- Jacobi equation under a normality hypothesis. The normality hypothesis requires that first-order necessary conditions of optimality hold in a form where the cost multiplier is nonzero. First, it is shown that if there is a suitable solution to the Hamilton-Jacobi equation (i.e. a verification function) and a nominal state trajectory which satisfies a certain compatibility condition, then that arc must be a minimizer. This is the sufficiency part. Second, it is shown that if \(x(\cdot)\) is a minimizer, then a suitably defined value function is a verification function associated with \(x(\cdot)\). This is the necessity part.
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 493292
zbMATH Keywords: optimal control
zbMATH Keywords: free end-time
zbMATH Keywords: necessary and sufficient conditions for local optimality
reviewed by: Markos Papageorgiou
MaRDI profile type: Publication
cites work: A Boundary Value Problem for the Minimum-Time Function
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description: scientific article; zbMATH DE number 493292