Attainability and Suboptimal Minimal Time Control of a Class of Biological Sequencing Batch Reactor

In this paper, geometric tools are used for the attainability study ofbiological Sequencing Batch Reactors (SBR). The objective is to find the set ofinitial conditions from which one can reach a final state target with an admissiblecontrol. The possible solutions can be determined easily once the reachabilityset has been characterized. In a second step, an optimal time control problem isconsidered. It consists in finding the switching instants between the different phasesof the bioreaction. Pontryagin’s Maximum principle is used to solve a part of thisproblem. A suboptimal solution is proposed allowing at most two commutations.A new problem is then considered where the criteria is parameterized by theswitching concentrations. A numerical solution is finally proposed to solve thisnew minimal time problem.