Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form

Adaptive fuzzy control is proposed for a class of affine nonlinear systems in strict-feedback form with unknown nonlinearities. The unknown nonlinearities include two types of nonlinear functions: one satisfies the “triangularity condition” and can be directly approximated by fuzzy logic system, while the other is assumed to be partially known and consists of parametric uncertainties. Takagi–Sugeno type fuzzy approximators are used to approximate unknown system nonlinearities and the design procedure is a combination of adaptive backstepping and generalized small gain design techniques. It is proved that the proposed adaptive control scheme can guarantee the uniformly ultimately bounded (UBB) stability of the closed-loop systems. Simulation studies are shown to illustrate the effectiveness of the proposed approach.