Guaranteed recursive non‐linear state bounding using interval analysis

Abstract

Abstract The problem considered here is state estimation in the presence of unknown but bounded state perturbations and measurement noise. In this context, most available results are for linear models, and the purpose of the present paper is to deal with the non‐linear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the perturbation and noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first estimator for which this claim can be made. The precision of the set estimate can be improved, at the cost of more computation. Theoretical properties of the estimator are studied, and computer implementation receives special attention. A simple illustrative example is treated. Copyright © 2002 John Wiley & Sons, Ltd.