This paper is concerned with the fixed-time synchronization of two chaotic systems, and further takes the stochastic noise into consideration. A novel smooth control protocol is developed to overcome the chattering problem caused by the signum function contained in the conventional finite/fixed-time controllers. In the light of the (stochastic) fixed-time stability theory, the sufficient conditions are derived for achieving the (stochastic) fixed-time synchronization of two chaotic systems, in which the upper bound of synchronization time can be estimated in advance. Finally, two classical chaotic systems are used to verify the validity of proposed theoretical results, which shows that fixed-time synchronization of chaotic systems is robust to noise perturbation.

本文关注的是两个混沌系统的固定时间同步，并进一步考虑了随机噪声。开发了一种新颖的平滑控制协议来克服由包含在传统有限/固定时间控制器中的符号函数引起的抖动问题。根据（随机）固定时间稳定性理论，推导出实现两个混沌系统（随机）固定时间同步的充分条件，其中同步时间的上界可以提前估计。最后，利用两个经典混沌系统验证了所提出理论结果的有效性，表明混沌系统的固定时间同步对噪声扰动具有鲁棒性。