Introduction

The project was developed to determine stability, pre stability , observability a DEDS system. DEDS, Discrete Event Dynamic Systems are dynamic systems (typically asynchronous) in which state transformations are triggered by the occurance of discrete events in the system. It is assumed that some of the events are controllable i.e., enabled or disabled . The goal of the DEDS system is to guide the behaviour of the system in a way that we consider desirable. It is further assumed that we are able to observe only a subset of the event, i.e., we can only see some of the events that are occuring in the system and not all.The issues considered in the development and their explanation is given in the following pages.

Stability: If a set of good states are known also known as good states, E, that we would like the DEDS to stay within or donot stay outside for an infinite time.So for each of the states The automated system will be able to tell whether any of the states are stable with respect to the reported good states. the advantage of the automation is we can change the good states at will and check to see the affect they have on the stability of a particular state or event. This rule also applies to states themselves whose events we can change at will to determine the change in their stabilty with respect to the good states.Stability of a state is determined using the following methods.

checking out whether all trajectories from the other states will visit E infinitely often Trying to guide the system using the controllable events in a way such that the system will visit the good states infinitely often.

Pre stability: When x belonging to X is pre-stable if all paths from x can go to E in a finite number of transitions, i.e., no path from x ends up in a cycle that does not go through E. The definition of pre-stability can be formalized as follows: Given a live system A and some E belonging to X, a state x belonging to X is pre- stable with respect to E (or E-per-stable) if for all x belonging to X such that |x| >= n, there exists y belonging to x such that y belongs to E. We say that a set of states is E-pre-stable if all its elements are E-pre-stable and a system A is pre-stable if X is E-pre-stable.

Observability: It is assumed that all events are not observable.The events that are considered as observable are those observable events in the system.Since it is not desirable to have the system generate arbitrarily long sequence of unobservable events in network. A necessary condition to gaurantee this is that the automation after removing the observable events must not be alive.

Utilization of DEDS

In developing an automated system the network to be analysed in a stored in a file format describing the Output states and events of each state and also whether each output state is controllable and observable is mentioned separately.The exact format of event description is explained further in separately in the examples page.

The project User interface is windowed into Four parts as follows:

• The Title Window
• The Menu Window
• The Output Window
• The User Input/Message Window

The Title Window

Has the Title of the project

The Menu Window

The Menu Window Has all the possible User Interaction Options with the system as follows:

• File Load
• Events
• E-state
• Stability
• Pre-stability
• Observer
• Exit

File Load Option:

Before the user can interact with the system the user has to load a file with the Discrete Event(s) Description along with the Description of the E-State.The file will be read by the system when this option is choosen. Errors if any will be posted in the Message Window.

Events Option:

Once the file is loaded into the system the user would like to see whether what he specified which happens to be syntactically right is read by the system the way he wanted it to understood.DEDS system lists all the events as specified by the user.For each state all the output events will be listed also specifying what is the state of the output event, The name of the event, Whether Controllable, Whether Observable will be mentioned.

E-state:

Shows all the e-states as understood by the DEDS system .

Stability:

When the user wants to find the stability of an state the user uses this option. The user will be asked to specify the state whose stability has to be found with respect to the Network.

Pre-Stability:

When the user wants to find the pre-stability of an state the user uses this option. The user will be asked to specify the state whose pre-stability has to be found with respect to the Network.

Observer:

When the user wishes to generate the observer for the system this options will be choosen. The main purpose of this Option is to generate an observer file. The system does this in Three stages all of which are shown in the examples page.

scans the table initially setup when scanning input file to determing whether a given state is controlloable or not is decided by seeing the parameter as suggested by the input of the user. A state is decided to be Cyclic or not by seeing for any given state whether the state has as output as itself then it is deemed Cyclic or else it is deemed not Cyclic. A state is decided as Estate by system because all the estates are presumed mentioned separately in the input file and stored in a separate table of estates. A state is thus said estate if it exists in estate table. if it does not then it is not a estate.These functions are made use of primarily by the following functions which determine stability , prestability, observability of the states and the network as the whole.

For each stage a separate output file will be generated. For the input *.stb file the output file will be *.obs, *.inp, *.out files.

Exit Option:

Exits from the system.

The Output Window

When the output is generated when finding the State Description, E-state Description, Observer all the output as performed for each intermediate stages is shown in this Window.

The User Input/Message Window

The System poses questions when interacting with the user and correspondingly the user interactes with the system in this window. Apart from this The user also interacts with the system in the Menu Window.

Kanniganti Radesh , B.Tech, (M.S.) , Computer Engg, University of Bridgeport.

Choices: