Linear quadratic optimal control via using dynamic compensator
The linear-quadratic (LQ) optimal problem based on dynamic compensation is considered for a general quadratic performance index in this paper. First, it is shown that there exists a dynamic compensator with a proper dynamic order such that the closed- loop system is asymptotically stable and its ass...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
ICIC International
2012
|
| Online Access: | http://www.ijicic.org/contents.htm http://hdl.handle.net/20.500.11937/17772 |
| _version_ | 1848749553737531392 |
|---|---|
| author | Guoshan, Z. Liu, L. Liu, Wan-Quan |
| author_facet | Guoshan, Z. Liu, L. Liu, Wan-Quan |
| author_sort | Guoshan, Z. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The linear-quadratic (LQ) optimal problem based on dynamic compensation is considered for a general quadratic performance index in this paper. First, it is shown that there exists a dynamic compensator with a proper dynamic order such that the closed- loop system is asymptotically stable and its associated Lyapunov equation has a symmetric positive-definite solution. Then, the quadratic performance index is derived to be a simple expression related to the symmetric positive-definite solution and the initial value of the closed-loop system. In order to solve the optimal control problem for the system, the proposed Lyapunov equation is transformed into a Bilinear Matrix Inequality (BMI) and a corresponding path-following algorithm to minimize the quadratic performance index is proposed in which an optimal dynamic compensator can be obtained. Finally, several numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed approach. |
| first_indexed | 2025-11-14T07:22:46Z |
| format | Journal Article |
| id | curtin-20.500.11937-17772 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:22:46Z |
| publishDate | 2012 |
| publisher | ICIC International |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-177722017-05-30T08:11:13Z Linear quadratic optimal control via using dynamic compensator Guoshan, Z. Liu, L. Liu, Wan-Quan The linear-quadratic (LQ) optimal problem based on dynamic compensation is considered for a general quadratic performance index in this paper. First, it is shown that there exists a dynamic compensator with a proper dynamic order such that the closed- loop system is asymptotically stable and its associated Lyapunov equation has a symmetric positive-definite solution. Then, the quadratic performance index is derived to be a simple expression related to the symmetric positive-definite solution and the initial value of the closed-loop system. In order to solve the optimal control problem for the system, the proposed Lyapunov equation is transformed into a Bilinear Matrix Inequality (BMI) and a corresponding path-following algorithm to minimize the quadratic performance index is proposed in which an optimal dynamic compensator can be obtained. Finally, several numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed approach. 2012 Journal Article http://hdl.handle.net/20.500.11937/17772 http://www.ijicic.org/contents.htm ICIC International restricted |
| spellingShingle | Guoshan, Z. Liu, L. Liu, Wan-Quan Linear quadratic optimal control via using dynamic compensator |
| title | Linear quadratic optimal control via using dynamic compensator |
| title_full | Linear quadratic optimal control via using dynamic compensator |
| title_fullStr | Linear quadratic optimal control via using dynamic compensator |
| title_full_unstemmed | Linear quadratic optimal control via using dynamic compensator |
| title_short | Linear quadratic optimal control via using dynamic compensator |
| title_sort | linear quadratic optimal control via using dynamic compensator |
| url | http://www.ijicic.org/contents.htm http://hdl.handle.net/20.500.11937/17772 |