Stochastic stabilization of the chaotic finance system via adaptive fixed-time control

This investigation concentrates on the stochastic fixed-time stabilization(SFxS) of the chaotic finance sys-tem(CFS) in noisy environment. The adaptive control and fixed-time control techniques are integrated successfully, which not only can stabilize the CFS within a fixed-time, but also not necessary to determine the related controlling gains beforehand. Particularly, the adaptive fixed-time control protocol is continuous and smooth, which strips out the signum function from the conventional fixed-time control schemes so that the chattering phenomenon can be eliminated effectively. Furthermore, according to the theory of stochastic fixed-time stability, the sufficient condition is deduced and the upper bound estimation of settling time(UPT) is also obtained, which is irrelevant to the initial states of CFS. Finally, simulation results validate the correctness and effectiveness of theoretical analysis.