A reduction technique for discrete generalized algebraic and difference Riccati equations

This paper proposes a reduction technique for the generalized Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalized discrete algebraic Riccati equation. In particular, an analysis on the eigenstructure of the corresponding e...

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Main Authors: Ferrante, A., Ntogramatzidis, Lorenzo
Format: Journal Article
Published: Taylor & Francis 2013
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/9318
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author Ferrante, A.
Ntogramatzidis, Lorenzo
author_facet Ferrante, A.
Ntogramatzidis, Lorenzo
author_sort Ferrante, A.
building Curtin Institutional Repository
collection Online Access
description This paper proposes a reduction technique for the generalized Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalized discrete algebraic Riccati equation. In particular, an analysis on the eigenstructure of the corresponding extended symplectic pencil enables to identify a subspace in which all the solutions of the generalized discrete algebraic Riccati equation are coincident. This subspace is the key to derive a decomposition technique for the generalized Riccati difference equation. This decomposition isolates a “nilpotent” part, which converges to a steady-state solution in a finite number of steps, from another part that can be computed by iterating a reduced-order generalized Riccati difference equation.
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spelling curtin-20.500.11937-93182017-09-13T14:48:44Z A reduction technique for discrete generalized algebraic and difference Riccati equations Ferrante, A. Ntogramatzidis, Lorenzo finite-horizon LQ problem extended symplectic pencil generalized discrete algebraic Riccati equation generalized Riccati difference equation This paper proposes a reduction technique for the generalized Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalized discrete algebraic Riccati equation. In particular, an analysis on the eigenstructure of the corresponding extended symplectic pencil enables to identify a subspace in which all the solutions of the generalized discrete algebraic Riccati equation are coincident. This subspace is the key to derive a decomposition technique for the generalized Riccati difference equation. This decomposition isolates a “nilpotent” part, which converges to a steady-state solution in a finite number of steps, from another part that can be computed by iterating a reduced-order generalized Riccati difference equation. 2013 Journal Article http://hdl.handle.net/20.500.11937/9318 10.1080/03081087.2013.834056 Taylor & Francis fulltext
spellingShingle finite-horizon LQ problem
extended symplectic pencil
generalized discrete algebraic Riccati equation
generalized Riccati difference equation
Ferrante, A.
Ntogramatzidis, Lorenzo
A reduction technique for discrete generalized algebraic and difference Riccati equations
title A reduction technique for discrete generalized algebraic and difference Riccati equations
title_full A reduction technique for discrete generalized algebraic and difference Riccati equations
title_fullStr A reduction technique for discrete generalized algebraic and difference Riccati equations
title_full_unstemmed A reduction technique for discrete generalized algebraic and difference Riccati equations
title_short A reduction technique for discrete generalized algebraic and difference Riccati equations
title_sort reduction technique for discrete generalized algebraic and difference riccati equations
topic finite-horizon LQ problem
extended symplectic pencil
generalized discrete algebraic Riccati equation
generalized Riccati difference equation
url http://hdl.handle.net/20.500.11937/9318