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
   
Announcements:
  • MP2 (including project proposal) due Nov 15, by 5 pm
  • The course is now cross listed as CS 5761

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.

   
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.
   
Syllabus  
References: A list of notes, papers and other courses can be found here
Paper Presentation Rubrics  
Tentative schedule:  

week

Date      

Topic

Content

 

Reading, etc.
  1.  

R   8/25

Intro

Overview

Slides

 
  1.  

T   8/30

Modeling

 

General formulation

Slides

Ch. 2,3 of LTS
  1.  

R   9/1

continuous systems, Discrete systems

Slides

  1.  

T   9/6

Discrete systems

Slides

 
  1.  

R   9/8

Composition and flood

Slides, full Slides

  1.  

T   9/13

Execution, Zeno behavior

Slides

 
  1.  

R   9/15

Paper presentations

Modeling 1, 2

  1.  

T   9/20

Analysis & Abstractions Stability

Slides

LTS Ch. 5
  1.  

R   9/22

Reachability

Slides

MP1 posted

  9a.

M   9/26

Slides Reach 7,8
  1.  

T   9/27

Paper presentations

Stability 3,Reachability 9

  1.  

R   9/29

Verification

No lecture – out of town

 

 
  1.  

T   10/4

Barrier certificates, SOS

Slides

Verification 12
  1.  

R   10/6

Simulation based methods

Slides

Verification 9
  1.  

T  10/11

No lecture – Fall break

 

 
  1.  
R  10/13

Temporal logic, Simulation, Bisimulation, model checking

Slides

Verification 1,6
MP1 due 10/14

  1.  

T  10/18

Slides

 
  1.  

R  10/20

Slides part2

 
  1.  

T  10/25

Paper presentations

Verification 2,14 MP2

  1.  

R  10/27

Control

Game theoretic methods

Slides

Control 3
  1.  

T   11/1

Slides

  1.  

R   11/3

Symbolic control

Slides

Control 4

  1.  

T   11/8

Paper presentations

Control 5

  1.  

R  11/10

Stochastic HS

General Stochastic HS, Abstractions, Reachabilty

Skeleton

Stochastic 3
  1.  

T  11/15

Abstraction, simulation function

Skeleton

SHS 5
MP2 & Project proposal due

  1.  

R  11/17

Different Topics

Paper presentations

Verification 13

  1.  

T  11/22

Paper presentations

SHS 4, Misc 4

  1.  

R  11/24

 

No lecture – Thanksgiving break

 

 
  1.  

T  11/29

Project Presentations

 

Presentation guidelines

R  12/1

 

M 12/12

Project write up due by 5 PM

Report guidelines