Eur. Phys. J. Plus (2018) 133: 13
https://doi.org/10.1140/epjp/i2018-11853-y

Regular Article

Robust control for fractional variable-order chaotic systems with non-singular kernel

¹ Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
² CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
³ Univ. Grenoble Alpes, F-38000, Grenoble, France
⁴ CEA LETI MINATEC Campus, F-38054, Grenoble, France

^* e-mail: jgomez@cenidet.edu.mx

Received: 16 November 2017
Accepted: 17 December 2017
Published online: 16 January 2018

Abstract

This paper investigates the chaos control for a class of variable-order fractional chaotic systems using robust control strategy. The variable-order fractional models of the non-autonomous biological system, the King Cobra chaotic system, the Halvorsen’s attractor and the Burke-Shaw system, have been derived using the fractional-order derivative with Mittag-Leffler in the Liouville-Caputo sense. The fractional differential equations and the control law were solved using the Adams-Bashforth-Moulton algorithm. To test the control stability efficiency, different statistical indicators were introduced. Finally, simulation results demonstrate the effectiveness of the proposed robust control.