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.