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 usual...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.展开更多
基金NSF under grants INT-0213651 and ECS-0624828NIH under grant 1 R21 EB001529-01A1
文摘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.
