Optimal Control Strategies for Composting Processes in Biocells with $L^1$ and $L^2$ type Cost Objectives.

We present a finite horizon optimal control problem for composting in biocell. The problem is based on a mathematical model, which describes the degradation of organic waste by an aerobic biomass. Solubilization of insoluble substrate and biomass decay phenomena are also taken into account. The degradation is controlled by monitoring the effects of oxygen concentration in the cell. The optimal strategy is determined by minimizing the total costs given by the final size of soluble substrate and the operating cost. We consider two different cases, where the operating cost is modeled by linear and quadratic function of the effort, respectively. It is shown that the total costs over the considered time interval are higher in the linear case than in the quadratic case. Moreover, when compared to the quadratic case, the linear case results in a higher reduction of soluble substrate concentration but it requires also a higher effort to control the degradation.