Observer design for a class of differential-algebraic systems - Application to a bioprocess model

Many physical processes are described by differential-algebraic equations. The numerical simulation of such models usually combines an ODE numerical method together with an optimisation algorithm. In this paper we give a nonlinear observer design permitting to estimate the unknown state without the use of an optimisation algorithm. Numerical simulations using the model of an aerobic culture of recombinant yeast are given to highlight the performance of the proposed observer.