A controller design method for nonlinear systems via a staged-transformation technique

Abstract

The paper addresses a controller design approach for nonlinear systems based on a staged-transformation technique. A new nonlinear state transformation is proposed to transform a complex single-input nonlinear system into a simple intermediate nonlinear model, a nonlinear state feedback is then introduced to transform the intermediate nonlinear model into a linear controllable canonical form. The optimal nonlinear controller to the primitive nonlinear system is derived via a staged-design method. Furthermore, an optimal tracking control law for nonlinear systems is developed. The simulation result of an inverted pendulum example shows that this approach is quite effective, and the nonlinear controller is robust to parameter perturbations.