(A) study on extended approximate feedback linearization of nonlinear systems with uncertain structure and high-order nonlinearity

Abstract

Generally, in real life, most of systems are expressed in the form of nonlinear system. It is a well-known fact that nonlinear systems usually have very rich and sometimes even unexpected behaviors such that classical linear system theories and techniques have severe limitations if we try to apply them to control nonlinear systems. So, many serious and meaningful researches have been conducted by many scientists and engineers to develop new theories over the linear system theories to mainly targeted for nonlinear systems such as backstepping control, variable structure control, gain scheduling control and feedback linearization control. Among the methods, the main idea of feedback linearization is that a vontroller is developed in a way that it cancels any nonlinear terms in a system to transform the original system models into the equivalent models of simpler form. However, there are also a number of shortcomings and limitations associated with the feedback linearization approach. They are (1) the exact cancelation of nonlinearity is impossible for the uncertain nonlinear system, (2) the class of feedback linearizable system is limited. Recently, some results have been appeared to make feedback linearization robust. The rigorous conditions for feedback linearization are summarized as controllability and involutivity, which are somewhat restrictive - in particular, the involutivity condition. Thus, to overcome this problem, many efforts have been made during the last decade. Among them, the approximate linearization method has been one of the dominant approaches. In practical systems, there are always some parameter uncertainty, model uncertainty, noise exogenous signals, etc. Thus, we propose a feedback linearizing controller with a dynamic diffeomorphism to treat a class of uncertain nonlinear systems that have unknown constant parameters and some model uncertainty. With the proposed method, we analytically show that some of uncertain systems which possess th...