Detectability for Nondeterministic Discrete Event Systems and Its Applications in Medical Diagnosis

In this paper,we extend our previous results on detectability to nondeterministic discrete event systems.Many practical systems are nondeterministic,especially those in biomedicine.Disease models of patients are usually nondeterministic because hardly anything is deterministic in biological systems.The goal is to determine or estimate the current and subsequent states of a system based on a sequence of observations when the initial state of the system is unknown.We say that a system is detectable if one can determine its state after observing some outputs.The observation includes partial event observation and/or partial state observation.We define four types of detectabilities:strong detectability,(weak) detectability,strong periodic detectability,and (weak) periodic detectability.We derive necessary and sufficient conditions for these detectabilities.These conditions can be checked by constructing an observer,which models the estimation of states under different observation.Furthermore,we apply the results to medical diagnosis by considering a realistic example of diagnosing whether a patient suffers from one of the following five similar diseases:(1) rheumatoid arthritis,(2) rheumatic arthritis,(3) systemic lupus eruthematosus,(4) bony ankylosis,or (5) spondylitis ankylopoietica.