Optimization of systems with a moving control
type: Item
instance of: scholarly article
zbMATH Open document ID: 0976.49003
author: M. K. Berdimuratov
author: S. I. Lyashko
author: D. A. Nomirovskij
author: L. I. Palienko
publication date: 2001-09-16T00:00:00Z
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1646391
zbMATH Keywords: optimization
zbMATH Keywords: point moving control
zbMATH Keywords: differential equation
zbMATH Keywords: quality criterion
zbMATH Keywords: optimal control
MaRDI profile type: Publication
title: Optimization of systems with a moving control
published in: Zhurnal Obchyslyuval'noïta Prykladnoï Matematyky
review text: The paper deals with the point moving control problem for a system described by the linear differential equation \(Lu=\sum_{i=1}^{l} \sum_{j=1}^{n}\delta(\overline x-\overline a_{i}(t))c_{ij}(t)\psi_{j} (\overline y)\), where \(L(\cdot)\) operates from \(D(L)\subset L_2(Q)\) into \(R(L)\subset W^{-s}\); \(Q=[0,T]\times\Omega\), \(\Omega=\Omega_{x}\times \Omega_{y}\), \(\Omega_{x}\subset R^{N_1}\), \(\Omega_{y}\subset R^{N_2}\); \(\overline x\in \Omega_{x}, \overline y\in \Omega_{y}\), \(\overline a_{i}(t)\in (W_2^1(0,T))^{N_1}\), \(c_{ij}(t)\in L_2(0,T)\), \(\psi_{j}(\overline y)\in L_2(\Omega_{y})\); \(W_2^1\) is the Sobolev space; \(h=(a(t),c(t))\) is a control. It is necessary to minimize the quality criterion \(J(u(h))=\sum_{i=1}^{k} \int_{Q} (u-u_{\partial}^{i})dQ\), where \(u_{\partial}^{i}\) is a given element from \(L_2(Q)\). The authors prove that under some conditions there exists an optimal control for the considered system.
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1646391