## Modeling and Analysis of Hybrid Systems

In this lecture we address foundations of the modeling and analysis of hybrid systems. Information for the summer semester 2012:

 Prerequisites: Basic knowledge in automata theory SWS: 3+1 Lecture times: Tuesday 13:15 – 14:15 (room 5056) Friday     13:15 – 14:30 (room 5056) Exercise: Tuesday 14:15 – 15:00 (room 5056) Start: April 03, 2012 Language: English or German (depending on the students’ preferences) Exam: Oral or written ECTS credits: 6

To deepen the lecture contents, weekly exercise sheets should be solved in two-men-groups. 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 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 modeling 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.

### The slides of the last lecture (SS 2011):

 Nr. Theme Slides 1. Introduction 2. The modeling of hybrid systems 3. Propositional and temporal logics 4. Timed automata 5. Model checking on timed automata 6. Rectangular automata 7. Linear hybrid automata 8. Reachability analysis of hybrid automata 9. Representations of the reachable sets 9.1. Convex polyhedra 9.2. Orthogonal polyhedra