Optimal boundary control and new Riccati equations for highly damped second-order equations
type: Item
instance of: scholarly article
title: Optimal boundary control and new Riccati equations for highly damped second-order equations
zbMATH Open document ID: 0817.49006
published in: Differential and Integral Equations
publication date: 1995-07-18T00:00:00Z
review text: The problem considered in this paper is governed by a system of the form \(w_{tt}- \Delta w- \Delta w_ t= 0\) in \(Q= \Omega\times (0, \infty)\), \(\Omega\subset \mathbb{R}^ n\). We have the boundary conditions \(w(x, 0)= w_ 0\), \(w_ t(x, 0)= w_ 1\), and \(w= u\) on \(\partial\Omega\times (0, \infty)\). The control is effectuated via the function \(u\) in order to minimize the functional \(J(u)= \int^ \infty_ 0 \int_ \Omega (Rw)^ 2 dx+ \int_{\partial\Omega} u^ 2 dx dt\). The author has carried out a complete study of the associated Riccati equation and corresponding optimal control and state. The problem is formulated in an abstract framework applying to more general problems as well.
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49J27
zbMATH DE Number: 597508
zbMATH Keywords: Riccati equation
zbMATH Keywords: optimal control
zbMATH Keywords: state
author: R. Triggiani
reviewed by: Emmanuel N. Barron
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 597508