Using hybrid automata for set-membership state estimation with uncertain nonlinear continuous-time systems

This paper deals with set membership state estimation for continuous-time systems from discrete-time measurements, in the unknown but bounded error framework. The classical predictor-corrector approach to state estimation uses interval Taylor methods for solving the prediction phase, which are known to have poor performance in presence of large model or input uncertainty. In this paper, we show how to derive more efficient predictors by using a nonlinear hybridization method which builds hybrid automata to characterize the boundaries of reachable sets. The derived continuous-discrete set membership predictor-corrector estimator is then tested with simulated data from a bioreactor. Our method is compared to classical continuous-time interval observers and is shown to have promising performance.