不确定分数阶多涡卷混沌系统自适应重复学习同步控制
Adaptive repetitive learning synchronization of uncertain fractional order multi-scroll chaotic systems

研究了不确定分数阶多涡卷混沌系统的自适应重复学习同步控制问题. 通过利用滞环函数, 设计了一类参 数可调的分数阶多涡卷混沌系统. 针对这类分数阶多涡卷混沌系统, 在考虑非参数化不确定性、周期时变参数化不 确定性、常参数化不确定性和外部扰动情况下, 提出了一种重复学习同步控制方案. 利用自适应神经网络技术补偿 了系统中的函数型不确定性, 通过自适应重复学习控制技术处理了周期时变参数化不确定性, 并利用自适应鲁棒学 习项处理了神经网络逼近误差和干扰的影响, 实现了主系统和从系统的完全同步. 综合利用分数阶频率分布模型和 类Lyapunov复合能量函数方法证明了同步误差的学习收敛性. 数值仿真验证了所提方法的有效性.
The adaptive repetitive learning synchronization problem of uncertain fractional order multi-scroll chaotic systems is investigated in this paper. A novel kind of fractional order multi-scroll chaotic system is designed by using hysteresis function, where the number of the scroll can be adjusted by different design parameters. The synchronization problem of this class of systems with non-parametric uncertainty, periodic time-varying parametric uncertainty, constant parametric uncertainty and external disturbances is considered and a repetitive learning based synchronization controller is presented. Adaptive neural network technique is utilized to compensate for the non-parametric uncertainty of the system, periodic time-varying parametric uncertainty is dealt with by adaptive repetitive learning scheme and the neural network approximation errors and external disturbance are handled by adaptive robust learning term. The synchronization error convergence is proven by using frequency distribution models scheme combing with Lyapunov-like energy function. Numerical simulation is given to verify the validity of the proposed method.