Finite-time inter-layer projective synchronization of Caputo fractional-order two-layer networks by sliding mode control

摘要

Finite-time inter-layer projective synchronization (FIPS) of Caputo fractional-order two-layer net-works (FTN) based on sliding mode control (SMC) technique is investigated in this article. Firstly, in order to realize the FIPS of FTN, a fractional-order integral sliding mode surface (SMS) is established. Then, through the theory of SMC, we design a sliding mode controller (SMCr) to ensure the appearance of sliding mode motion. According to the fractional Lyapunov direct method, the trajectories of the system are driven to the proposed SMS, and some novel sufficient conditions for FIPS of FTN are derived. Furthermore, as two special cases of FIPS, finite-time inter-layer synchronization and finite-time interlayer anti-synchronization for the FTN are studied. Finally, this paper takes the fractional-order chaotic Lu's system and the fractional-order chaotic Chen's system as the isolated node of the first layer system and the second layer system, respectively. And the numerical simulations are given to demonstrate the feasibility and validity of the proposed theoretical results. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.