To control uncertain strict-feedback chaotic systems, the adaptive backstepping technique is a popular method, yet this method requires repeatedly differentiating virtual control inputs, which will result in the “explosion of complexity” problem. In this paper, an alternative control method for uncertain strict-feedback chaotic systems without using backstepping technique is presented. We first translate the uncertain strict-feedback chaotic system into a new straightforward normative system whose states are unmeasurable, and then, an observer is designed to estimate the unknown states of the transformed system. A new recurrent neural network, namely fuzzy echo state network (FESN), is constructed to approximate the lumped uncertainty of the normative system. The semi-globally stability of the closed-loop system can be guaranteed by the FESN sliding mode controller that only uses one FESN and one adaptation law. Comparative simulations are put forward to verify the derived theoretical results.

为了控制不确定的严格反馈混沌系统，自适应反推技术是一种流行的方法，但这种方法需要反复微分虚拟控制输入，这将导致“复杂性爆炸”问题。本文提出了一种不使用反推技术的不确定严格反馈混沌系统的替代控制方法。我们首先将不确定的严格反馈混沌系统转化为状态不可测量的新的直接规范系统，然后设计一个观察器来估计转换后系统的未知状态。构建了一种新的循环神经网络，即模糊回波状态网络（FESN）来逼近规范系统的集总不确定性。仅使用一个FESN和一个自适应律的FESN滑模控制器可以保证闭环系统的半全局稳定性。提出了比较模拟来验证推导的理论结果。