Lecture: Modelling and analysis of hybrid systems



  • The second exam will take place on Wednesday 16th September starting at 16:00 in room AHI.
Prequisites: Basic knowledge in automata theory
SWS: 3+1
Lecture times: Monday 15:15 – 16:00 (room AH 3)

Tuesday 12:15 – 13:45 (room 5056)
Exercise: Monday 16:00 – 16:45 (room AH 3)
Start: April 13, 2015
Language: English or German (depending on the students’ preferences)
Exam: Written:

  • 1st exam 27.07.2015 14:30-16:30, room AH I & II
  • Einsicht: 03.08.2015 10:30-12:30, room 5052
  • 2nd exam 16.09.2015 16:00-18:00, room AH I
  • Einsicht: 23.09.2015 09:00-11:00, room AH I
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.

Current lecture slides (might be modified during the semester):

# Subject Files
0 Introduction 00_intro, 00_intro_annotated
1 Hybrid automata 01_hybrid, 01_hybrid_annotated_2015
2 Logics 02_discrete02_discrete_annotated_2015
3 Timed automata 03_timed, 03_timed_annotated_2015
4 Modelchecking timed automata 04_mc_timed, 04_mc_timed_annotated_2015
5 Rectangular automata 05_rectangular, 05_rectangular_annotated_2015
5b Undecidability 05b_undecidability
6 Linear hybrid automata I 06_linear, 06_linear_annotated_2015
7 Analysis 07_analysis
8 N/A There is no lecture 8 this semester (internal numbering)
9 Polyhedra 09_polyhedra, 09_polyhedra_annotated
10a LHA1 reachability 10a_LHA1_reachability, 10a_LHA1_reachability_annotated
10b LHA2 reachability 10b_LHA2_reachability, 10b_LHA2_reachability_annotated
11 Taylor models 11_taylor

The lecture script can be found here (handout).


Exercise Files
Exercise 1 exercise_1exercise_1_solution
Exercise 2 exercise_2, exercise_2_solution
Exercise 3 exercise_3, exercise_3_solution
Exercise 4 exercise_4, exercise_4_solution
Exercise 5 exercise_5, exercise_5_solution
Exercise 6 exercise_6, exercise_6_solution
Exercise 7 exercise_7, exercise_7_solution
Exercise 8 exercise_8, exercise_8_solution
Exercise 9 exercise_9, exercise_9_solution
Exercise 10 exercise_10exercise_10_solution


Here you can find exams from the past semesters: