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.

质量反应动力学化学系统的动力学由Feinberg-Horn-Jackson图建模，在“零缺陷假设”下，溶液的行为众所周知，分为两种情况：如果系统不是弱可逆的，则存在没有平衡，也没有周期解，如果网络在每个化学计量子空间中都是弱可逆的，则仅存在一个平衡点，并且该点是渐近稳定的。通过改变温度，可以获得一个单一的输入控制系统，在本文中，我们研究了在批处理时间内最大化一种物种的产量的问题。我们的目的是提出基于Pontryagin最大值原理的几何技术和结果，以计算闭环最优解。通过使用两个测试台示例来说明问题的复杂性：