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| Instructor: |
Hadas Kress-Gazit |
| Time and Place: |
T,R 10:10-11:25, 111 Upson Hall |
| Office Hours: |
T 3-4 PM in 210 Upson Hall or by appointment |
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| Announcements: |
- MP2 (including project proposal) due Nov 15, by 5 pm
- The course is now cross listed as CS 5761
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Course description:
Hybrid systems are dynamical systems that have continuous dynamics, modeled by differential equations, as well as discrete dynamics, modeled by automata. These systems are used as a modeling and analysis framework in many fields such as robotics, embedded systems, mechatronic, real time software, air traffic control, systems biology, and process control since they naturally capture the phenomena arising when digital (discrete) computation is combined with the physical (continuous) world.
This course will discuss the modeling of hybrid systems, the analysis and simulation of their behavior, different control methodologies as well as verification techniques. To complement the theoretical aspect,
several state of the art tools will be introduced. New and emerging topics in hybrid systems research will be
presented as well.
As the field of hybrid systems is a truly interdisciplinary one, drawing researchers from dynamical systems, control theory, computer aided verification, automata theory and other fields, one of the goals of this course
is to teach students the language that will allow them to bridge the gap between these traditionally disjoint
disciplines. |
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| Prerequisites: Undergraduate level courses in linear algebra and differential equations. Knowledge of Linear system theory and automata theory is helpful. This course is intended for students from different
disciplines and as such will provide the necessary background material. |
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| Syllabus |
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| References: |
A list of notes, papers and other courses can be found here |
| Paper Presentation Rubrics |
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| Tentative schedule: |
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week |
Date |
Topic |
Content |
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Reading, etc. |
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R 8/25 |
Intro |
Overview |
Slides |
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T 8/30 |
Modeling |
General formulation |
Slides |
Ch. 2,3 of LTS |
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R 9/1 |
continuous systems, Discrete systems |
Slides |
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T 9/6 |
Discrete systems |
Slides |
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R 9/8 |
Composition and flood |
Slides, full Slides |
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T 9/13 |
Execution, Zeno behavior |
Slides |
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R 9/15 |
Paper presentations |
Modeling 1, 2 |
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T 9/20 |
Analysis & Abstractions |
Stability
|
Slides |
LTS Ch. 5 |
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R 9/22 |
Reachability |
Slides |
MP1 posted |
9a. |
M 9/26 |
Slides |
Reach 7,8 |
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T 9/27 |
Paper presentations |
Stability 3,Reachability 9 |
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R 9/29 |
Verification |
No lecture – out of town |
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T 10/4 |
Barrier certificates, SOS |
Slides |
Verification 12 |
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R 10/6 |
Simulation based methods |
Slides |
Verification 9 |
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T 10/11 |
No lecture – Fall break |
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R 10/13 |
Temporal logic, Simulation, Bisimulation, model checking |
Slides |
Verification 1,6
MP1 due 10/14 |
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T 10/18 |
Slides |
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R 10/20 |
Slides part2 |
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T 10/25 |
Paper presentations |
Verification 2,14 MP2 |
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R 10/27 |
Control |
Game theoretic methods |
Slides |
Control 3 |
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T 11/1 |
Slides |
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R 11/3 |
Symbolic control |
Slides |
Control 4 |
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T 11/8 |
Paper presentations |
Control 5 |
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R 11/10 |
Stochastic HS |
General Stochastic HS, Abstractions, Reachabilty |
Skeleton |
Stochastic 3 |
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T 11/15 |
Abstraction, simulation function |
Skeleton |
SHS 5
MP2 & Project proposal due |
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R 11/17 |
Different Topics |
Paper presentations |
Verification 13 |
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T 11/22 |
Paper presentations |
SHS 4, Misc 4 |
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R 11/24 |
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No lecture – Thanksgiving break |
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T 11/29 |
Project Presentations |
Presentation guidelines |
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R 12/1 |
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M 12/12 |
Project write up due by 5 PM |
Report guidelines |
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