On the continuity of the speed function of a linear system in the critical case
type: Item
instance of: scholarly article
title: On the continuity of the speed function of a linear system in the critical case
zbMATH Open document ID: 0846.49001
author: A. G. Rodionova
author: E. L. Tonkov
published in: Russian Mathematics
publication date: 1996-01-03T00:00:00Z
review text: The paper deals with the dynamic object described by the linear differential equation \[ \dot z= F(z,\nu), \qquad (z,\nu)\in \mathbb{R}^n \times V_0. \] Given the quality functional \[ J(\omega (\cdot))= \lim_{\alpha\to \infty} {1\over {2\alpha}} \int^\alpha_{-\alpha} g(z (t),\nu(t)) dt \] where the control \(\nu: \mathbb{R}^1\to V_0\) is a measurable and periodic function in a compact set \(V_0 \subset \mathbb{R}^m\), the main purpose of the paper is to minimize the functional \(J\). The text is badly organized and the English is poor and incorrect. Moreover, taking into account that the problem does not contain new theoretical elements, one should state that the paper is rather little useful.
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 815650
zbMATH Keywords: optimization in abstract spaces
zbMATH Keywords: optimal control of linear objects
reviewed by: Władysław Hejmo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 815650