Approximate feedback linearization for nonlinear systems

The purpose of this paper is to explain a design method of an approximate feedback linearization. Our procedure shows first the problem formulation and then clarifies the approximate feedback linearization method. In this method, we settle a state transformation matrix in order to transform approximately the nonlinear system into a controllable canonical form. After that, we apply a nonlinear control input making the approximation term small, and use a standard nonlinear linearization method. That makes our system in the new coordinates becomes a stable linear one. Lastly, through the application to the ACROBOT, we show the effectiveness of this new method and compare it to a previous method.