Nonlinear Adaptive Control Based on Differential Flatness Theory

Abstract

This chapter analyzes differential flatness theory-based adaptive fuzzy control for complex nonlinear dynamical systems. It is shown that all single-input single-output dynamical systems admit static feedback linearization and can be transformed to a linear canonical (Brunovsky) form. For the latter description the design of a flatness-based adaptive fuzzy controller becomes possible. Moreover, it is shown that multi-input multi-output dynamical systems which admit dynamic feedback linearization can be transformed to a decoupled and linear canonical form for which the design of the flatness-based adaptive fuzzy controller is a straightforward procedure. Moreover, for nonlinear systems that admit dynamic feedback linearization the transformation to a decoupled and linear canonical form is also possible in several cases. For such systems, one can follow again a systematic procedure for the design of the flatness-based adaptive fuzzy controller.