Lecture: Modelling and analysis of hybrid systems


  • On 31.05.2016 both hours will be exercise (no lecture). Note: time and room change (2359|0.10 from 10:15 – 11:4)!
  • On 24.05.2016 both hours will be lecture (no exercise).
  • On 03.05.2016 there will be no lecture (Fachschaftsvollversammlung).
  • On 05.05.2016 there will be no lecture (Christi Himmelfahrt).
  • On 26.06.2016 there will be no lecture (Frohnleichnam).
  • On 31.05.2016 the lecture will take place in room 2359|0.10 from 10:15 – 11:45.
  • On 16.06.2016 the lecture will take place in room 2359|222.
Prequisites: Basic knowledge in automata theory
SWS: 3+1
Lecture times: Tuesday 12:15 – 13:00 (room 5056)

Thursday 14:15 – 15:45 (room 5056)
Exercise: Tuesday 13:00 – 13:45 (room 5056)
Language: English or German (depending on the students’ preferences)
Start: 14.04.2016
Exam: 1st exam:
09.08.2016, 13:15 – 15:15, rooms AHI and AHII
2nd exam:
21.09.2016, 16:00 – 18:00, rooms AHI and AHII
ECTS credits: 6
L2P L2P room

To deepen the lecture contents, weekly exercise sheets should be solved in two-men-groups and handed in before the exercises. We provide sample solutions for the exercises, video recordings, the slides of the lecture, and a lecture script in L2P. Registration in the campus system and in L2P is required.

What are hybrid systems?

Hybrid systems are systems with mixed discrete and continuous behaviour. Typical examples are physical systems which continuously evolve over time and are controlled by some discrete controller, e.g., a chip or a computer.

Why modelling and analysis?

The behaviour of hybrid systems is often safety-critical. For example, in case of an accident an airbag can save the life of the car driver, but only if the airbag reacts in time. To assure the correct functioning of such safety-critical hybrid systems, their automatic synthesis and analysis is of high importance.

Lecture content:

First we introduce hybrid automata to model hybrid systems. Then we define certain classes of hybrid automata with increasing expressive power. For each class we discuss whether the reachability problem is decidable, and develop algorithms for their analysis. Finally we discuss methods for the over-appoximative representation of state sets and show how they can be used for reachability analysis.


Here we will make past exams available.


SS 14: no lecture (sabbatical)