Synchronization of fractional-order chaotic systems using unidirectional adaptive full-state linear error feedback coupling

Abstract

Based on the stability theory of fractionalorder system, a novel unidirectional adaptive full-state linear error feedback coupling scheme is extended to control and synchronize all of fractional-order differential (FOD) chaotic systems with in-commensurate (and commensurate) orders. The feedback strength is adaptive to an updated law rather than prescribed as a constant. The convergence speed of feedback strength is regulated by a constant. With rigorous linear algebraic theorems and precisely numerical matrix computations, a reasonable interval in which the ultimate final control strength dwells is suggested, and the reliability of synchronization state is guaranteed. It demonstrates that the unidirectional full-state linear feedback coupling scheme can be adopted to control and synchronize FOD chaotic systems directly. Numerical simulations of three representative FOD chaotic systems illustrate the effectiveness of the proposed scheme.

Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters

“…Finally, Control strategy 3 corresponds to the one reported in [6] , which does not need any knowledge of the system parameters, but it uses three control signals U 1 , U 2 , U 3 and three adjustable parameters k 1 , k 2 , k 3 . Basically, Control strategy 3 uses a feedback control in the form…”

“…We can find in literature many works related to adaptive synchronization, whose results can be applied to the adaptive synchronization of fractional Lorenz systems. Different techniques have been proposed in these works, such as modified projective adaptive synchronization [1,4,5] , adaptive full-state linear error feedback [6][7][8] , adaptive sliding mode control [9][10][11][12] , fuzzy generalized projective synchronization [13] , among others [14] . However, these techniques use the maximum possible number of control sig-nals, which in the case of the fractional Lorenz system analyzed in this work is three.…”

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

“…At the same time, fractional-order differential equations have been proved to be an excellent tool in the modelling of many phenomena [9][10][11]. Recently, some important advances on dynamical behaviors such as chaos phenomena, Hopf bifurcation, synchronization control, and stabilization problems for fractional-order systems or fractional-order practical models have been reported in [12][13][14][15][16]. These proposed results show the superiority and importance of fractional calculus and effectively motivate the development of new applied fields.…”

Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order

“…Synchronization of the fractional-order chaotic Lü system was investigated in [18]. After that, many control schemes were proposed for the synchronization and anti-synchronization of fractional-order chaotic systems such as active sliding mode control [19], linear state error feedback control [20], nonlinear control [21], and so on. Huang and Cao [22] studied anti-synchronization of a fractional-order chaotic financial system.…”