Analysis of switching strategies for the optimization of periodic chemical reactions with controlled flow-rate

TL;DR

This paper analyzes optimal switching strategies for periodic chemical reactions with controlled flow-rate, using Pontryagin's principle and Chen-Fliess expansion to derive analytical cost estimates for non-control-affine systems.

Contribution

It introduces a novel approach to optimize non-isothermal chemical reactions with non-control-affine dynamics and state-dependent costs using switching time parametrization.

Findings

Optimal controls are piecewise constant.

Analytical cost estimates are derived for small periods.

The method applies to non-control-affine, nonlinear systems.

Abstract

An isoperimetric optimal control problem with non-convex cost is considered for a class of nonlinear control systems with periodic boundary conditions. This problem arises in chemical engineering as the maximization of the product of non-isothermal reactions by consuming a fixed amount of input reactants. It follows from the Pontryagin maximum principle that the optimal controls are piecewise constant in the considered case. We focus on a parametrization of optimal controls in terms of switching times in order to estimate the cost under different switching strategies. We exploit the Chen-Fliess functional expansion of solutions to the considered nonlinear system with bang-bang controls to satisfy the boundary conditions and evaluate the cost analytically for small periods. In contrast to the previous results in this area, the system under consideration is not control-affine, and the integrand of the cost depends on the state. This approach is applied to non-isothermal chemical reactions with simultaneous modulation of the input concentration and the volumetric flow-rate.