Boundedness of optimal trajectories
type: Item
instance of: scholarly article
title: Boundedness of optimal trajectories
zbMATH Open document ID: 0613.49003
DOI: 10.1007/BF01159569
author: A. I. Panasyuk
author: V. I. Panasyuk
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: The paper deals with the system \(\dot x=f(x,u)\), \(u\in U\subset R^ m\), \(x\in H\subset R^ n\), with the following optimality criterion: \[ I(x(\cdot),0,T)=\int^{T}_{0}F(x,u)dt\to \min,\quad T>0, \] where H is a closed set, U is compact, f and F are of class C in an open neighbourhood of H, u is a measurable function in U, x(0)\(\in X_ 0\subset R^ n\), x(T)\(\in X_ T\subset R^ n\), T is finite and fixed. In the standard theory of optimal control, a criterion based on the boundedness of the function f is often used in the proofs of the existence of an optimal control (i.e. \(\max_{u\in U}\| f(x,u)\|\) is bounded if \(\| x\| \to \infty\), where \(\| \cdot \|\) is the Euclidean norm). This paper gives some new criteria which are some generalizations of that one mentioned above. The criteria suggested in the paper can be used for the cases: a) fixed x(0) and x(T); b) fixed x(0) and free x(T); c) free x(0) and x(T).
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 3992267
zbMATH Keywords: boundedness
zbMATH Keywords: existence of an optimal control
reviewed by: Władysław Hejmo
MaRDI profile type: Publication
cites work: Q4199096
cites work: Q3036174
description: scientific article; zbMATH DE number 3992267