Predefined-Time Polynomial-Function-Based Synchronization of Chaotic Systems via a Novel Sliding Mode Control

Abstract

In the context of chaotic secure communication, this paper is concerned with the predefinedtime polynomial-function-based synchronization of chaotic systems via sliding mode control. Firstly, a novel hybrid synchronization scheme among multiple chaotic systems based on polynomial function is defined. Subsequently, based on a new predefined-time stability criterion, a novel multi-power integral terminal sliding mode control algorithm is designed to realize the predefined-time polynomial-functionbased synchronization. Finally, the secure communication simulation is presented to verify the feasibility and efficiency of the proposed synchronization scheme. The polynomial-function-based synchronization not only uses the addition and subtraction of vectors, but also uses the power multiplication of vectors, which makes the nonlinear structure of the composed drive system more complex, so that the communication scheme is more secure. Applying the sliding mode control algorithm designed in this work, the synchronization time can be preset off-line without estimation, moreover, the ratio between the formation time and the convergence time of sliding mode can also be distributed in advance, which is more flexible. INDEX TERMS Polynomial-function-based synchronization, Predefined-time synchronization, Chaotic secure communication, Multi-power integral terminal sliding mode control, Settling time function.

Terminal Sliding‐Mode Control of Uncertain Robotic Manipulator System with Predefined Convergence Time

“…Among these methods, the Lyapunov-function-based PTC algorithm proposed in [39] has the advantages of simple structure and easy implementation. us, in recent two years, the PTC algorithm of [39] has been applied to synchronization of chaotic systems [40][41][42][43] and trajectory tracking control of robotic manipulator systems [44]. In particular, for the uncertain robotic manipulator system, the authors in [44] combined the PTC algorithm of [39] with the SMC to construct a robust predefined-time SMC which has greatly promoted the development of predefined-time control for the uncertain robotic manipulator system.…”