Abstract
This paper researches the issue of the finite-time combination-combination (C-C) synchronization (FTCCS) of fractional order (FO) chaotic systems under multiple stochastic disturbances (SD) utilizing the nonsingular terminal sliding mode control (NTSMC) technique. The systems we considered have different characteristics of the structures and the parameters are unknown. The stochastic disturbances are considered parameter uncertainties, nonlinear uncertainties and external disturbances. The bounds of the uncertainties and disturbances are unknown. Firstly, we are going to put forward a new FO sliding surface in terms of fractional calculus. Secondly, some suitable adaptive control laws (ACL) are found to assess the unknown parameters and examine the upper bound of stochastic disturbances. Finally, combining the finite-time Lyapunov stability theory and the sliding mode control (SMC) technique, we propose a fractional-order adaptive combination controller that can achieve the finite-time synchronization of drive-response (D-R) systems. In this paper, some of the synchronization methods, such as chaos control, complete synchronization, projection synchronization, anti-synchronization, and so forth, have become special cases of combination-combination synchronization. Examples are presented to verify the usefulness and validity of the proposed scheme via MATLAB.
Highlights
Chaos is not an accidental or individual event, but a universal existence in various macro and micro systems in the universe
One has adopted the active nonlinear control method to address the issue of modified projective synchronization for the fractional order (FO) chaotic systems with noise disturbance in Ref. [20]
In the light of finite-time Lyapunov stability theory and the sliding mode control (SMC) technique, we propose an FO adaptive combination controller and some appropriate adaptive control laws (ACL)
Summary
Chaos is not an accidental or individual event, but a universal existence in various macro and micro systems in the universe. With full consideration of system uncertainties and external disturbances in the given time as well as the unknown system parameters, no researchers have considered this situation There is another fact that we must note that the aforementioned papers focused on the single D-R system for the synchronization scheme. In response to this situation, we are going to consider the finite-time combination– combination (C-C) synchronization (FTCCS) of FO chaotic systems with different structures and unknown parameters under multiple SD via the NTSMC technique.
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