Stochastic fixed-time synchronization of chaotic systems via smooth control

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.

Automated summary

This study proposes a novel smooth control protocol for fixed-time synchronization of chaotic systems, considering the effects of stochastic noise. The results demonstrate robustness of fixed-time synchronization to noise perturbation.