Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

Abstract

In this paper, the sliding-mode control method was used to control a class of general nonlinear fractional-order systems which covers a wide class of chaotic systems. A novel sliding manifold with an additional nonlinear part which achieved better control performance was designed. Furthermore, a novel fixed-time reaching law with a fractional adaptive gain is proposed, where the reaching time to the sliding manifold is determined by the first positive zero of a Mittag–Leffler function and is independent of initial conditions. We have provided some instructions on tuning the parameters of the proposed reaching law to avoid exacerbating the chattering phenomenon. Finally, simulation examples are presented to validate all results.

Keywords

• sliding mode control
• fractional order systems
• fixed-time reaching law
• Mittag–Leffler function