## International Journal of Differential Equations

### Time-Optimal Control of Systems with Fractional Dynamics

#### Abstract

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.

#### Article information

Source
Int. J. Differ. Equ., Volume 2010, Special Issue (2010), Article ID 461048, 16 pages.

Dates
Received: 1 August 2009
Accepted: 5 December 2009
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399869

Digital Object Identifier
doi:10.1155/2010/461048

Mathematical Reviews number (MathSciNet)
MR2592741

Zentralblatt MATH identifier
1203.49031

#### Citation

Tricaud, Christophe; Chen, YangQuan. Time-Optimal Control of Systems with Fractional Dynamics. Int. J. Differ. Equ. 2010, Special Issue (2010), Article ID 461048, 16 pages. doi:10.1155/2010/461048. https://projecteuclid.org/euclid.ijde/1485399869

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