|Continuous control functions:||1|
|Interior point equalities:||2|
This batch reactor problem describes the consecutive reaction of some substance A via substance B into a desired product C.
The system is interacted with via the control function which stands for the temperature. The goal is to produce as much of substance B (which can then be converted into product C) as possible within the time limit.
The optimal control problem is given by
and represent the concentrations of A and B at timepoint respectively. The control function represents the temperature.
The starting time and end time are given by .
This solution was computed using JuMP with a collocation method and 300 discretization points. The differential equations were solved using the explicit Euler Method. The source code can be found at Batch reactor (JuMP).
The optimal objective value of the problem is .
Model descriptions are available in