Special solutions in singular optimization problems
type: Item
instance of: scholarly article
title: Special solutions in singular optimization problems
zbMATH Open document ID: 0593.49022
published in: Automation and Remote Control
publication date: 1985-01-01T00:00:00Z
review text: Dynamic systems with generalized controls are studied. Such systems occur in various problems of space navigation, heat engineering and from other domains. If the control u(t) is allowed to belong to the space \(L^ 1\), then it is not possible to find the state in the class of ordinary functions. The concept of generalized solution is based on generalized functions of zero order (measures \(u(t)=da(t)/dt\), where a(t) is a vector function of bounded variation). For such a solution to be unique, the usual concept of weak convergence of measures is slightly modified. The maximum principle is applied and a singular optimal control is derived.
Mathematics Subject Classification ID: 49K30
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 49L99
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 3953676
zbMATH Keywords: generalized controls
zbMATH Keywords: weak convergence of measures
zbMATH Keywords: maximum principle
zbMATH Keywords: singular optimal control
author: Yu. V. Orlov
reviewed by: Viorel Arnăutu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3953676