A minimum time control problem for aerobic degradation processes in biocell composting plants

We introduce a mathematical model for the composting process in biocells. The
model includes several phenomena, like the aerobic biodegradation of the soluble substrate by means of a bacterial population, the hydrolysis of insoluble
substrate, and the biomass decay. We investigate the best strategies to reduce
substrate components in minimal time by controlling the effects of cell oxygen
concentration on the degradation phenomenon. It is shown that singular controls are not optimal for this model and the optimal control time profiles are of
bang or bang-bang type. The occurrence of switching curves is discussed. In the
case of a bang-bang control we prove that optimal control profiles have a unique
switching time and the corresponding switching curve is determined.