Direct adaptive fuzzy control of nonlinear systems in pure feedback form

In this paper, a direct adaptive fuzzy tracking control is proposed for a class of uncertain single-input single-output nonlinear pure feedback systems. The nonlinear functions in systems are completely unknown, and are not linearly parameterized. Takagi-Sugeno type fuzzy systems are used to directly approximate the desired control input signal instead of the unknown nonlinearities in system. Moreover, the proposed adaptive fuzzy controller has a simpler form and requires only one adaptation parameter. As a result, the proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed-loop system are bounded. The efficacy of the proposed algorithm is investigated by an illustrative simulation example of magnetic levitation.