A novel adaptive predefined-time sliding mode control scheme for synchronizing fractional order chaotic systems

In this paper, a novel adaptive predefined-time sliding model control scheme is presented for synchronizing fractional order chaotic systems subject to model uncertainties and external disturbances. A new sufficient criterion for predefined-time stability is proposed and proven to be valid by using the zero distribution property of sine functions. Based on the proposed criterion, a novel adaptive fractional order predefined-time sliding mode surface is designed and it is rigorously proven that the error states could converge to zero within a predefined time. Finally, a novel adaptive fractional order controller is proposed to ensure that the designed sliding mode surface can be reached within a predefined time. Numerous simulation results demonstrate that compared with the existing fixed-time control scheme, the proposed control scheme has the advantage of a simpler structure, fewer parameters and stronger robustness to the variation of initial values.