keywords: Adaptive approach, chaos control, hyperchaotic, memoritive system, synchronization
This paper studies the control and synchronization of hyperchaotic memoristive circuits with unknown parameters using adaptive control approach. The designed adaptive nonlinear controllers globally control and synchronize two identical hyperchaotic memoristive systems evolving from different initial conditions. The adaptive approach is suitable for addressing uncertainties in systems parameters and environmental disturbances that can badly affect control and synchronization performance. The effectiveness and feasibility of the designed nonlinear controllers is verified and demonstrated numerically.
Aguilar-López R, Martnez-Guerra R & Perez-Pinacho C 2014. Nonlinear observer for synchronization of chaotic systems with application to secure data transmission. European Physical J. Special Topics, 223, 1541–1548. Bao BC, Liu Z & Xu JP 2010. Transient chaos in smooth memristor oscillator, Chinese Physics B, 19(3): 030510-1 - 030510-6. Boutayeb M, Daroach M& Rafaralahy H 2002.Generalized state-space observers for chaotic synchronization and secure communication. IEEE Trans. Circuits. Syst. I, 49(3): 345–349. Cuomo KM, Oppenheim AV & Strogatz SH 1993. Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits Syst. II, Express Briefs, 40: 626–633. Di LC, Liao XF & Wong DW 2005. Lag synchronization of hyperchaos with application to secure communications. Chaos Solitons & Fractals, 23(1): 183–193. Elabbasy EM, Agiza HN & Dessoky MM 2006. Adaptive synchronization of a hyperchaotic system with uncertain parameter. Chaos Solitons & Fractals, 30(5): 1133. Eisencraft M, Fanganiello RD, Grzybowski JMV, Soriano DC, Attux R, Batista AM, Macau EEN, Monteiro LHA, Romano JMT, Suyama R & Yoneyama T 2012. Chaos-based communication systems in non-ideal channels. Commun. Nonlinear Sci. & Numer. Simul., 17(12): 4707–4718. Feki M 2003. An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons & Fractals,18(1): 141–148. Filali RL, Benrejeb M & Borne P 2014. On observer-based secure communication design using discrete-time hyperchaotic systems.Commun.Nonlinear Sci & Numer.Simul.,19(5): 1424–1432. Guan XP, Fan ZP & Chen CL 2002.Chaos Control and Its Application in Secure Communication.National Defence Industry Press, Beijing, pp. 1-37. Ho MC, Hung YC & Chou CH 2002.Phase and anti-phase synchronization of two chaotic systems by using active control. Physics Letters, A 296(1): 43–48. Liu YJ, Tong SC, Wang W & Li YM 2009. Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications. Int. J. Control Automation Sys., 7(4): 681 – 690. Ma DZ, Zhang HG, Wang ZS & Feng J 2010. Fault tolerant synchronization of chaotic systems based on T-S fuzzy model with fuzzy sampled-data controller. Chinese Physics, B19(5): 050506. Mainieri R & Rehacek J 1999. Projective synchronization in three-dimensional chaotic systems.Physical Review Letters, 82: 3042–3045. Michael GR, Arkady SP & Jurgen K 1996. Phase synchronization of chaotic oscillators. Physical Review Letters, 76(11): 1804–1807. Olusola O I, Vincent UE & Njah AN 2009. Global chaos synchronization of coupled parametrically excited pendula. Pramana Journal, 73: 1011–1022. Pan L, Zhou WN, Fang A & Li DQ 2010. A novel active pinning control for synchronization and anti-synchronization of new uncertain unified chaotic systems. Nonlinear Dynamics, 62(1–2): 417–425. Pecora LM, Carroll TL 1990. Synchronization in chaotic system. Physical Review Letters, 64(8): 821 – 824. Pikovsky A, Rosenblum M & Kurths J 2001. Synchronization: A Universal Concept in Non-Linear Sciences. Cambridge University Press, United Kingdom, pp. 1 – 354. Ren HP, Baptista MS & Grebogi C 2013. Wireless communication with chaos. Physical Review Letters, 110: 184101 - 184104. Sundar S & Minai AA 2000. Synchronization of randomly multiplexed chaotic systems with applications to communication. Physical Review Letters, 85(25): 5456–5459. Wang YW & Guan ZH 2006. Generalized synchronization of continuous chaotic system. Chaos Solitons & Fractals, 27(1): 97–101. XingyuanWang N & YaqinWang J 2011. Adaptive control for synchronization of a four-dimensional chaotic system via a single variable. Nonlinear Dynamics, 65: 311–316. Yang SS & Duan CK 1998. Generalized synchronization in chaotic systems.Chaos Solitons & Fractals, 9(10): 1703–1707. Ying T& Chu LO 1997.Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication.Int. J. Bifurcation & Chaos, 7(3): 645–667. Zhang HG, Ma TD, Huang GB & Wang ZL 2010. Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Transactions on Systems, Man & Cybernetics, Part B, 40(3): 831–844. Zhang Y & Sun J 2004. Chaotic synchronization and anti-synchronization based on suitable separation. Physics Letters, A330(6): 442–447.