Explore The Exact Linearization Method Of Nonlinear Systems

In this dissertation, the problems of exact linearization techniques for affine systems are investigated. Affine systems are a class of the most important nonlinear systems, which appear in many practical fields. Nonlinearity is one of the most common properties of the system behaviors in the world. It is very complex and hence is hard to cope with. Usually, nonlinear systems can be modeled by a group of nonlinear differential equations. In mathematics, it is very difficult to find an approach available for analyzing the dynamic behaviors of all these nonlinear equations. Hence, in nonlinear analysis, different approaches are developed to study different class of nonlinear systems, which has become an inherent essence in nonlinear analysis.In recent decades, nonlinear geometric approach is proven to be one the most efficient methods for the analysis and synthesis of affine control systems in both theoretic and engineering fields. However, some serious defects also appear in the implementations of it. Hence, it is of much interest to improve the performance of the existing nonlinear geometric approach. To this end, this thesis studies the following two topics on improving the existing skills of geometric approach in exact linearization as well as H-infinity controller designs for affine systems.(i) The existing conditions for exactly-linearizing an affine system are improved, by which, a much more general representation of exact linearization of affine systems is obtained, which is of certain potential impacts in the controller design for affine systems. In order to obtain this result, some new concepts called the linear invariant set of smooth vector field, and the generation set of smooth vector are proposed for affine systems. The relationships between these two concepts and the different forms of smooth vector field in different local coordinates are discussed, based on which, some improved conditions for the exact linearizaion of SISO affine nonlinear system are obtained.(ii) A design technique of H-infinity controllers is proposed for SISO affine nonlinear system Via exact linearization method. Inherently, it is well-known that the process of exact linearization is not robust at all. It relies on the preciosity of the system models very much. To overcome this shortcoming, a nonlinear state feedback controller is designed to ensure the behaviors of close-loop system satisfy a certain H-infinity performance specification. The simulations show that the proposed controller is very effective to solve such a problem.