Some Structural Properties of Reaction Systems Useful For Estimation and Control

The objective of this text is to give an overview of some structural properties of the dynamical models of reaction systems, in particular (but not uniquely) of chemical and biochemical systems as well as environmental and ecological systems, that can be interesting for the analysis and the design of process estimation and control tools. We shall in particular consider the notion of reaction invariants (that will allow us to rewrite part of the system dynamics in a way that is independent of the reaction kinetics) and of singular perturbations (slow/fast dynamics) (that will allow us to generalize the notion of quasi steady states). We also consider a transformation that allows us to diagonalize the stoichiometric coefficient matrix (useful in the implementation of some parameter estimators) and a simple condition based on the system reaction network that allows us to emphasize the possible presence of inverse response/nonminimum phase. Finally, the link between adaptive linearizing control and PI control will be discussed. Links with some important research of Dominique Bonvin will also be emphasized