In this work, a sliding mode control (SMC) method and a composite learning SMC (CLSMC) method are proposed to solve the synchronization problem of chaotic fractional-order neural networks (FONNs). A sliding mode surface and an adaptive law are constructed to update parameter estimation. The SMC ensures that the synchronization error asymptotically tends to zero under a strict permanent excitation (PE) condition. To reduce its rigor, online recording data together with instantaneous data is used to define a prediction error about the uncertain parameter. Both synchronization error and prediction error are used to construct a composite learning law. The proposed CLSMC method can ensure that the synchronization error asymptotically approaches zero, and it can accurately estimate the uncertain parameter. The above results obtained in the CLSMC method only requires an interval-excitation (IE) condition which can be easily satisfied. Finally, comparative results reveal the control effects of the two proposed methods.

在这项工作中，提出了滑模控制（SMC）方法和复合学习SMC（CLSMC）方法来解决混沌分数阶神经网络（FONN）的同步问题。构造滑模表面和自适应定律以更新参数估计。SMC确保在严格的永久激励（PE）条件下，同步误差渐近趋于零。为了降低其严格性，在线记录数据与瞬时数据一起用于定义有关不确定参数的预测误差。同步误差和预测误差均用于构造复合学习定律。所提出的CLSMC方法可以确保同步误差渐近逼近零，并且可以准确地估计不确定参数。在CLSMC方法中获得的上述结果仅需要可以轻松满足的间隔激励（IE）条件。最后，比较结果揭示了两种方法的控制效果。