Instructor
George J. Pappas, Department of Electrical and Systems Engineering, University of Pennsylvania
Lecture and Office Hours
Lectures are Monday and Wednesday, 4:30-5:50pm in Moore 216. Office hours will be on Tuesdays 2-3pm in my Levine 460 office. Feel free, to walk in my office anyother time that I look reasonably free. You can of course also email me at pappasg @ seas.upenn.edu
Course description
Hybrid systems are systems that have both continuous and discrete aspects. Due to their expressive power, hybrid systems have been used as modeling framework in many fields, such as embedded systems, robotics, real-time software, transportation systems, process control, communication networks, and biological systems. Starting with some basic introductory material, the course will cover a number of contemporary topics in hybrid systems. We will conside topics focusing on modeling and simulation, stability of hybrid systems, verification of hybrid systems, together with an introduction to relevant software tools. We shall also discuss the use of hybrid systems in modeling real systems, such as robotics, biological systems, transportation systems, etc. Other relevant topics, such as, systems abstraction, controller synthesis, and stochastic hybrid systems will also be covered, depending on time and interests.
Prerequisites
While the course will benefit most students that have strong understanding of control theory, optimization, in addition to automata theory or logic, the course is open to all graduate students with sufficient mathematical maturity. Also, it is assumed that the students have some working knowledge on some programming language, such as C or MATLAB. The course will provide a short review on the necessary background material.
Schedule
The following schedule is tentative and subject to change:
Date |
Lecture | Presentation | Suggested Reading Materials |
| January 14 | MODELING: Introduction to hybrid systems | Slides | Chapters 1 & 2 of J. Lygeros' lecture notes |
| January 19 | No class: Martin Luther King Day | ||
| January 21 | REVIEW: Continuous systems | Slides | Chapters 1 & 2 of J. Lygeros' lecture notes |
| January 26 | REVIEW: Discrete systems | Slides | Chapter 1 of P. Tabuada lecture notes (on Blackboard) |
| January 28 | REVIEW: Introduction to verification | Slides | |
| February 2 | MODELING: Hybrid automata | Slides | Chapter 3 of J. Lygeros' lecture notes |
| February 4 | MODELING: Hybrid automata | Slides | Chapter 3 of J. Lygeros' lecture notes |
| February 9 | MODELING: Switched systems and applications | Slides | Papers on switched systems and some applications |
| February 11 | MODELING: Mixed Logical Dynamical(MLD) models | Slides | Papers on MLD systems |
| February 16 | STABILITY: Switched Systems | Slides | Papers on switched systems |
| February 18 | STABILITY: Stability in embedded and wireless control | Slides | Papers on switched systems |
| February 23 | NO CLASS | ||
| February 25 | VERIFICATION: Discrete abstractions of hybrid systems | Slides | Chapters of P. Tabuada lecture notes (on Blackboard) and this paper |
| March 2 | VERIFICATION: Discrete abstraction of hybrid systems | Slides | Chapters of P. Tabuada lecture notes (on Blackboard) and this paper |
| March 4 | VERIFICATION: Discrete abstraction of hybrid systems | Slides | Chapters of P. Tabuada lecture notes (on Blackboard) and this paper |
| March 9 | No class: Spring break | ||
| March 11 | No class: Spring break | ||
| March 16 | VERIFICATION: Reachability analysis using zonotopes | Slides | Papers on zonotopes by Antoine Girard |
| March 18 | VERIFICATION: Simulation-based approaches | Slides | Paper on Stateflow/Simulink testing |
| March 23 | APPROXIMATION: Metrics for discrete and continuous systems | Slides | Paper on approximation metrics |
| March 25 | CONTROL: Control over time-triggered architectures | ||
| March 30 | CONTROL: Control over muli-hop networks | ||
| April 1 | CONTROL: Model predictive approaches | ||
| April 6 | STOCHASTIC: Hybrid systems and control | ||
| April 8 | STOCHASTIC: Applications to biology | ||
| April 13 | No class: Hybrid Systems (HSCC) Conference | ||
| April 15 | No class: Hybrid Systems (HSCC) Conference | ||
| April 20 | Brief project presentations | ||
| April 22 | Brief project presenations | ||
| April 27 | Brief project presentations |
References
Given the young age of the field, there are not many textbooks on the subject. Insted there are some recent research monographs that we will selectively use:
- A.J. van der Schaft, J.M. Schumacher, An Introduction to hybrid dynamical systems, Lecture Notes in Control and Information Sciences, Vol. 251, Springer-Verlag, London, 2000.
- P. Tabuada, Verification and control of hybrid systems: a symbolic approach, preprint
- D. Liberzon, Switching in systems and control, Birkhauser, 2003
- J. Lygeros, Lecture notes on hybrid systems, 2003
For each lecture, we will also be posting relevant papers on the website.
Software tools
A variety of software tools for hybrid systems modeling and analysis have been developed over the past decade. I have assembled many of thes on the following wiki site. Course projects based on tool modeling or development are encouraged.
Grading
Course grade will depend on a some homeworks (30%) and your class project (70%). Candidate class projects could be applying hybrid system tecniques in a particular problem of ineterst, theoretical development in the area of hybrid systems, and using computational tools for modeling and analyzing relevant applications. Literaure review will be accepted, in which case student will select papers of interest from the upcoming HSCC 2009 for detailed review.