Observer Normal Form with Output Injection

Abstract

AbstractThis chapter firstly presents the pioneering work of Krener [6, 7], for the purpose of transforming a general nonlinear system into the so-called nonlinear observer normal form with output injection. As it has been already mentioned in Chap. 1, this form contains a linear part which is of Brunovsky’s canonical form, and a nonlinear part which is only function of measurable variables (i.e., input and output). A set of geometric conditions have been deduced to guarantee the existence of such a change of coordinates (a diffeomorphism) which transforms the studied nonlinear dynamical system into the proposed observer normal form with output injection. In addition, a constructive method has been proposed to facilitate the deduction of this diffeomorphism. After that, we consider how to extend such a method to treat nonlinear systems with inputs, for which the additional Lie bracket conditions need to be considered. Due to the special form of this observer normal form with output injection, a simple Luenberger-like observer [8] can be designed which yields a linear dynamics for the observation error. The concrete design procedures for this type of observer will be discussed in the last section of this chapter.