Backstepping design of uncertain nonlinear systems based on adaptive fuzzy approximation

A novel adaptive fuzzy approach is proposed in this paper to control a class of uncertain strict-feedback nonlinear systems. The approach employs nonlinearly parameterized fuzzy systems to approximate the unknown nonlinear functions in the design of the controlled system, which removes the restriction that basis functions of the fuzzy systems must be known. Following a backstepping procedure, an adaptive fuzzy controller is obtained which guarantees that all signals in the closed-loop system are bounded and the output of the controlled system converges to a small neighborhood of the given reference signal. The main advantages of the proposed approach are that it does not require the fuzzy approximators with known basis functions, and the computation burden of the controller is reduced by managing to decrease the on-liner parameters. An example is included to demonstrate the effectiveness of the approach.