Hybrid synchronization of n–scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback

• Published in: Archives of control sciences Vol. 22; no. 3; pp. 343 - 365
• Main Authors: Rasappan, Suresh, Vaidyanathan, Sundarapandian
• Format: Journal Article
• Language: English
• Published: Warsaw Versita 01.11.2012; De Gruyter Poland
• Subjects: backstepping control; chaos; Chaos theory; Control systems; Control theory; Design engineering; Feedback; hybrid-synchronization; Lur’e system; Mathematical models; n-scroll Chua system; Synchronism; Synchronization
• ISSN: 1230-2384; 2300-2611
• DOI: 10.2478/v10170-011-0028-9

This paper investigates the backstepping control design with novel feedback input approach for controlling chaotic systems to guarantee the complete synchronization as well as the anti-synchronization of chaotic systems, viz. n-scroll Chua (K. Wallace et.al. 2001) and Lur’e chaotic systems. Our theorems on hybrid synchronization for n-scroll Chua and Lur’e (J.Suyken et.al. 1997) chaotic systems is established using Lyapunov stability theory. Based on the Lyapunov function, the backstepping control is determined to tune the controller gain based on the precalculated feedback control inputs. The backstepping scheme is recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. Since the Lyapunov exponents are not required for these calculations, the backstepping control method is effective and convenient to synchronize the chaotic systems. Mainly this technique gives the flexibility to construct a control law. Numerical simulations are also given to illustrate and validate the hybrid synchronization results derived in this paper