Hamiltonian Feedback Design for Mass Action Law Chemical Reaction Networks

A special polynomial state feedback structure is proposed for open chemical reaction networks obeying the mass action law (MAL-CRNs) that stabilizes them for any of their admissible positive set of parameters. The proposed feedback makes the closed-loop system a reversible CRN that enables a generalized Hamiltonian description assuming that their number of reversible reactions is less or equal that the number of species. The design is based on solving a mixed integer linear optimization problem (MILP). A simple example is used to illustrate the basic concepts and the design method.