Necessary and sufficient conditions of minimum in optimal control problems with sliding modes and generalized controls
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions of minimum in optimal control problems with sliding modes and generalized controls
zbMATH Open document ID: 0554.49010
author: V. A. Dubovitskij
published in: Automation and Remote Control
publication date: 1984-01-01T00:00:00Z
review text: Some necessary and sufficient conditions for optimality of sliding modes and generalized controls (measures) in Mayer-type problems for general nonlinear control systems are studied. The optimality is understood in the sense of a weak minimum and in the sense of a non-local minimum specific for sliding modes. There are no assumptions concerning the number of basic controls which are Lipschitzian functions while the coefficients are measurable functions; the optimal sliding regime is assumed to be singular. By using some earlier results of Russian mathematicians the necessary and sufficient conditions for optimality are obtained in abstract form and next in analytical form and are illustrated by two examples. The sufficient conditions are also sufficient for minimum problems in the class of generalized control measures.
reviewed by: Z.Wyderka
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49K30
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 28A20
zbMATH DE Number: 3883084
zbMATH Keywords: sliding modes
zbMATH Keywords: generalized controls
zbMATH Keywords: Mayer-type problems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3883084