Adaptive Controller using Fuzzy Modeling and Sigmoid Generated Fixed Point Transformation

The great majority of the adaptive nonlinear control design are based on Lyapunov's 2nd or commonly referred to as the Direct method. In the last years the "Sigmoid Generated Fixed Point Transformation (SGFPT)" has been introduced for replacing the Lyapunov technique. This systematic method has been proposed for the generation of whole families of Fixed Point Transformations. In addition it has been extended from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO) systems. Recently, several model building issues are increasingly replaced by soft-computing based methods. In spite of the classical hard-computing methods the intelligent methodologies are able to deal with imprecisions, uncertainties, etc. by an efficient and robust way. Fuzzy logic is widely used for modeling complex and ill-defined systems. In this paper we apply the fuzzy modeling in the SGFPT control design. The applicability of the proposed scheme is confirmed by the adaptive control of the inverted pendulum system. In the investigations an "affine", and a "soft computing-based" model were compared. Simulation results validate that the presented technique fulfills the performance criteria.