A Resetting Observer for Linear Time-Varying Systems with Application to Dynamic Positioning of Marine Surface Vessels

Abstract

This brief presents a resetting observer for linear time-varying (LTV) systems. The motivation for the observer is better handling of unmodeled dynamics and reactiveness to external disturbances without compromising steady-state performance. A reset is triggered if the output estimation error exceeds predefined bounds. The proposed observer uses a finite-time observer (FTO) approach to calculate corrected state estimates after a reset is triggered. The FTO equations are derived for LTV systems, and a method for calculating the state transition matrices online is presented. The observer equations are formulated in a hybrid dynamical systems framework, and sufficient conditions for uniform global preexponential stability are given. The method is applied to observer design for dynamic positioning (DP) of marine surface vessels. Numerical simulations as well as model scale experiments of this application show promising results, with improved transient performance compared to state-of-the-art observers.