Adaptive synchronization of fractional-order memristor-based Chua's system

Abstract

Adaptive synchronization of fractional-order memristor-based Chua's circuit is discussed in this paper. Two adaptive synchronization schemes are presented for the fractional-order memristor-based Chua's circuit based on the stability theory of fractional-order differential system, the drive-response concept and the adaptive control principle. Also the case of only one parameter known and the case of all the other parameters fully unknown are discussed. The results show that controller parameters can be adjusted to enhance the convergence rate of the error system. Finally, numerical simulations are drawn to demonstrate these results.

Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

“…where α, β are fractional orders of the states of the systems (8) and (9), respectively, such that 0 < α, β ≤ 1. X, Y ∈ R n are the state variables, A, B ∈ R n×n are the coefficient of the linear parts, and F, G are nonlinear parts such that F, G : R n → R n of the systems (8) and (9), respectively.…”

“…U (X, Y ) is the control input to be determined later. It can be added to the response system (9), to realize the synchronization between the systems (8) and (9).…”

“…Latterly, several techniques and methods have been improved and applied for chaos control and synchronization. Two adaptive synchronization schemes have been analyzed for the fractional-order memristor-based Chua's circuit in [9]. Robust fractional order sliding mode control technique [10] has been applied for synchronization of two fractional-order chaotic systems with external disturbance.…”

Synchronization for linear singularly perturbed complex networks with coupling delays

“…investigated synchronization problem for an array of coupled complex discrete-time networks in the simultaneous presence of both the discrete and distributed time delays. Wang, Jian, and Yu (2014) discussed adaptive synchronization of fractional-order memristor-based Chua's system. Kermania and Sakly (2014) proposed the stability condition for a class of switched nonlinear timedelay systems.…”

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

“…Recently, a number of control schemes have been developed to achieve various synchronization of memristor-based systems and complex systems. The adopted synchronization schemes include adaptive control [30][31][32], backstepping control [33], fuzzy control [8], impulsive control [34,35], etc. The realized synchronization types include complete synchronization [36,37], anti-synchronization [32], projective synchronization [23,38], lag synchronization [24,39], combination synchronization [40,41], compound synchronization [10], etc.…”