一类非线性混沌系统的自适应滑模同步

基于自适应滑模控制方法,研究一类非线性混沌系统在模型不确定和外部扰动的情况下的同步问题。设计一种新的非奇异终端滑模面,并证明其稳定性。利用Lyapunov稳定性理论,推导出一种滑模控制律,将误差系统轨迹驱动到滑模面上,保证滑模运动的发生。应用上述控制方案得到一类带有模型不确定性和外部扰动项的整数阶及分数阶非线性混沌系统的同步。以分数阶Victor-Carmen系统为例进行数值仿真,验证了本研究提出的滑模控制技术的适用性和有效性,并验证了本研究的理论结果。

Adaptive sliding mode synchronization of a class of nonlinear chaotic systems

The synchronization of a class of nonlinear chaotic systems with model uncertainties and external disturbances was studied based on adaptive sliding mode control. A novel nonsingular terminal sliding surface was proposed and its stability was proved. On the basis of Lyapunov stability theory, a sliding mode control law was derived to force the trajectory of the synchronization error systems onto the sliding surface and to guarantee the occurrence of the sliding motion. The proposed control scheme was applied to synchronize chaos of integer order and fractional-order nonlinear chaotic systems in the presence of both model uncertainties and external disturbances. A numerical simulation taking the fractional Victor-Carmen system as the example demonstrated the applicability and efficiency of the proposed sliding mode control technique and verified the theoretical results of the research.