Considering Slow Manifold Based Model Reduction for Multiscale Chemical Optimal Control Problems

TL;DR

This paper explores using slow manifold-based model reduction techniques to efficiently solve optimal control problems in multiscale chemical reaction systems, aiming to improve computational performance and enable real-time applications.

Contribution

It demonstrates how attracting manifold computation methods can be applied to reduce model complexity in chemical kinetics optimal control problems.

Findings

Model reduction improves numerical efficiency.

Attracting manifold methods effectively handle stiffness.

Potential for real-time control in chemical processes.

Abstract

Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore, optimal control problems which contain ordinary differential equations as infinitesimal constraints are even more difficult to handle. Model reduction might offer an approach to improve numerical efficiency as well as avoiding stiffness of such models. We show in this paper in benchmark fashion how attracting manifold computation methods could be exploited to solve optimal control more efficiently while having in mind the ambitious long-term goal to apply them to real-time control problems in chemical kinetics.