Cyber-Physical Systems (CPS) are dynamical systems that have both continuous and discrete components. CPS can form a unifying modeling framework for many different scientific and engineering problems. Examples include - but are not limited to - embedded systems, robotics, real-time software, power networks, transportation systems, process control, biological systems, etc.

The course will start with a review of necessary background material such as modeling frameworks for continuous and discrete-time dynamical systems. Then, the course will discuss modeling, simulation, analysis and design of hybrid systems. The term hybrid systems commonly refers to a comprehensive class of modeling formalisms which constitute the basis for a mathematical approach to CPS. Presentations of existing hybrid systems tools will complement the theoretical material of the class. New and emerging topics in theoretical CPS research will be presented as well.

The goal of the course is to provide students with the necessary foundations to apply hybrid systems theory in their own research and to motivate them to look into interesting research problems in the field of CPS. A secondary goal will be to develop a common language that will bridge the gap between traditionally disjoint disciplines such as computer science and classical engineering fields.


  • Classroom: BYAC 190
  • Date/Time: MW 6:20pm-7:35pm
  • Instructor: Georgios Fainekos
  • Electronic contact: fainekos at asu dot edu
  • Office: BYENG 474
  • Office hours: M 4-5pm, W 2-3pm


An undergraduate course in calculus is mandatory. An undergraduate course in linear algebra is preferred. Some knowledge about linear systems and automata theory is an advantage. However, the course will provide a short review on the necessary background material. Finally, it is assumed that the students are familiar with some programming language, such as C or MATLAB.


I will mainly follow the book:

However, we will also be using research papers that I will make available on Blackboard.

Recommended textbooks:

Other related textbooks:

  • 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.
  • D. Liberzon, Switching in systems and control, Birkhauser, 2003
  • E. A. Lee, P. Varaiya, Structure and Interpretation of Signals and Systems, 2002


There will be three homework sets and one course project. The homework sets make up 40% of the final grade. The final project makes up the remaining 60%.

Homework is due at the end of the class on the due date (usually two weeks after the homework is announced). Homeworks turned in late get only 40% of the score.

Homework must be submitted individually and it should be the result of individual effort. Having said that, discussions with your classmates on the homework problems are allowed. Projects should also be individual, unless you make a good case why the project will require more than one member.

Project ideas:

  • Literature review from last ESWeek or CPSWeek
  • Modeling/Simulation/Verification/Synthesis/Implementation
  • A theoretical problem which could lead to publication
  • Something related to your own research

Project deliverables:

Course Subjects (tentative)

  • Review: Continuous systems theory
  • Review: Discrete event systems
  • Modeling frameworks and systems properties
  • Modeling and simulation tools
  • Introduction to verification
  • Reachability and safety analysis
  • Hybrid systems in biology
  • Stability analysis of hybrid systems
  • Controller design and synthesis
  • Approximate abstractions
  • Path planning in robotics
  • Stochastic hybrid systems
  • Scheduling in control systems


  • 2010.02.01:
    New time: 6:20pm
  • 2010.02.01:
    New classroom: BYAC 190
  • Announcements will be mainly posted on Blackboard


  • Hybrid System Tools: A wiki page with an extensive collection of software tools for verifying/analyzing hybrid systems
  • UPPAAL: A model checker for timed automata
  • PVS: A theorem prover for higher order logic
  • Tempo: A tool for developing TIOA/HIOA specifications and translating them to UPPAAL and PVS

Information :: Schedule
G. Fainekos // Last update@2010.01.25