Interval observers for uncertain biological systems

We present a technique for the dynamic estimation of bounds on unmeasured variables (or parameters) of an uncertain dynamical system. Our approach is purely deterministic and relies on interval observers: from (possibly time varying) intervals on the uncertainty and measurements, we compute guaranteed intervals for the unmeasured variables. This method is applicable for a class of non-linear systems met in several biological modellings: two examples are shown, one model of a three stages structured population, and one of biological water treatment.