Indistinguishability analysis and observer design for size-structured cell populations

Abstract

The observability property of population balance equations with biomass measurements is addressed within the framework of indistinguishable trajectories. The population balance equation is described by a partial integro-differential equation which is coupled with an ordinary differential equation for the nutrient dynamics. For the semi-discretized model equations, the dynamics of indistinguishable trajectories are derived and evaluated for the special case of equal partitioning at cell division revealing that the observability property is guaranteed as long as the nutrient concentration is not depleted. Based on these results, an observer is designed and tested in simulation to estimate the cell population distribution using biomass measurements in a batch bioreactor for the case of a bi-structured population.