Design and Practical Use of Probabilistic Observers for Mass-balance Based Bioprocess Models

In this paper, the design of probabilistic observers for mass-balance based bioprocess models is investigated. It is assumed that the probability density function of every uncertain parameter, input and/or initial state is known a priori. Then, the probability density functions of the state variables are obtained, at any time, by considering the image of this initial probability density function by the flow of the dynamical system. In comparison to classical open-loop interval observers, the method provides information on the confidence level of the estimates rather than simple upper and lower bounds. The numerical implementation of the method is closely considered and an application to an industrial anaerobic digester is detailed.