A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Abstract

In this paper, attempts are made to design a novel time-varying switching surface in sliding mode control which enables us to synchronize two fractional chaotic systems precisely at any arbitrary pre-specified time. For both Caputo (C) and Riemann-Liuville (RL) derivatives, control laws based on Lyapunov stability theorem are derived. The proposed method is completely robust against existence of uncertainties and exogenous disturbances due to eliminating the reaching phase. Since the sign function is replaced by fractional RL integral of the sign function, the chattering is removed. The simulation results in different scenarios are reported to show the effectiveness of the proposed method.

The Tracking Control of the Variable-Order Fractional Differential Systems by Time-Varying Sliding-Mode Control Approach

“…A global sliding-mode control is proposed, which is continuous and free of chattering. In [51], the synchronization of two FO chaotic systems was studied by use of a novel time-varying SMC precisely at any arbitrary pre-specified time. By an adaptive FO terminal SMC strategy with higher convergence precision, the problem of the tracking control for the linear motor was investigated in [52].…”

Dynamic analysis and fractional-order adaptive sliding mode control for a novel fractional-order ferroresonance system

“…Twenty years ago, Oustaloup and partners proposed the first fractionalorder controller CRONE. [23] Then a variety of fractional-order control methods have been proposed, such as fractional-order PID control, [24] fractional-order sliding mode control, [25,26] fractional-order optimal control, [27] etc. Sliding mode control (SMC) is an effective robust control strategy.…”