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International Journal of Differential Equations
Volume 2010 (2010), Article ID 461048, 16 pages
http://dx.doi.org/10.1155/2010/461048
Research Article

Time-Optimal Control of Systems with Fractional Dynamics

Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, Utah State University, 41260 Old Main Hill, Logan, UT 84322-4160, USA

Received 1 August 2009; Accepted 5 December 2009

Academic Editor: Wen Chen

Copyright © 2010 Christophe Tricaud and YangQuan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.