Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

Abstract

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

A Robust Control Method forQ-SSynchronization between Different Dimensional Integer-Order and Fractional-Order Chaotic Systems

“…Until now, a variety of control schemes have been proposed to study the problem of chaos synchronization between different dimensional systems such as modified function projective synchronization [20], generalized matrix projective synchronization [21], generalized synchronization [22][23][24], inverse generalized synchronization [25], full state hybrid projective synchronization [26], Q-S synchronization [27], increased order synchronization [28,29], and reduced order generalized synchronization [30]. Amongst all kinds of synchronization, Q-S synchronization has been extensively considered [31][32][33][34][35][36][37][38][39], due to its universality and its great potential applications in applied sciences and engineering.…”