State-estimators for chemical reaction networks of Feinberg-Horn-Jackson zero deficiency type

TLDR: In this article, the authors provide a necessary and sufficient condition for detectability of observers, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type.

Abstract: One of the most interesting questions in control theory is that of constructing observers. Observers compute estimates of the internal states of a dynamical system, using data provided by measurement probes or partial state information. For linear systems, Luenberger observers (also known as "deterministic Kalman filters" since they amount to Kalman filters designed without regard to the statistics of measurement noise) provide a general solution, but, for nonlinear systems, establishing generally applicable conditions for existence and convergence of observers is an open and active area of research. This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type.