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

• Published in: Chaos, solitons and fractals Vol. 189; p. 115610
• Main Authors: Sun, Yunkang, Chen, Yuquan, Wang, Bing, Ma, Cheng
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2024
• Subjects: Chaotic system synchronization; Fractional order chaotic system; Predefined-time convergence; Sliding mode control; Chaotic system synchronization; Predefined-time convergence; Sliding mode control; Fractional order chaotic system
• ISSN: 0960-0779
• DOI: 10.1016/j.chaos.2024.115610

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. •A novel predefined-time convergence criterion with an adaptive gain is proposed, which is rigorously proven by using the zero distribution property of sine functions.•A novel adaptive fractional order sliding mode surface with fewer tuning parameters is designed, with which the error system will converge to zero within a predefined-time.•A novel sliding mode controller with a predefined-time reaching law is proposed, with which the error system will reach the sliding mode surface within a predefined-time.