Probabilistic observers for a class of uncertain biological processes

In this paper, probabilistic observers are considered for a class of continuous biological processes described by mass-balance-based models. It is assumed that the probability density functions (PDFs) of the uncertain parameters and inputs of the model, as well as the PDFs of the missing initial conditions are known. Then, the PDFs of the unmeasured state variables are obtained, at any time, by considering the image of these initial PDFs by the flow of the dynamic model (differential system). In comparison to classical open-loop asymptotic and interval observers, the method provides information on the confidence level of the estimates rather than simple upper and lower bounds. Moreover, unlike Kalman filters, probabilistic observers are not restricted to Gaussian distributions for the uncertain parameters. The design and application of a probabilistic observer to an industrial wastewater treatment plant is presented. Finally, a number of practical considerations is discussed in connection to both implementation and utilization issues.