The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control
The purpose of this paper is to investigate the role that the so-called constrained generalized Riccati equation plays within the context of continuous-time singular linear–quadratic (LQ) optimal control. This equation has been defined following the analogy with the discrete-time setting. However, w...
| Main Authors: | , |
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| Format: | Journal Article |
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Pergamon
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/6074 |
| _version_ | 1848744972285640704 |
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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 | The purpose of this paper is to investigate the role that the so-called constrained generalized Riccati equation plays within the context of continuous-time singular linear–quadratic (LQ) optimal control. This equation has been defined following the analogy with the discrete-time setting. However, while in the discrete-time case the connections between this equation and the linear–quadratic optimal control problem have been thoroughly investigated, to date very little is known on these connections in the continuous-time setting. This note addresses this point. We show, in particular, that when the continuous-time constrained generalized Riccati equation admits a solution, the corresponding linear–quadratic problem admits an impulse-free optimal control. We also address the corresponding infinite-horizon LQ problem for which we establish a similar result under the additional constraint that there exists a control input for which the cost index is finite. |
| first_indexed | 2025-11-14T06:09:57Z |
| format | Journal Article |
| id | curtin-20.500.11937-6074 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:09:57Z |
| publishDate | 2014 |
| publisher | Pergamon |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-60742017-09-13T14:41:02Z The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control Ferrante, A. Ntogramatzidis, Lorenzo Generalized discrete algebraic Riccati equation LQ optimal control The purpose of this paper is to investigate the role that the so-called constrained generalized Riccati equation plays within the context of continuous-time singular linear–quadratic (LQ) optimal control. This equation has been defined following the analogy with the discrete-time setting. However, while in the discrete-time case the connections between this equation and the linear–quadratic optimal control problem have been thoroughly investigated, to date very little is known on these connections in the continuous-time setting. This note addresses this point. We show, in particular, that when the continuous-time constrained generalized Riccati equation admits a solution, the corresponding linear–quadratic problem admits an impulse-free optimal control. We also address the corresponding infinite-horizon LQ problem for which we establish a similar result under the additional constraint that there exists a control input for which the cost index is finite. 2014 Journal Article http://hdl.handle.net/20.500.11937/6074 10.1016/j.automatica.2014.02.014 Pergamon restricted |
| spellingShingle | Generalized discrete algebraic Riccati equation LQ optimal control Ferrante, A. Ntogramatzidis, Lorenzo The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control |
| title | The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control |
| title_full | The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control |
| title_fullStr | The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control |
| title_full_unstemmed | The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control |
| title_short | The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control |
| title_sort | generalized continuous algebraic riccati equation and impulse-free continuous-time lq optimal control |
| topic | Generalized discrete algebraic Riccati equation LQ optimal control |
| url | http://hdl.handle.net/20.500.11937/6074 |