Transformations of Nonlinear Systems to High-Order Generalized Chained Forms

Abstract

A variety of stabilization methods for nonlinear systems in chained form can be found in the literature. However, very few results exist in the area of systematically converting a general nonlinear system with two inputs to a chained form. This paper presents an algorithm for the conversion of a class of nonlinear systems with two inputs to a high-order chained, or generalized chained, form. The feedback transformation accomplishing this conversion is derived, provided certain conditions hold, by solving a system of partial differential equations. The proposed algorithm is illustrated by means of a physically motivated example, namely an under-actuated surface vessel.