A novel fractional order adaptive Sliding Mode Controller design for chaotic Arneodo systems synchronization

This note proposes a novel Fractional Sliding Mode Control (FASMC) scheme design with an adaptive control law for the synchronization of two nonlinear fractional-order Arneodo-type chaotic systems. Following the SMC control methodology, a fractional order dynamical sliding surface is defined and a new self-tuning control law with an adaptive gain is proposed. The resulting sliding mode controller is able to make a fractional chaotic system with state uncertainties (slave system) follow another fractional-order chaotic system (master system) without important oscillations. The proposed design development provides a stability analysis using Lyapunov theory and a numerical example is presented to demonstrate the effectiveness of this fractional adaptive control methodology.