Optimalitypreserving Reduction of Chemical Reaction Networks
Abstract
Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology, CRN parameters such as the kinetic reaction rates can be used as control inputs to steer the system toward a given target. Unfortunately, the resulting optimal control problem is nonlinear, therefore, computationally very challenging. We address this issue by introducing an optimalitypreserving reduction algorithm for CRNs. The algorithm partitions the original state variables into a reduced set of macrovariables for which one can define a reduced optimal control problem from which one can exactly recover the solution of the original control problem. Notably, the reduction algorithm runs with polynomial time complexity in the size of the CRN. We use this result to reduce reachability and control problems of largescale proteininteraction networks and vaccination models with hundreds of thousands of state variables.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.08553
 arXiv:
 arXiv:2301.08553
 Bibcode:
 2023arXiv230108553L
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control