Geometric optimal control techniques to optimize the production of chemical reactors using temperature control

The dynamics of mass reaction kinetics chemical systems is modeled by the Feinberg-Horn-Jackson graph and under the ``zero deficiency assumption'', the behavior of the solutions is well known and splits into two cases: if the system is not weakly reversible there exists no equilibrium, nor periodic solution and if the network is weakly reversible in each stoichiometric subspace there exists only one equilibrium point and this point is asymptotically stable. By varying the temperature, one gets a single input control system and in this article we study the problem of maximizing the production of one species during the batch time. Our aim is to present the geometric techniques and results based on the Pontryagin maximum principle to compute the closed loop optimal solution. The complexity of the problem is illustrated by using two test bed examples: a sequence of two irreversible reactions and the McKeithan scheme. (C) 2019 Elsevier Ltd. All rights reserved.