Toward a Geometric Theory in the Time-Minimal Control of Chemical Batch Reactors

In this article we outline a geometric theory for the time-minimal control of chemical batch reactors by analyzing the equations from Pontryagin's maximum principle applied to the optimal control problem. This theory is used for computing the optimal feedback law for a batch reactor in which three species $X,Y,Z$ are reacting according to the scheme $X\rightarrow Y\rightarrow Z$ and every reaction in the sequence obeys first-order kinetics. The control variable is the derivative of the temperature in the reactor, and the terminal condition is a specified ratio of concentrations of species $X$ and $Y$.