Novel Flexible Sliding Mode Control for Projective Synchronization of Mismatched Time-Delayed Fractional-Order Nonlinear
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RESEARCH PAPER
Novel Flexible Sliding Mode Control for Projective Synchronization of Mismatched Time-Delayed Fractional-Order Nonlinear Systems with Unknown Parameters and Disturbances Susan Razmara1 • Meisam Yahyazadeh1
•
Hassan Fatehi Marj1
Received: 27 February 2020 / Accepted: 13 October 2020 Ó Shiraz University 2020
Abstract In this paper, the problem of projective synchronization between time-delayed fractional-order nonlinear systems with mismatched fractional orders, non-identical time-delays, unknown parameters and external disturbances is investigated. To solve this problem, a time-delayed fractional-order integral sliding surface is firstly introduced. Then, based on the fractional-order Lyapunov stability analysis and sliding mode control strategy, a novel flexible robust control scheme which includes the compensation controller, the sliding mode controller and the adaptive controller is derived that ensures the projective synchronization error dynamical system operates in the sliding mode. Furthermore, the necessary conditions for the error dynamics to be globally asymptotically stable in the sliding mode are determined. Finally, the validity of the achieved theoretical results is verified by a numerical example. The advantages of the proposed control scheme in comparison with previous approaches are also shown. Keywords Flexible sliding mode control Projective synchronization Mismatched fractional orders Non-identical timedelays Unknown parameters and disturbances
1 Introduction Chaos is an interesting and complex phenomenon. Chaotic systems have exotic features like high sensitivity to initial states. The butterfly effect is the name of this feature (Gleick 1997; Guan and Qin 2016). Due to this feature, chaos was considered as a harmful phenomenon for a long time until Pecorra and Carroll first presented the definition for synchronization of chaotic systems in 1990 (Pecora and Carroll 1990). Over the past few decades, chaos synchronization has received more attention due to its applications in many fields such as information processing, electronic circuits, secure communications and encryption-decryption (Xie et al. 2002; Aghababa and Aghababa 2012; Ahmad et al. 2018; Wang et al. 2019).
& Meisam Yahyazadeh [email protected] 1
Department of Electrical Engineering, Faculty of Engineering, Vali-e-Asr University of Rafsanjan, 7718897111 Rafsanjan, Iran
In the past years, chaotic systems described by fractional calculus have been used more often than the those which are described by classical calculus in applications of synchronization, especially in the field of secure communication process (Durdu and Uyarog˘lu 2017; Jia et al. 2018). This is due to the following reasons: (1) Fractional calculus has infinite memory. Therefore, it can describe nonlinear phenomena more accurately compared to classical calculus. (2) Fractional calculus provides more adjustable variables for the model and thus, as a powerful mathematical instrument can model chaotic systems more precisely compared to clas
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