Approximate feedback linearization for nonlinear systems and its application to the ACROBOT

In this paper, we consider a design method of approximate feedback linearization for nonlinear systems to which the exact linearization method is not applicable. We adopt a two-step procedure to solve the approximate linearization. First, a state transformation matrix is settled, so that the nonlinear system is transformed approximately into the controllable canonical form. Second, a standard nonlinear linearization method is used to transform the controllable canonical form into a stable linear system. Finally, the application of the proposed method to the ACROBOT, which is known as a system to which the exact linearization method cannot be applied, is shown to illustrate the effectiveness of the proposed method.