A new technique is proposed in this paper to synchronize chaotic systems. A time-synchronized predefined-time sliding mode control is designed such that the error dynamics between the drive and response systems converge to the origin simultaneously and within the predefined time. To realize the proposed notion of stability, a new sliding surface is introduced, and control laws are defined. The stability of the error dynamics and sliding surfaces is proved in the sense of Lyapunov by considering the effect of both smooth and non-smooth disturbances. Subsequently, two recently developed chaotic systems are successfully synchronized using the designed controller. A multi-wing chaotic system and a two-wing chaotic system are, respectively, taken as the drive and the response systems, and there is the coexistence of attractors in both systems. Further, the efficacy of the controller is validated using MATLAB simulations.

中文翻译：

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两个不同混沌系统之间的时间同步预定义时间同步

本文提出了一种同步混沌系统的新技术。设计了时间同步的预定义时间滑模控制，使得驱动系统和响应系统之间的误差动态在预定义时间内同时收敛到原点。为了实现所提出的稳定性概念，引入了新的滑动面，并定义了控制律。通过考虑光滑和非光滑扰动的影响，在李亚普诺夫意义上证明了误差动力学和滑动面的稳定性。随后，两个最近开发的混沌系统使用设计的控制器成功同步。分别将多翼混沌系统和双翼混沌系统作为驱动系统和响应系统，两个系统中都存在吸引子共存。此外，控制器的功效通过 MATLAB 仿真进行了验证。