Research On Detectability Of Fuzzy Discrete Event Systems

Discrete event system is a dynamic systems whose state is triggered by discrete events.It is important for system security to know the running status.State estimation is an important research direction of discrete event system which has been successfully applied in automatic control system.However,States and events are always some vague and subjective in real life.The introduction of fuzzy set into automata,which is play a foundation role in fuzzy discrete event systems,which is widely used in biomedical and automatic control systems.In this thesis,the detectability of the current state and the initial state in fuzzy discrete event systems is studied.In order to estimate the current and subsequent states of fuzzy discrete event systems,a detectability of fuzzy discrete event systems is proposed in this thesis.Firstly,the undistinguishable strings are introduced to characterize the same observable behavior for any minimal observable events.Then an observer based on minimal observable events is constructed,and the one-to-one correspondence between the undistinguishable strings and the non-unit cycle of the observer is established,and a necessary and sufficient condition for fuzzy detectability are obtained.At the same time,an algorithm for verifying detectability of fuzzy discrete event systems is presented.The applications of detectability of fuzzy discrete event systems are illustrated by example analysis.In addition,the fuzzy detectability method proposed in this thesis is also applicable to the crisp discrete event systems.In order to estimate the initial states of fuzzy discrete event systems,we define I-detectability of fuzzy discrete event systems which based on minimal observable events.Through analysis the influence of initial state and the degree of fuzzy events,an I-observer based on minimal observable events is constructed and the correspondence between the I-detectability and Initial-state-determination loop.At the same time,a necessary and sufficient condition for fuzzy I-detectability and an algorithm for verifying I-detectability are obtained.