Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach
© 2015 The Franklin Institute. In this paper, the linear quadratic regulation problem is investigated for discrete-time antilinear systems. Two cases are considered: finite time state regulation and infinite time state regulation. First, the discrete minimum principle is generalized to the complex d...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Elsevier Ltd
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/27097 |
| _version_ | 1848752168802189312 |
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| author | Wu, A. Qian, Y. Liu, Wan-Quan Sreeram, V. |
| author_facet | Wu, A. Qian, Y. Liu, Wan-Quan Sreeram, V. |
| author_sort | Wu, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2015 The Franklin Institute. In this paper, the linear quadratic regulation problem is investigated for discrete-time antilinear systems. Two cases are considered: finite time state regulation and infinite time state regulation. First, the discrete minimum principle is generalized to the complex domain. By using the discrete minimum principle and dynamic programming, necessary and sufficient conditions for the existence of the unique optimal control are obtained for the finite time regulation problem in terms of the so-called anti-Riccati matrix equation. Besides, the optimal value of the performance index under the optimal control is provided. Furthermore, the optimal regulation problem on an infinite interval is investigated under the assumption that the considered time-invariant antilinear system is controllable. The resulted closed-loop system under the optimal control turns out to be asymptotically stable. |
| first_indexed | 2025-11-14T08:04:20Z |
| format | Journal Article |
| id | curtin-20.500.11937-27097 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:04:20Z |
| publishDate | 2014 |
| publisher | Elsevier Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-270972017-09-13T15:31:39Z Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach Wu, A. Qian, Y. Liu, Wan-Quan Sreeram, V. © 2015 The Franklin Institute. In this paper, the linear quadratic regulation problem is investigated for discrete-time antilinear systems. Two cases are considered: finite time state regulation and infinite time state regulation. First, the discrete minimum principle is generalized to the complex domain. By using the discrete minimum principle and dynamic programming, necessary and sufficient conditions for the existence of the unique optimal control are obtained for the finite time regulation problem in terms of the so-called anti-Riccati matrix equation. Besides, the optimal value of the performance index under the optimal control is provided. Furthermore, the optimal regulation problem on an infinite interval is investigated under the assumption that the considered time-invariant antilinear system is controllable. The resulted closed-loop system under the optimal control turns out to be asymptotically stable. 2014 Journal Article http://hdl.handle.net/20.500.11937/27097 10.1016/j.jfranklin.2015.02.023 Elsevier Ltd restricted |
| spellingShingle | Wu, A. Qian, Y. Liu, Wan-Quan Sreeram, V. Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach |
| title | Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach |
| title_full | Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach |
| title_fullStr | Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach |
| title_full_unstemmed | Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach |
| title_short | Linear quadratic regulation for discrete-time antilinear systems: An anti-Riccati matrix equation approach |
| title_sort | linear quadratic regulation for discrete-time antilinear systems: an anti-riccati matrix equation approach |
| url | http://hdl.handle.net/20.500.11937/27097 |