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M08 – BERLIN 29/02/2016 ‐ 04/03/2016

Control of discrete event systems


Jörg Raisch
Technische Universität Berlin
http://www.control.tu-berlin.de/User:Joerg_Raisch
raisch@control.tu-berlin.de
    
     Laurent Hardouin
    ISTIA University of Angers
    perso-laris.univ-angers.fr/~hardouin/
    laurent.hardouin@univ-angers.fr

Abstract

In many areas of application, properties that are interesting from a control point of view are naturally characterised via (timed or untimed) sequences of discrete events. This is true for many manufacturing and transportation systems, but also holds for processes from other application domains on certain levels of abstraction. The dynamic behaviour of such processes is described by Discrete Event Systems (DES). This course will provide an introduction to DES and does not require any background knowledge on this subject. We will address modelling, analysis and (optimal) control aspects. The course will cover language and behavioural models, characterising DES by sets of finite or infinite strings of discrete events, and their realisations in terms of Petri net and finite automaton, or state machine, models. It will discuss the basic ideas of Supervisory Control Theory, aiming at providing minimally restrictive control for problems where both the plant and the specification can be modelled by finite automata. The optimal (just-in-time) feedforward control and feedback control for a subclass of Timed Petri nets that describe synchronisation phenomena will be presented. Finally, we will address the question whether finite state abstractions can be used to design control for infinite state systems

Topics

1) Introduction

2) Petri Nets
2.1. Petri Net Graphs
2.2. Petri Net Dynamics
2.3. Special Classes of Petri Nets
2.4. Analysis of Petri Nets
2.5. Control of Petri Nets
2.6. Timed Petri Nets

3) Dioid Algebras
3.1. Timed Event Graphs (TEGs) with Holding Times
3.2. The Max-Plus Algebra and Residuation Theory
3.3. State Equations for TEGs in the Max-Plus Algebra
3.4. Optimal Control (Just-in-Time Control)
3.5. Closed Loop Control and State Estimation

4) Supervisory Control Theory
4.1. Languages and Automata
4.2. Maximally Permissive Control
4.3. Control Implementation by Finite Automata

5) Abstraction Based Control