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...
| Main Authors: | , |
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| Format: | Journal Article |
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Taylor & Francis
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/9318 |
| _version_ | 1848745914368262144 |
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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. |
| first_indexed | 2025-11-14T06:24:56Z |
| format | Journal Article |
| id | curtin-20.500.11937-9318 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:24:56Z |
| publishDate | 2013 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |