In this article we consider a control system modelling a batch reactor in whichthree species X1, X2, X3 are reacting according to thescheme X1 → X2 → X3, each reaction being irreversible. The control is the temperature T of the reactions or the derivative of thistemperature with respect to time. The terminal constraint is to obtain a given concentration of the product X2 at the end of the batch.The objective of our study is to introduce and to apply all the mathematical tools to compute the time optimal control as aclosed-loop function. This work can be used to optimize the yield of chemical batch reactors.
