STOCHASTIC HYBRID SYSTEMS
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Audience
This advanced lecture (Vertiefungsvorlesung) addresses Master students in Computer Science, Mathematics, Bioinformatics, CuK or Computerlinguistics.
Contents
The aim of this course is to expose participants to Stochastic Hybrid Systems. Theoretical results will be illustrated and motivated by applications in different important fields.
Stochastic hybrid systems are systems that combine continuous dynamics with discrete/logic components and are affected by uncertainty. From a theoretical point of view, the study of this class of systems is particularly challenging because they exhibit the complexities that arise from the interaction of
• discrete-event systems,
• continuous dynamics, and
• stochastic processes, either affecting the discrete-event
system transitions or entering the continuous dynamics.
Emphasis will be placed on theoretical advances for this complex and diverse class of systems, in particular on
• stochastic hybrid modeling
• compositional specification
• reachability analysis
• model checking
• hybrid observer design
Motivation for the theoretical results will be provided by a number of key applications:
• air traffic management
• automotive systems
• communication networks
• mathematical finance
Dates
The module is offered March 12-23, 2007 as a block course. We usually start at 9:00 in the morning, with about 2 hrs of lecture in the morning, and exercise sessions on some of the afternoons.
Further details will become available here and at the CMS.
| Topic | Date | Instructor | Notes | |
| 0. | Introduction; Timed Automata | 12-03-2007 | Holger Hermanns | |
| 1. | Measure theory, Probabilities, Stochastic Processes | 12-03-2007 | Holger Hermanns | |
| 2. | Discrete time Markov Chains | 13-03-2007 | Holger Hermanns | |
| 3. | Continuous time Markov Chains | 14-03-2007 | Holger Hermanns | |
| 4. | Markov jump processes; Piecewise Deterministic Markov Processes | 15-03-2007 | Manuela Bujorianu | |
| 5. | Brownian Motion, Wiener Processes | 16-03-2007 | Manuela Bujorianu | |
| 6. | Ordinary Differential Equations, Hybrid Systems | 19-03-2007 | Holger Hermanns | |
| 7. | Applications of Hybrid Systems and Stochastic Processes | 20-03-2007 | Holger Hermanns | |
| 8. | Stochastic Differential Equations, Diffusion Processes | 21-03-2007 | Manuela Bujorianu | |
| 9. | Stochastic Hybrid Systems | 22-03-2007 | Manuela Bujorianu | |
| 10. | Applications of Stochastic Hybrid Systems | 23-03-2007 | Manuela Bujorianu |
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Instructor
 | Prof. Dr.-Ing. Holger Hermanns |
| Dr. Manuela L. Bujorianu |
Literature
See:
infobib.cs.uni-sb.de/frames/vorlesungen/stochastichybridsystems.html