State observer-based fuzzy echo state network sliding mode control for uncertain strict-feedback chaotic systems without backstepping

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.