Fuzzy adaptive control for SISO nonlinear uncertain systems based on backstepping and small-gain approach

With the combination of the adaptive backstepping technique and small-gain approach, the adaptive fuzzy tracking control for a class of uncertain single-input and single-output (SISO) nonlinear systems with unmodeled dynamics, dynamic disturbances, unknown dead zone output and unmeasurable states is studied. The designed controller guarantees that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the output of the closed-loop system converges to a small neighborhood of the desired output. In addition, only three adaptive parameters need to be updated online, which simplifies the structure of the controller and promotes the implementation of the proposed scheme in engineering. A Nussbaum-type function is introduced to overcome the difficulty caused by the non-sensitivity of the output in the dead band. A simulation example is given to show the effectiveness of the proposed algorithm.