Lecture: Modelling and analysis of hybrid systems


Prequisites: Basic knowledge in automata theory
SWS: 3+1
Lecture times:

Monday 14:30 – 16:00 (room AH V)

Tuesday 10:30 – 12:00 (room AH VI)

Exercise: TBA
Language: English or German (depending on the students’ preferences)
Start: 08.04.2019
Exam: 1st exam:
06.08.2019, 14:30 – 16:30, room Gr and Ro
2nd exam:
07.09.2019, 10:30 – 12:30, room Ro
ECTS credits: 6

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 (i.e. the problem to decide whether any state from a given target set is reachable in a model) is decidable, and develop algorithms for their analysis. Besides exact methods, we consider also over-appoximative computations. Finally, we discuss extensions of hybrid automata models and their analysis methods to cover also random (probabilistic) aspects of hybrid systems.


Here we will make past exams available.


SS 14: no lecture (sabbatical)