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The Scientific World Journal
Volume 2014 (2014), Article ID 521625, 8 pages
http://dx.doi.org/10.1155/2014/521625
Research Article

On Fractional Model Reference Adaptive Control

Institute of System Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai 264001, China

Received 19 August 2013; Accepted 30 October 2013; Published 16 January 2014

Academic Editors: A. Atangana, S. C. O. Noutchie, and A. Secer

Copyright © 2014 Bao Shi et al. 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

This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology.