Design of hierarchical terminal sliding mode control scheme for fractional-order systems

This study presents a novel fractional hierarchical terminal sliding mode control (SMC) scheme for finite-time stabilisation of non-autonomous fractional-order dynamical systems. It is assumed that the fractional-order system is disturbed by some model uncertainties and external noises. A novel fractional hierarchical terminal sliding surface is proposed and its finite time convergence to the origin is shown. Based on the fractional Lyapunov stability theorem and SMC theory, a robust sliding mode switching control law is derived to ensure the existence of the sliding motion in finite time. It is mathematically proved that the states of the error can reach the proposed hierarchical terminal sliding surface in finite time. The introduced method is applied for synchronisation of the fractional-order chaotic Arneodo and Genesio systems to show the usefulness of the method. Furthermore, two non-autonomous fractional-order systems, namely Van der Pol equation and gyro system, are successfully stabilised using the proposed strategy to confirm the theoretical results of this study.