Parameter Identification and the Finite-Time Combination–Combination Synchronization of Fractional-Order Chaotic Systems with Different Structures under Multiple Stochastic Disturbances

Weiqiu Pan, Tianzeng Li, Muhammad Sajid, Safdar Ali and Lingping Pu
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Weiqiu Pan: College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Tianzeng Li: College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Muhammad Sajid: Faculty of Materials and Chemical Engineering, Yibin University, Yibin 644000, China
Safdar Ali: College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Lingping Pu: College of Liquor, Sichuan University of Science and Engineering, Zigong 643099, China

Mathematics, 2022, vol. 10, issue 5, 1-26

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.

Keywords: fractional-order chaotic system; finite-time synchronization; adaptive sliding mode control; stochastic disturbance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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