Abstract: In this paper, a novel adaptive sliding mode approach for synchronization combining the fractional calculus with terminal sliding mode control is proposed. The scheme is applied to synchronize a class of fractional-order simple pendulum chaotic systems in the presence of model uncertainties and external disturbances. First, based on the fractional calculus a new nonsingular fractional-order terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is analytically proved using the fractional Lyapunov stability theorem. Then, for the case that the bounds of the uncertainties and external disturbances are assumed to be unknown in advance, appropriate adaptive laws are proposed. Afterwards, based on ideas of the adaptive laws and finite-time control, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite peroid. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, a numerical simulation is presented to demonstrate the applicability and effectiveness of the proposed scheme.

Key words: fractional-order systems, terminal sliding mode, chaos synchronization, adaptive control, simple pendulum systems