Synchronization and Antisynchronization of a Class of Chaotic Systems With Nonidentical Orders and Uncertain Parameters

Abstract

In this paper, we study the synchronization of a class of uncertain chaotic systems. Based on the sliding mode control and stability theory in fractional calculus, a new controller is designed to achieve synchronization. Examples are presented to illustrate the effectiveness of the proposed controller, like the synchronization between an integer-order system and a fraction-order system, the synchronization between two fractional-order hyperchaotic systems (FOHS) with nonidentical fractional orders, the antisynchronization between an integer-order system and a fraction-order system, the synchronization between two new nonautonomous systems. The simulation results are in good agreement with the theory analysis and it is noted that the proposed control method is of vital importance for practical system parameters are uncertain and imprecise.

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

“…where δ corresponds to the adaptive gain that can be used to handle the convergence speed, then the controlled system (11) , (13) , 14is uniformly stable.…”

“…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.…”

Observer and descriptor satisfying incremental quadratic constraint for class of chaotic systems and its applications in a quadrotor chaotic system

“…al [29] worked on different type of synchronization using active backstepping input for hyper-chaotic systems. In 2015, two non-identical integer and fractional order chaotic systems are considered for synchronization [30] using sliding mode controller. Muñoz-Vázquez et.…”

A New Generalized-Type of Synchronization for Discrete-Time Chaotic Dynamical Systems

“…Chaos (hyperchaos) synchronization has been received a great deal of interest from many feilds [3][4][5][6]. Various methods and different types of synchronization have been developed [7][8][9][10], but most of works have concentrated on continuous-time chaotic systems rather than discrete-time chaotic systems.…”