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So far it could be observed how some shortcomings of finite automata used for DEDS modeling were overcome by Petri nets and Grafcet. This is mainly due to the latter’s ability to specify the parallel activities of subsystem states and concurrency of events. However, a certain imperfection of both persists. Difficulties in visualizing large and complex DEDS require to apply a sort of hierarchical decomposition. Another tool for coping with this problem is statecharts (Havel 1987 and Fogel 1997, 1998).

Statecharts use the same notions as the tools mentioned above, namely state and event, and are based on the basic transition system as well. They represent structure and dynamic behavior in a drawn graphical form. Their set-theoretic and functional description is possible, too. The next section introduces their concepts and Section 11.3 presents their applications to DEDS.

Finite automata, Petri nets, Grafcet, statecharts, , are tools for DEDS specification and analysis. They represent a system as a whole or its chosen parts. The function of the control system to be designed requires specific extensions of the expression means in order to enable a reactive performance of the control in a feedback system structure.

Generating a DEDS model is a highly creative process. There are many ways how to achieve this goal. However, precise and exhausting hints for it do not exist. Rather there are several supporting methodologies. One of useful practical ways is to first elaborate a model of the complete system as it appears to an observer with the control included. Second, a model of the system control is to be elaborated, which may serve for the control function analysis and writing control programs.

The basic notion of discrete event dynamic systems (DEDS) was introduced in Chapter 1. Finite automata and Petri nets have been studied as powerful models of DEDS for their behavior modeling and control. It has been shown that the states and transitions are key features of both models.

Consider an event-driven system being in its initial state. The complete behavior of the system is given by all possible event strings beginning in the initial state. The event strings are formally described by Equations (1.11) and (1.12).

Job scheduling or operation scheduling is a typical problem frequently appearing within DEDS. The core of the problem consists in how to achieve an optimal distribution of jobs or operations among the processing units or servers available in the system under various criteria. In other words, the problem is the optimal allocation of the system resources (Frankovič and Budinská 1998).

Typical environments in which a scheduling problem occurs are flexible manufacturing systems, distributed computer systems, database systems, and other. For example, flexible manufacturing systems (FMS) usually consist of product processing or machining units, measuring and testing equipments, transportation facilities, manipulators and robots, intermediate storages, input and output devices. Various methods have been developed for scheduling problems (Engell 1989; Li , 1995; Zhou and Venkatesh, 1998).

It has been discussed earlier in this book that process control means control of the basic processes at the level responsible for direct control. It is the control level or layer closest to the system processes. A hierarchically higher level is the coordination level of the basic processes. Here, the co-ordination is considered as a selection of servers performing basic processing, if there are more options. For example, in flexible manufacturing systems it is a selection of production units if there are more options to realize a prescribed technological recipe. One of coordination aims is to accomplish the required jobs in the minimum time span.