Interval Observers for non monotone systems. Application to bioprocess models

We develop an interval observer working in closed loop, for thestate variables estimation of systems whose modelling isuncertain, as it is generally the case for bioprocess models. Theconsidered class of systems consists in a linear component and anonlinear part. The nonlinear part contains the uncertainty butdoes not necessarily fulfil the monotonicity conditions requiredto design an interval observer. We rewrite this term as the sum ofan increasing and of a decreasing function, and then propose aclosed loop interval observer whose error dynamics is acooperative system. A bundle of observers is then generated byappropriately varying the observer gains. A reinitialisationprocedure allows to improve the interval estimation andconvergence rate. The observer performance is illustrated with atwo dimensional model for a wastewater treatment process.