有限狀態機有限狀態識別與控制之矩陣方法

Abstract

The response of a nontrivial sequential machine to specified excitations becomes unpredictable if the state of the machine is unknown. On the other hand, the response of the machine can always be predicted if the initial state is unknown.Hence one of the basic problems in the study of sequential machines is to identify the state of the machine under investigation.Once the state is identified,the behavior of the machine under all future circumstances becomes predictable, and definite steps may then be taken to force the machine into various modes of operation at the discretion of the investigator.The former class of problems comes under the broad category of problems usually termed the state identification problems, and the latter problem is commonly known as the control problem in sequential machines.One of the most important state identification problems is that of identifying the unknown initial state if the machine, called the initial state identification problem or diagnosing problem;whereas , another important state identification problem is relating to that of identifying the terminal state of the machine, known as the terminal state identification problem or homing problem, of which the special case is the synchronizing problem.The solution to either of these state identification problems constitutes the solution to the basic problem of rendering the machine predictable to the investigator.In the present paper, instead of resorting to the conventioal procedure of using the transistion table and the corresponding response tree, use is made of the transistion matrix trpresentation of the machine and its higher-order forms to solve the aforementioned state identification and control problems.The developed approach is not only simple,but very systematic , and completely algorithmic , and thus lends itself to easy computer implementation.