Design 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 of every uncertain parameter, input and/or initial state is known a priori. Then, the probability density of the state variables is obtained, at any time, by considering the image of this initial probability density 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. Applications to an anaerobic wastewater treatment process are described in order to illustrate the method.