Non-conventional Control Design by Sigmoid Generated Fixed Point Transformation Using Fuzzy Approximation

Lyapunov\u2019s 2nd or Direct method is recognized as being the primary tool of adaptive control of nonlinear dynamic systems. The great majority of the adaptive nonlinear control design rest on Lyapunov\u2019s stability theorem. Recent findings have revealed that the Robust Fixed Point Transformation-based method can succesfully replace the Lyapunov technique. Later the \u201cSigmoid Generated Fixed Point Transformation (SGFPT)\u201d has been introduced. This systematic method has been proposed for the generation of whole families of Fixed Point Transformations. Its extension from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO) systems has also been given. In recent times, the great majority of model building issues are replaced by \u201cSoft Computing\u201d techniques. In contrast to the classical mathematical methods the intelligent methodologies are able to cope with ill-defined systems, disturbances and missing information by an efficient and robust way. Especially fuzzy logic has become to be used to model complex systems. This contribution makes an attempt to utilize the advantages of fuzzy approximation in the SGFPT control design. The theoretical investigations are validated by the adaptive control of the inverted pendulum. Comparative analysis have been carried out between the \u201caffine\u201d and the \u201csoft computing-based\u201d models. Results of numerical simulations confirm the applicability and efficiency of the proposed method