Nonlinear Control Based On Differential Geometry

“Nonlinear control systems” is a subject that deals with the analysis and the design of nonlinear control systems, i.e., the analysis and the design of control system that contains at least one nonlinear component [1]. The classic methods used in the study of the linear systems, particularly the frequency analysis, are not applicable to nonlinear systems [2]. Thus, different approaches are required in order to treat nonlinear systems. Even when considering a linear approach, if the required operation range gets larger, a linear controller may fail. It may become unstable or decrease the desired control performance. In these cases, techniques of nonlinear control may provide better performance. Examples of possible approaches may consider the system linearization around operation points and provide a gain schedule as well as a parameters adaptation (adaptive control). The exact feedback linearization and the approximate feedback linearization use a negative feedback signal that makes the closed loop system to have a linear behavior [1]. The present work consists of detailing with these two last techniques. 2. Using a Geometric Nonlinear Control to Analyse Necessary and Suficient Conditions To Feedback Linearization