Global Controllability of Chemical Reactions

TL;DR

This paper investigates the global controllability of chemical reactions using control theory and Lie algebra, identifying conditions under which reactions are controllable and how to control specific reaction steps.

Contribution

It introduces a Lie-algebra based framework for analyzing the controllability of nonlinear chemical reaction systems and characterizes controllability conditions for various reaction types.

Findings

Reactions are controllable almost everywhere if all rate coefficients are controls.

Certain reaction steps can be controlled using only one rate coefficient.

The paper provides a general definition and analysis of consecutive reactions.

Abstract

Controllability of chemical reactions is an important problem in chemical engineering science. In control theory, analysis of the controllability of linear systems is well-founded, however the dynamics of chemical reactions is usually nonlinear. Global controllability properties of chemical reactions are analyzed here based on the Lie-algebra of the vector fields associated to elementary reactions. A chemical reaction is controllable almost everywhere if all the reaction rate coefficients can be used as control inputs. The problem where one can not control all the reaction rate coefficients is also analyzed. The reaction steps whose reaction rate coefficients need to be control inputs are identified. A general definition of consecutive reactions is given, and it turns out that they are controllable almost everywhere by using the reaction rate coefficient of only one reaction step as control input.