A New Robust Finite-Time Synchronization and Anti-Synchronization Method for Uncertain Chaotic Systems by Using Adaptive
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A New Robust Finite-Time Synchronization and Anti-Synchronization Method for Uncertain Chaotic Systems by Using Adaptive Estimator and Terminal Sliding Mode Approaches Wanghui Li1 · Ganghua Bai1 · Hashem Imani Marrani2 Received: 17 March 2020 / Accepted: 24 September 2020 © Brazilian Society for Automatics--SBA 2020
Abstract In this paper, a new robust adaptive finite-time synchronization method has been proposed for chaotic systems by considering model uncertainties and external disturbances. The finite-time synchronization between master and slave systems is achieved under terminal sliding mode control method. The most important innovation of this paper is designing of an adaptive law to estimate the unknown upper bound of the disturbance and uncertainty. To handle the disturbances/uncertainties with unknown upper bounds and get finite-time synchronization, the adaptive law is combined with terminal sliding mode control method. Numerical simulation results and comparative studies show the effectiveness of proposed method. Keywords Synchronization · Anti-synchronization · Finite-time synchronization · Terminal sliding mode control · Robust adaptive finite-time synchronization
1 Introduction Chaos as an interesting complex nonlinear phenomenon in nature can be applied to various fields of science and technology, such as population dynamics, engineering, biomedical systems analysis, fluid dynamics, economics, electric circuits, cryptology, nonlinear circuits, synchronization, and so on. Schiff et al. (1994), Chen and Lai (1998), Guan and Liu (2010), Liu and Guan (2011), Liu (2012), Wang et al. (2002, 2012), Zhang et al. (2013), Buscarino et al. (2012), Wu et al. (2007), Kiliç et al. (2006), Rong and Xiaoning (1998). Many chaotic systems with different characteristics are reported in the works of the literature for instance Lorenz (1963), Lü et al. (2002), Rössler (1976, 1979), Bhalekar-Gejji (Singh et al. 2014), Chen system (Chen and Ueta 1999), etc. One of the fundamental subjects in chaotic systems is the issue of synchronization. Both chaos and synchronization are
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Wanghui Li [email protected] Hashem Imani Marrani [email protected]
1
Electronic Information Engineering College, Hebi Polytechnic, Henan 458030, China
2
Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran
significant concepts in science, from a philosophical along with a practical point of view. Synchronization is essential for a wide range of natural phenomena, from cosmology and natural rhythms like heart beating (Strogatz 2003) and hand clapping (Néda et al. 2000) to superconductors (Wiesenfeld et al. 1996), lasers technology (Winful and Rahman 1990; Oliva and Strogatz 2001; Hirosawa et al. 2013) and other engineering problems (Eckhardt et al. 2007; Strogatz et al. 2005; Belykh et al. 2017; Wu et al. 2019; Ren et al. 2019; Karimi 2012; Karimi 2011). Due to the wide applications of synchronization (Zhang et al. 2008; Pecora et al. 1997; Chen et al. 2004), the problem of synchronization for chaot
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