Lec. Notes Piazza KeYmaera Autolab
Cyber-physical systems (CPSs) combine cyber
capabilities (computation and/or communication) with physical
capabilities (motion or other physical processes).
Cars, aircraft, and robots are prime examples, because they
move physically in space in a way that is determined
by discrete computerized control algorithms.
Designing these algorithms to control
CPSs is challenging due to their tight coupling with physical behavior.
At the same time, it is vital that these algorithms be correct,
since we rely on CPSs for safety-critical tasks like keeping aircraft from colliding.
In this course we will strive to answer the fundamental question posed by Jeannette Wing:
"How can we provide people with cyber-physical systems they can bet their lives on?"
Students who successfully complete this course will:
- Understand the core principles behind CPSs.
- Develop models and controls.
- Identify safety specifications and critical properties of CPSs.
- Understand abstraction and system architectures.
- Learn how to design by invariant.
- Reason rigorously about CPS models.
- Verify CPS models of appropriate scale.
- Understand the semantics of a CPS model.
- Develop an intuition for operational effects.
The cornerstone of our course design are hybrid programs (HPs), which capture relevant dynamical aspects of CPSs in a simple programming language with a simple semantics. One important aspect of HPs is that they directly allow the programmer to refer to real-valued variables representing real quantities and specify their dynamics as part of the HP.
This course will give you the required skills to formally analyze the CPSs that are all around us -- from power plants to pace makers and everything in between -- so that when you contribute to the design of a CPS, you are able to understand important safety-critical aspects and feel confident designing and analyzing system models. It will provide an excellent foundation for students who seek industry positions and for students interested in pursuing research.
15-122 Principles of Imperative Computation (or equivalent)
15-251 Great Theoretical Ideas in Computer Science (or equivalent)
21-122 Integration, Differential Equations, and Approximation (or equivalent)
This course covers the basic required mathematical and logical background of cyber-physical systems. You will be expected to follow extra background reading material, which we will provide, as needed.
This course counts as a Logics/Languages elective in the Computer Science curriculum.
- TEXTBOOK: (optional)
Logical Analysis of Hybrid Systems:
Proving Theorems for Complex Dynamics.
Springer, Heidelberg, 2010. 426 pages. ISBN 978-3-642-14508-7.
[bib | ✂ | doi | book | web | errata | abstract]
Foundations of Cyber-Physical Systems.
Lecture Notes, Computer Science Department, Carnegie Mellon University. 2013.
[bib | ✂ | pdf | textbook | course | abstract]
- André Platzer.
- METHOD OF EVALUATION:
Grading will be based on a set of homework assignments (20%), labs (50%), a midterm exam (10%), and a final exam (20%).
Grading is based on points giving the above percentages approximately.
Midterm: 150 points, Wed 10/09 during lecture time. Closed book, one double-sided sheet of hand-written notes permitted. Final: 300 points, 12/12 1pm-4pm, GHC 4307. Closed book, one double-sided sheet of hand-written notes permitted.
The instructors greatly appreciate the help by other members of the Logical Systems Lab, especially Khalil Ghorbal, Stefan Mitsch, Jan-David Quesel.