### Discrete Event Systems

#### Course Description

Basic properties of discrete event systems. Differences between time driven and event driven systems. Discrete states and discrete state space. Basics of the graph theory. Automata and languages. Markov processes. Modeling and simulation of discrete event systems (DES). Static and dynamic Petri nets. Max plus algebra. String algebra. Matrix description of DES. DES analysis. Observability. Stability, conflicts, livelocks and deadlocks. DES synthesis. Controllability. Feedback and DES supervisory control. DES examples (transportation systems, warehouses, manufacturing systems, computer systems).

#### General Competencies

Students will be able to analyze discrete event systems and design and implement supervisory control algorithms based on the automata, max plus and Petri nets theories.

#### Learning Outcomes

1. recognize discrete event systems
2. explaine functioning of discrete event systems
3. apply formal modelling methods of discrete event systems
4. analyze structural properties of discrete event systems based on Petri net model
5. develop control algorithms for discrete event systems
6. analyze discrete event systems by using max-plus algebra

#### Forms of Teaching

Exercises

problem solving exercises are part of lectures, with active participation of students

Laboratory Work

practical implementation of acquired knowledge on the laboratory model of discrete event system

Continuous Assessment Exam
Laboratory Exercises 0 % 30 % 0 % 30 %
Homeworks 0 % 20 % 0 % 20 %
Mid Term Exam: Written 0 % 20 % 0 %
Final Exam: Written 0 % 30 %
Exam: Written 50 % 50 %

#### Week by Week Schedule

1. Basic properties of discrete event systems. Differences between time driven and event driven systems. Discrete states and discrete state space.
2. Basics of the graph theory
3. Automata and languages
4. DES transition equation. Modeling and simulation of discrete event systems (DES); Static Petri nets
5. Static Petri nets
6. Dynamic Petri nets. Coulored Petri nets; Max plus algebra
7. Max plus algebra.
8. midterm exam
9. String algebra; Matrix description of DES
10. Matrix description of DES.
11. DES analysis. Observability.
12. Stability, conflicts, livelocks and deadlocks.
13. DES synthesis. Controllability.
14. Feedback and DES supervisory control. DES examples - transportation systems, warehouses
15. final exam

#### Study Programmes

Control Engineering and Automation -> Electrical Engineering and Information Technology (Profile)

#### Literature

C.G. Cassandras, S. Lafortune (1999.), Introduction to Discrete Event Systems, Kluwer
F. Baccelli, G. Cohen, G.J. Olsder, J.P. Quadrat (1995.), Synchroniyation and Linearity: An Algebra for Discrete Event Systems, MIT Press
S. Bogdan, F.L. Lewis, Z. Kovacic, J. Mireles (2005.), Manufacturing Systems Control Design, Springer-Verlag

#### Lecturers

4 ECTS
L1 English Level
L1 e-Learning
30 Lecturers
0 Exercises
4 Laboratory exercises