具有可变系数的三维混沌系统的稳定性控制与电路实现

Stability Control and Circuit Implementation of a Novel 3D Chaotic System with Variable Coefficient

摘要: 本文基于改进型混沌电路模块化设计的方法，设计并搭建了具有可变系数的三维自治混沌系统的模拟电路实现，观察了实际电路产生的混沌运动曲线。而后，通过对该系统进行稳定性控制，使其不再产生混沌(或周期)运动而是全局渐近稳定于平衡点原点，且所设计的控制器对于该系统非线性部分系数的变化具有一定的鲁棒性。在此基础上，通过在实际电路中设计并加入相应的控制器电路，实现了实际电路由混沌运动状态迅速被稳定于平衡点原点的过程。

Abstract: In this paper, an analog circuit implementation of the three-dimensional autonomous chaotic sys-tem with variable coefficient is presented based on the modified module-based approach to chaotic circuit design. The chaotic phase portraits of the circuit are given to illustrate the good qualitative agreement between the numerical simulation and the experimental realization. Then, a linear feedback controller is designed via the Lyapunov stability theory so that the system is no longer chaotic or periodic but globally asymptotically converges to the equilibrium point at the origin. The designed controller is robust to the coefficient change of the nonlinear item. Moreover, after adding the controller circuit to the whole circuit implementation, the rapid change from chaos to convergence can be observed on the oscilloscope.