Observer design for time scale systems

Abstract

In this thesis, the problem of state signals estimation and diagnosis on time scale systems is addressed. We will try to develop new observers for this category of systems, starting first by introducing certain adaptive nonlinear observers for fault diagnosis and the time scale Kalman filter. We establish from the time scale Kalman filter a generalization of the discrete version of the extended Kalman filter to the time scale case, we will also propose an extension of the adaptive nonlinear state observers for fault diagnosis on time scales. The calculations and demonstrations are mainly based on the tools and notions introduced in the theory of time scale analysis. The effectiveness of the observers studied or developed will be illustrated through the numerical simulations results. We also make a comparative study between the discrete and time scale versions of the extended Kalman filters in a target tracking scenario.