Generalized Finite-Horizon Linear-Quadratic Optimal Control
The linear-quadratic (LQ) problem is the prototype of a large number of optimal control problems, including the fixed endpoint, the point-to-point, and several H 2/H 8 control problems, as well as the dual counterparts. In the past 50 years, these problems have been addressed using different techniq...
| Main Authors: | , |
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| Format: | Book Chapter |
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Springer-Verlag
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/33349 |
| _version_ | 1848753921205469184 |
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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 linear-quadratic (LQ) problem is the prototype of a large number of optimal control problems, including the fixed endpoint, the point-to-point, and several H 2/H 8 control problems, as well as the dual counterparts. In the past 50 years, these problems have been addressed using different techniques, each tailored to their specific structure. It is only in the last 10 years that it was recognized that a unifying framework is available. This framework hinges on formulae that parameterize the solutions of the Hamiltonian differential equation in the continuous-time case and the solutions of the extended symplectic system in the discrete-time case. Whereas traditional techniques involve the solutions of Riccati differential or difference equations, the formulae used here to solve the finite-horizon LQ control problem only rely on solutions of the algebraic Riccati equations. In this article, aspects of the framework are described within a discrete-time context. |
| first_indexed | 2025-11-14T08:32:11Z |
| format | Book Chapter |
| id | curtin-20.500.11937-33349 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:32:11Z |
| publishDate | 2014 |
| publisher | Springer-Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-333492019-02-19T05:36:13Z Generalized Finite-Horizon Linear-Quadratic Optimal Control Ferrante, A. Ntogramatzidis, Lorenzo The linear-quadratic (LQ) problem is the prototype of a large number of optimal control problems, including the fixed endpoint, the point-to-point, and several H 2/H 8 control problems, as well as the dual counterparts. In the past 50 years, these problems have been addressed using different techniques, each tailored to their specific structure. It is only in the last 10 years that it was recognized that a unifying framework is available. This framework hinges on formulae that parameterize the solutions of the Hamiltonian differential equation in the continuous-time case and the solutions of the extended symplectic system in the discrete-time case. Whereas traditional techniques involve the solutions of Riccati differential or difference equations, the formulae used here to solve the finite-horizon LQ control problem only rely on solutions of the algebraic Riccati equations. In this article, aspects of the framework are described within a discrete-time context. 2014 Book Chapter http://hdl.handle.net/20.500.11937/33349 10.1007/978-1-4471-5102-9_202-1 Springer-Verlag restricted |
| spellingShingle | Ferrante, A. Ntogramatzidis, Lorenzo Generalized Finite-Horizon Linear-Quadratic Optimal Control |
| title | Generalized Finite-Horizon Linear-Quadratic Optimal Control |
| title_full | Generalized Finite-Horizon Linear-Quadratic Optimal Control |
| title_fullStr | Generalized Finite-Horizon Linear-Quadratic Optimal Control |
| title_full_unstemmed | Generalized Finite-Horizon Linear-Quadratic Optimal Control |
| title_short | Generalized Finite-Horizon Linear-Quadratic Optimal Control |
| title_sort | generalized finite-horizon linear-quadratic optimal control |
| url | http://hdl.handle.net/20.500.11937/33349 |