A Chattering-Free Finite-Time Robust Synchronization Scheme for Uncertain Chaotic Systems

Aghababa MP, Aghababa HP (2013) Adaptive finite-time synchronization of non-autonomous chaotic systems with uncertainty. J Comput Nonlinear Dyn 8:031006 Bhat SP, Bernstein DS (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38:751–766 Cai N, Jing Y, Zhang S (2010) Modified projective synchronization of chaotic systems with disturbances via active sliding mode control. Commun Nonlinear Sci Numer Simul 15:1613–1620 Cao L, Chen X (2015) Input–output linearization minimum sliding mode error feedback control for synchronization of chaotic system. Proc Inst Mech Eng Part I J Syst Control Eng 229(8):685–699 Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9:1465–1466 Chen Y, Wu X, Gui Z (2010) Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control. Appl Math Model 34:4161–4170 Chen Y, Shi Z, Lin C (2014) Some criteria for the global finite-time synchronization of two Lorenz–Stenflo systems coupled by a new controller. Appl Math Model 38:4076–4085 Chen X, Park JH, Cao J, Qiu J (2017) Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances. Appl Math Comput 308:161–173 Chen X, Park JH, Cao J, Qiu J (2018) Adaptive synchronization of multiple uncertain coupled chaotic systems via sliding mode control. Neurocomputing 273(C):9–21 Du H, Shi P (2016) A new robust adaptive control method for modified function projective synchronization with unknown bounded parametric uncertainties and external disturbances. Nonlinear Dyn 85:355–363 Etemadi S, Alasty A, Salarieh H (2006) Synchronization of chaotic systems with parameter uncertainties via variable structure control. Phys Lett A 357:17–21 Fang L, Li T, Li Z, Li R (2013) Adaptive terminal sliding mode control for anti-synchronization of uncertain chaotic systems. Nonlinear Dyn 74:991–1002 Fedele G, Ferrise A, Chiaravalloti F (2016) Uncertain master–slave synchronization with implicit minimum saturation level. Appl Math Model 40:1193–1198 Feng Y, Han F, Yu X (2014) Chattering free full-order sliding-mode control. Automatica 50:1310–1314 Feng Y, Han F, Yu X (2016) Reply to Comments on’Chattering free full-order sliding-mode control’Automatica 50 (2014) 1310-1314. Automatica (J IFAC) 72:255–256 Fu G (2012) Robust adaptive modified function projective synchronization of different hyperchaotic systems subject to external disturbance. Commun Nonlinear Sci Numer Simul 17:2602–2608 Genesio R, Tesi A (1992) Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28:531–548 Huang X, Lin W, Yang B (2005) Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica 41:881–888 Kwon O, Park JH, Lee S (2011) Secure communication based on chaotic synchronization via interval time-varying delay feedback control. Nonlinear Dyn 63:239–252 Li S, Tian YP (2003) Finite time synchronization of chaotic systems. Chaos Solitons Fractals 15:303–310 Li H, Liao X, Li C, Li C (2011) Chaos control and synchronization via a novel chatter free sliding mode control strategy. Neurocomputing 74(17):3212–3222 Liu Y, Li L, Feng Y (2016) Finite-time synchronization for high-dimensional chaotic systems and its application to secure communication. J Comput Nonlinear Dyn 11:051028 Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141 Mei J, Jiang M, Wang J (2013) Finite-time structure identification and synchronization of drive-response systems with uncertain parameter. Commun Nonlinear Sci Numer Simul 18:999–1015 Park KB, Lee JJ (1996) Comments on “A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators”. IEEE Trans Autom Control 41:761–762 Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821–824 Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398 Salarieh H, Shahrokhi M (2008) Adaptive synchronization of two different chaotic systems with time varying unknown parameters. Chaos Solitons Fractals 37:125–136 Slotine JJE, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs Tran XT, Kang HJ (2015) Robust adaptive chatter-free finite-time control method for chaos control and (anti-) synchronization of uncertain (hyper) chaotic systems. Nonlinear Dyn 80:637–651 Utkin VI (1978) Sliding modes and their application in variable structure systems. Mir Publishers, Moscow Vaidyanathan S, Azar AT (2015) Anti-synchronization of identical chaotic systems using sliding mode control and an application to Vaidyanathan–Madhavan chaotic systems. In: Azar A, Zhu Q (eds) Advances and applications in sliding mode control systems. Springer, Cham, pp 527–547 Vargas JA, Grzeidak E, Gularte KH, Alfaro SC (2016) An adaptive scheme for chaotic synchronization in the presence of uncertain parameter and disturbances. Neurocomputing 174:1038–1048 Wang H, Han Z, Xie Q, Zhang W (2009) Finite-time chaos synchronization of unified chaotic system with uncertain parameters. Commun Nonlinear Sci Numer Simul 14:2239–2247 Yang T, Wu CW, Chua LO (1997) Cryptography based on chaotic systems. IEEE Trans Circuits Syst I Fundam Theory Appl 44:469–472 Yau HT (2004) Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos Solitons Fractals 22:341–347 Zhihong M, Paplinski AP, Wu HR (1994) A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators. IEEE Trans Autom Control 39:2464–2469