Interval Observer Design Based on Taylor Models for Nonlinear Uncertain Continuous-Time Systems

Abstract

In most applications in control engineering not all state variables can be measured. Consequently, state estimation is performed to reconstruct the non-measurable states taking into account both system dynamics and the measurement model. If the system is subject to interval bounded uncertainties, an interval observer provides a guaranteed estimation of all states. The estimation consists of a recursive application of prediction and correction steps. The prediction step corresponds to a verified integration of the system model describing the system dynamics between two points of time at which measured data is available. In this paper, a Taylor model based integrator is used. Considering the state enclosures obtained in the prediction step, the correction step reconstructs states and parameters from the uncertain measurements with the help of a measurement model. The enclosures of states and parameters determined by the interval observer are consistent with both system and measurement models as well as all uncertainties.