The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure
In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+Δ of each solution X: The first part is trivial, in the sense that i...
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| Format: | Journal Article |
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2015
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| Online Access: | http://hdl.handle.net/20.500.11937/44957 |
| _version_ | 1848757148639559680 |
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| author | Ntogramatzidis, Lorenzo Ferrante, A. |
| author_facet | Ntogramatzidis, Lorenzo Ferrante, A. |
| author_sort | Ntogramatzidis, Lorenzo |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+Δ of each solution X: The first part is trivial, in the sense that it is an explicit expression of the addend X0 which is common to all solutions, so that it does not depend on the particular X. The second part can be – depending on the structure of the considered generalized Riccati equation – either a reduced-order discrete-time regular algebraic Riccati equation whose associated closed-loop matrix is non-singular, or a symmetric Stein equation. The proposed reduction is explicit, so that it can be easily implemented in a software package that uses only standard linear algebra procedures. |
| first_indexed | 2025-11-14T09:23:29Z |
| format | Journal Article |
| id | curtin-20.500.11937-44957 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:23:29Z |
| publishDate | 2015 |
| publisher | undefined |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-449572017-09-13T14:18:22Z The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure Ntogramatzidis, Lorenzo Ferrante, A. Generalized Riccati equations In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+Δ of each solution X: The first part is trivial, in the sense that it is an explicit expression of the addend X0 which is common to all solutions, so that it does not depend on the particular X. The second part can be – depending on the structure of the considered generalized Riccati equation – either a reduced-order discrete-time regular algebraic Riccati equation whose associated closed-loop matrix is non-singular, or a symmetric Stein equation. The proposed reduction is explicit, so that it can be easily implemented in a software package that uses only standard linear algebra procedures. 2015 Journal Article http://hdl.handle.net/20.500.11937/44957 10.1016/j.sysconle.2014.11.001 undefined fulltext |
| spellingShingle | Generalized Riccati equations Ntogramatzidis, Lorenzo Ferrante, A. The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure |
| title | The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure |
| title_full | The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure |
| title_fullStr | The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure |
| title_full_unstemmed | The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure |
| title_short | The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure |
| title_sort | discrete-time generalized algebraic riccati equation: order reduction and solutions’ structure |
| topic | Generalized Riccati equations |
| url | http://hdl.handle.net/20.500.11937/44957 |