Finite-time inter-layer projective synchronization of Caputo fractional-order two-layer networks by sliding mode control |
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| Authors: | Xifen Wu Haibo Bao Jinde Cao |
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| Institution: | 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, PR China;2. School of Mathematics, Southeast University, Nanjing Jiangsu 210096, PR China;3. Yonsei Frontier Lab, Yonsei University, Seoul 03722, PR Korea;1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China;2. School of Mathematics, Southeast University, Nanjing 210096, China, and Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea;3. School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, Jiangsu 224051, China;4. Department of Mathematics, School of Arts, Science & Humanities, SASTRA DEEMED UNIVERSITY, Thanjavur 613401, Tamil Nadu, India;1. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, China;2. Space Control and Inertial Technology Research Center, Harbin Institute of Technolog, Harbin 150001, China |
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| Abstract: | Finite-time inter-layer projective synchronization (FIPS) of Caputo fractional-order two-layer networks (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 inter-layer anti-synchronization for the FTN are studied. Finally, this paper takes the fractional-order chaotic Lü’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. |
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