Optimal control problems via a direct method
type: Item
instance of: scholarly article
title: Optimal control problems via a direct method
zbMATH Open document ID: 0764.34019
DOI: 10.1007/BF01766306
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1992-09-27T00:00:00Z
review text: The paper deals with the minimization problem of a cost functional associated to a nonlinear control process defined in a fixed time interval. The cost functional is of a general form. The paper is organized as follows. First, sufficient conditions are given in order that the considered nonlinear boundary value control problem is solvable by using suitable finite dimensional control spaces. The structure of the relative solution set with respect to these finite dimensional control spaces and its relationship with the solution set corresponding to the entire control space \(L^ r([0,1],R^ m)\) (where \(1\leq r\leq\infty)\) are also studied. Furthermore, based on the properties of this set, conditions ensuring the existence of quasisolutions and that of solutions of the minimization problem are established. These conditions differ according to \(r\neq\infty\) or \(r=\infty\).
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 59778
zbMATH Keywords: minimization
zbMATH Keywords: cost functional
zbMATH Keywords: nonlinear control process
zbMATH Keywords: fixed time interval
zbMATH Keywords: nonlinear boundary value control problem
zbMATH Keywords: finite dimensional control spaces
zbMATH Keywords: relative solution
zbMATH Keywords: quasisolutions
author: Paolo Nistri
MaRDI profile type: Publication
cites work: Topological methods for the global controllability of nonlinear systems
cites work: Q5542360
cites work: Q3777854
cites work: Periodic control problems for a class of nonlinear periodic differential systems
cites work: The existence of optimal controls
cites work: Q5596501
cites work: Q3706043
description: scientific article; zbMATH DE number 59778