A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system
The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant su...
| Main Authors: | , , |
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| Format: | Journal Article |
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Pergamon
2008
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| Online Access: | http://hdl.handle.net/20.500.11937/2947 |
| _version_ | 1848744093093462016 |
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| author | Prattichizzo, D. Ntogramatzidis, Lorenzo Marro, G. |
| author_facet | Prattichizzo, D. Ntogramatzidis, Lorenzo Marro, G. |
| author_sort | Prattichizzo, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the original system, and the optimal feedback gain is computed as the friend matrix of the resolving subspace. This study yields a new computational framework for the cheap LQ regulator, relying only on the very basic and simple tools of the geometric approach, namely the algorithms for controlled and conditioned invariant subspaces and invariant zeros. |
| first_indexed | 2025-11-14T05:55:59Z |
| format | Journal Article |
| id | curtin-20.500.11937-2947 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T05:55:59Z |
| publishDate | 2008 |
| publisher | Pergamon |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-29472017-09-13T14:32:14Z A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system Prattichizzo, D. Ntogramatzidis, Lorenzo Marro, G. Hamiltonian system Continuous-time systems Geometric techniques Cheap LQ problem The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the original system, and the optimal feedback gain is computed as the friend matrix of the resolving subspace. This study yields a new computational framework for the cheap LQ regulator, relying only on the very basic and simple tools of the geometric approach, namely the algorithms for controlled and conditioned invariant subspaces and invariant zeros. 2008 Journal Article http://hdl.handle.net/20.500.11937/2947 10.1016/j.automatica.2008.02.009 Pergamon fulltext |
| spellingShingle | Hamiltonian system Continuous-time systems Geometric techniques Cheap LQ problem Prattichizzo, D. Ntogramatzidis, Lorenzo Marro, G. A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system |
| title | A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system |
| title_full | A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system |
| title_fullStr | A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system |
| title_full_unstemmed | A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system |
| title_short | A new approach to the chap LQ regulator exploiting the geometric properties of the Hamiltonian system |
| title_sort | new approach to the chap lq regulator exploiting the geometric properties of the hamiltonian system |
| topic | Hamiltonian system Continuous-time systems Geometric techniques Cheap LQ problem |
| url | http://hdl.handle.net/20.500.11937/2947 |