Diagnosability of stochastic chemical kinetic systems: a discrete event systems approach

We consider the problem of detecting events of interest in a stochastic chemical kinetic system from the perspective of discrete-event systems theory. We define a class of discrete-event systems, timed stochastic automata, that is well-suited for modeling stochastic chemical kinetics and define tA-tAA-diagnosability, two appropriate notions of diagnosability for this class of system. We develop the construction of a timed stochastic diagnoser that is used to provide online updates of the probability that an event of interest has occurred and a means for offline testing of diagnosability conditions. The results of the paper are illustrated using a model of stochastic gene expression.