Robust adaptive finite‐time and fixed‐time synchronization of chaotic systems with smooth control

2021 ◽  
Author(s):  
Jie Wu ◽  
Ru‐ru Ma
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Fixed Time ◽  
Smooth Control ◽  
Robust Adaptive

Fixed time synchronization of a class of chaotic systems based via the saturation control

2021 ◽  
Vol 67 (4 Jul-Aug) ◽  
pp. 041401
Author(s):  
Jiaojiao Fu ◽  
Runzi Luo ◽  
Meichun Huang ◽  
Haipeng Su
Keyword(s):  
Upper Bound ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Fixed Time ◽  
Stability Theorem ◽  
Backstepping Method ◽  
Time Stability ◽  
Saturation Control ◽  
New Chaotic System ◽  
Upper Bound Estimate

In this paper, we discuss the fixed time synchronization of a class of chaotic systems based on the backstepping control with disturbances. A new and important fixed time stability theorem is presented. The upper bound estimate formulas of the settling time are also given which are different from the existing results in the literature. Based on the new fixed time stability theorem, a novel saturation controller for the fixed time synchronization a class of chaotic systems is proposed via the backstepping method. Finally, the new chaotic system is taken as an example to illustrate the applicability of the obtained theory.

scholarly journals Finite Time Synchronization for Fractional Order Sprott C Systems with Hidden Attractors

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Cui Yan ◽  
He Hongjun ◽  
Lu Chenhui ◽  
Sun Guan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Engineering Practice ◽  
Fractional Order Systems ◽  
Spectral Entropy ◽  
Hidden Attractors ◽  
Finite Time Stability ◽  
Peculiar Phenomenon

Fractional order systems have a wider range of applications. Hidden attractors are a peculiar phenomenon in nonlinear systems. In this paper, we construct a fractional-order chaotic system with hidden attractors based on the Sprott C system. According to the Adomain decomposition method, we numerically simulate from several algorithms and study the dynamic characteristics of the system through bifurcation diagram, phase diagram, spectral entropy, and C0 complexity. The results of spectral entropy and C0 complexity simulations show that the system is highly complex. In order to apply such research results to engineering practice, for such fractional-order chaotic systems with hidden attractors, we design a controller to synchronize according to the finite-time stability theory. The simulation results show that the synchronization time is short and the robustness is stable. This paper lays the foundation for the study of fractional order systems with hidden attractors.

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