Adaptive fuzzy H∞ stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach

A novel adaptive fuzzy controller with H_∞ performance is proposed for a wide class of strict-feedback canonical nonlinear systems. The systems may possess a class of uncertainties referred to as unstructured uncertain functions, which are not linearly parameterized and have no prior knowledge of the bound. The Takagi-Sugeno-type fuzzy logic systems are used to approximate the uncertainties and a systematic design procedure is developed for synthesis of adaptive fuzzy control with H_∞ performance, which combines the backstepping technique and generalized small gain approach. The method preserves the three advantages, those are, the semiglobal uniform ultimate bound of adaptive control in the presence of unstructured uncertainties can be guaranteed, the adaptive mechanism with only one learning parameter is obtained and the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques can be removed. Performance and limitations of proposed method are discussed and illustrated with simulation results.