State Observer-Based Fuzzy Echo State Network Sliding Mode Control for Uncertain Strict-Feedback Nonlinear Systems Without Backstepping

For uncertain strict-feedback nonlinear systems (SFNSs), the adaptive back stepping control is a popular method, yet this method requires repeatedly differentiating virtual control inputs, which will result in the "explosion of complexity" problem. In this article, an alternative control method for uncertain SFNSs without the backstepping technique is presented. We fifirst translate the uncertain SFNS 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-global 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 theoretical derivation results