Discrete Event Systems And Fuzzy Discrete Event System Controllability And Observability

Discrete event system is a natural and man-made dynamic system whose state space is discrete and instantaneous events over time.In the most study of supervisory control theory about discrete event system at present,the theory initiated by Ramadge and Wonham(short for RW) is the most common research which is based on the logical level and its theorical background is the automata of computer science and formal language.However,situations in our real life are always somewhat imprecise.The theory of fuzzy set has been proved to be a good method for dealing with such uncertainty.To overcome this difficulty in the supervisory control theory of traditional discrete event system,Lin and Ying incorporated fuzzy set theory together with discrete event system and introduced the concept of fuzzy discrete event system.Thus a scientific method of dealing with uncertain and fuzzy problems in our real life is provided by the supervisory control theory of fuzzy discrete event system.In this thesis,we mainly study the relationship of controllability between crisp and fuzzy discrete event system.Together with the relationship of observability between the two systems.In Chapter 2,firstly,we introduce the concepts of controllability for crisp and fuzzy discrete event system respectively.Secondly,we study the relationship of controllability between the two systems and obtain such a result:If a fuzzy language is controllable,then its every strong cut language is controllable.Conversely,if all the strong cut languages of the fuzzy language are controllable,then the fuzzy language is controllable.Finally,some simple applications of this result are provided.In Chapter 3,similarly,at first,we provide the concepts of observability for crisp and fuzzy discrete event system respectively.Further,we study that whether a similar perfect result of observability still exists between crisp discrete event system and fuzzy one under the partially observable architecture.The research indicates that if a fuzzy language is observable then its every strong cut language is observable. However,the converse is not true.At last,certain conditions are given so that the converse is true,that is,suppose that E_c(?)E_o and all strong cut languages of a fuzzy language are not only observable but also controllable.