Extended algebraic Riccati equations in the abstract hyperbolic case
type: Item
instance of: scholarly article
title: Extended algebraic Riccati equations in the abstract hyperbolic case
zbMATH Open document ID: 0961.49003
DOI: 10.1016/S0362-546X(00)85007-5
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-05-10T00:00:00Z
review text: The paper is concerned with the optimal quadratic cost problem over an infinite (time) horizon, and the related algebraic Riccati equation, associated with the abstract equation \[ y_t= Ay+ Bu\in [{\mathcal D}(A^*)]',\quad y(0)= y_0\in Y, \] subject to the hypothesis of the abstract hyperbolic dynamics and with a fully unbounded control operator \(B\). The cost function is \[ J(u,y)= \int^\infty_0 [\|Ry(t)\|^2_Y+ \|u(t)\|^2_U] dt,\quad R\in{\mathcal L}(Y), \] where \(U\) (control) and \(Y\) (state) are two separable Hilbert spaces, and the optimal control problem is \[ \text{minimize} J(u,y)\text{ over all }u\in L_2(0,\infty; U). \] The paper studies this optimal control problem and the related algebraic Riccati equation on \({\mathcal D}(A)\) in the abstract hyperbolic case and provides a quantitative analysis, based on a regularization/approximation approach, of how to achieve a suitable extension of \(B\) so that the algebraic Riccati equation is satisfied on \({\mathcal D}(A)\). The theory presented is illustrated by a computable example.
reviewed by: Sebastian Aniţa
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 1472210
zbMATH Keywords: hyperbolic-like equation
zbMATH Keywords: optimal quadratic cost problem
zbMATH Keywords: algebraic Riccati equation
zbMATH Keywords: optimal control
author: Viorel Barbu
author: Irena Lasiecka
author: R. Triggiani
MaRDI profile type: Publication
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full work available at URL: s0362-546x(00)85007-5
OpenAlex ID: W2024810729
description: scientific article; zbMATH DE number 1472210