Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

This paper concerns the problem of fixed-time synchronization of master-slave Lorenz systems. The adaptive control and fixed-time control strategies are successfully integrated so that not only the Lorenz systems can be synchronized within a fixed-time, but also the related controlling gains are not necessary to select beforehand. Distinguished from the conventional fixed-time control schemes, the proposed controller do not contain the signum function anymore, thereby the chattering behavior is avoided owing to its smoothness. The synchronizing condition is deduced according to the theory of fixed-time stability, and the upper bound of settling time is also estimated, which is irrelevant to the initial states of Lorenz systems. Apart from the correctness and effectiveness of theoretical analysis is validated by simulating Lorenz systems, the spirit of adaptive fixed-time control strategy is applied into synchronizing two finance systems finally.

Automated summary

This paper combines adaptive control and fixed-time control strategies to achieve fixed-time synchronization of master-slave Lorenz systems. This method does not require pre-selection of controlling gains and avoids chattering behavior by eliminating the use of the signum function. The synchronizing condition is deduced based on the theory of fixed-time stability, and the upper bound of settling time is independent of the initial states of Lorenz systems. Experimental results validate the effectiveness of this method in synchronizing finance systems.