Differential and algebraic Riccati equations with application to boundary/point control problems: Continuous theory and approximation theory
type: Item
instance of: scholarly article
title: Differential and algebraic Riccati equations with application to boundary/point control problems: Continuous theory and approximation theory
zbMATH Open document ID: 0754.93038
published in: Lecture Notes in Control and Information Sciences
publication date: 1993-01-23T00:00:00Z
review text: After being discriminated into two classes according to respective abstract assumptions, the optional control problem, abstract equation \(y_ t=Ay+Bu\), \(y(0)=y_ 0\), together with the cost functional \[ J(u,y)=\int^ T_ 0[\| Ry(t)\|^ 2_ z+\| u(t)\|^ 2_ u]dt+\| Gy(t)\|^ 2_ w, \] is discussed in the notes, where \(R\) and \(G\) are observation operators. The main attention is put on the existence of Riccati operator \(p(t)\), which is the solution to the associated Riccati equation, differential when \(T<\infty\) or algebraic when \(T=\infty\). To justify the abstract theory, some illustrative examples of boundary/point control problems for partial differential equations and of numerical approximation are given.
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93-02
zbMATH DE Number: 52890
zbMATH Keywords: cost functional
zbMATH Keywords: Riccati operator
zbMATH Keywords: Riccati equation
author: Irena Lasiecka
author: R. Triggiani
reviewed by: Weigao Ge
MaRDI profile type: Publication
DOI: 10.1007/BFB0006880
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description: scientific article; zbMATH DE number 52890