News
- 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)
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| Exercise: | Monday 16:00 – 16:45 (room AH 3) |
| Start: | April 13, 2015 |
| Language: | English or German (depending on the students’ preferences) |
| Exam: | Written:
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| 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_discrete, 02_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).
Exercises
| Exercise | Files |
| Exercise 1 | exercise_1, exercise_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_10, exercise_10_solution |
Exams
Here you can find exams from the past semesters:
- SS2013: exam_ss13_1
Evaluation
SS 10: lecturer and lecture (ss10)
SS 11: lecturer (ss11) lecture (ss11)
SS 12: lecturer (ss12) lecture (ss12)
SS 13: lecturer (ss13) lecture (ss13)
SS 15: lecture (ss15)