An isoperimetric optimal control problem for a non-isothermal chemical reactor with periodic inputs

- Mathematical models of nonlinear reactions of the type “A → product” are considered.
- Periodic modulations of the inlet concentration and the temperature are applied.
- The performance maximization is treated as an isoperimetric optimal control problem.
- A theoretical estimate of the optimal number of switchings is obtained.
- Simulation results illustrate the improvement by using bang-bang controls.

In this paper, we study the optimal control problem for a continuous stirred tank reactor (CSTR) that represents a reaction of the type “A → product”. The reactor dynamics is described by a nonlinear system of ordinary differential equations controlled by two inputs: the inlet concentration and the inlet temperature. We formulate the problem of maximizing the average product of this reactor for a fixed consumption of the input component over a period of time. This kind of isoperimetric optimal control problem is analyzed by using the Pontryagin maximum principle with Lagrange multipliers. We show that the optimal controls are bang-bang and propose an upper bound for the number of switchings for the linearized problem with periodic boundary conditions. Numerical simulations confirm that our control strategy can be used to improve the reactor performance over a specified period of time in comparison to the steady-state operation.