Nonlinear Observers, Normal Forms and Model Reduction

University Of California-Davis, Davis CA

Investigators

Abstract

0204390 Krener This proposal is for research on several promising new approaches to designing an observer for a nonlinear control system, including linearization of the state error dynamics, backstepping and multiple extended Kalman filters. In order to decide which type of observer is appropriate for a given nonlinear system, one needs a classification of the range of possibilities. Therefore a study of the normal forms of a nonlinear system under a group action that is appropriate to observer design is also proposed. A control system is a mathematical model of a real world process. It has inputs and outputs which model the way the way the system interacts with the external world and has state variables, which describe the internal memory of the system. The state evolves according to some dynamical model driven by the inputs and the output is some function of the state and possibly the input. The fundamental problem of control systems is to close the loop in such a way as to achieve stability. We wish to use negative feedback based on the current state to stabilize the system to some desirable operating regime. But usually the current state is not directly measurable so we must design an observer to estimate it from the past inputs and outputs. The development of nonlinear observer design methodologies is a paramount problem of systems theory and its applications. There is no current approach that is effective for all nonlinear systems.