Time-Optimal Control of Systems with Fractional Dynamics
We introduce a formulation for the time-optimal control problems of systems displaying fractional dynamics in the sense of the Riemann-Liouville fractional derivatives operator. To propose a solution to the general time-optimal problem, a rational approximation based on the Hankel data matrix of the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/461048 |
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| _version_ | 1849683237361680384 |
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| author | Christophe Tricaud YangQuan Chen |
| author_facet | Christophe Tricaud YangQuan Chen |
| author_sort | Christophe Tricaud |
| collection | DOAJ |
| description | We introduce a formulation for the time-optimal control
problems of systems displaying fractional dynamics in the sense of the
Riemann-Liouville fractional derivatives operator. To propose a solution
to the general time-optimal problem, a rational approximation based on
the Hankel data matrix of the impulse response is considered to emulate
the behavior of the fractional differentiation operator. The original problem is then reformulated according to the new model which can be solved
by traditional optimal control problem solvers. The time-optimal problem is extensively investigated for a double fractional integrator and its
solution is obtained using either numerical optimization time-domain
analysis. |
| format | Article |
| id | doaj-art-c953538783834eecb9141ecf7eb4f47e |
| institution | DOAJ |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-c953538783834eecb9141ecf7eb4f47e2025-08-20T03:23:58ZengWileyInternational Journal of Differential Equations1687-96431687-96512010-01-01201010.1155/2010/461048461048Time-Optimal Control of Systems with Fractional DynamicsChristophe Tricaud0YangQuan Chen1Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, Utah State University, 41260 Old Main Hill, Logan, UT 84322-4160, USACenter for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, Utah State University, 41260 Old Main Hill, Logan, UT 84322-4160, USAWe introduce a formulation for the time-optimal control problems of systems displaying fractional dynamics in the sense of the Riemann-Liouville fractional derivatives operator. To propose a solution to the general time-optimal problem, a rational approximation based on the Hankel data matrix of the impulse response is considered to emulate the behavior of the fractional differentiation operator. The original problem is then reformulated according to the new model which can be solved by traditional optimal control problem solvers. The time-optimal problem is extensively investigated for a double fractional integrator and its solution is obtained using either numerical optimization time-domain analysis.http://dx.doi.org/10.1155/2010/461048 |
| spellingShingle | Christophe Tricaud YangQuan Chen Time-Optimal Control of Systems with Fractional Dynamics International Journal of Differential Equations |
| title | Time-Optimal Control of Systems with Fractional Dynamics |
| title_full | Time-Optimal Control of Systems with Fractional Dynamics |
| title_fullStr | Time-Optimal Control of Systems with Fractional Dynamics |
| title_full_unstemmed | Time-Optimal Control of Systems with Fractional Dynamics |
| title_short | Time-Optimal Control of Systems with Fractional Dynamics |
| title_sort | time optimal control of systems with fractional dynamics |
| url | http://dx.doi.org/10.1155/2010/461048 |
| work_keys_str_mv | AT christophetricaud timeoptimalcontrolofsystemswithfractionaldynamics AT yangquanchen timeoptimalcontrolofsystemswithfractionaldynamics |