Optimal temperature control of a lobster plant

Optimal control theory is used to determine the best temperature history for an aquaculture facility to raise lobsters most economically. The differential equations for lobster growth and lobster cost are given and the optimal control problem is solved. Some sample numerical results are presented and the interactions of these theoretical results with practical considerations are discussed. Solutions are presented for both local optimal trajectories (two year lobsters) and global optimal trajectories (three year lobsters). The same approach is applicable to other species under consideration for aquaculture such as other crustacea, mollusks, and finned fish.