Verification and Control of Cyber-Physical Systems (CSCI 5854, Spring 2017)

Course Information
  • Class Timings: Tuesday-Thursday 5:00 - 6:15 PM

  • Class Location: ECCR 139

  • Instructor: Sriram Sankaranarayanan

  • Pre-Requisites: Background in Embedded Systems or Control Theory.

    • Undergraduate level calculus and some exposure to CS theory.

  • Office Hours: TBA.

  • Watch this space for important announcements.


Assignments will be posted here.

Lecture Schedule and Notes

The schedule of lectures shown below is subject to change. We will post lecture notes for most topics and videos for selected topics. We will strive to post all material well in advance. Please take a look through them, and come prepared for class.

ID Date Topics Covered Lecture Notes
1 Jan 17th Cyber-Physical Systems : Motivation lectures/l1.html
2 Jan 19th Finite state machines as synchronous models lectures/l2.html
3 Jan 24th Nondeterministic models. lectures/l3.html
4 Jan 26th Composition, Events and Communication between models. lectures/l4.html
5 Jan 31st Safety Verification: Overview of Model Checking
6 Feb 2nd Demo of Spin. Introduction to SAT/SMT solvers
7 Feb 7 Bounded model checking for reachability
8 Feb 9 Bounded model checking (Conclusion)
9 Feb 14 Continuous systems. Ordinary Differential Equations
10 Feb 16 Basic theory of ODEs. Existence and Uniqueness
11 Feb 21 Linear ODEs and introduction to feedback control
12 Feb 28 Linear systems: reachability analysis
13 Mar 2 Linear systems: stability
14 Mar 7 Controllability, pole placement and LQR
15 Mar 9 Nonlinear reachability analysis
16 Mar 14 Nonlinear stability: linearization (Hartman Grobman Theorem)
17 Mar 16 Nonlinear stability: Lyapunov functions

Syllabus (Topics Covered)

Topics Covered
  1. Mathematical Models of Systems and Their Properties

    1. Structure of Feedback Control Systems: Hands-On Introduction

    2. Continuous Time Models: Ordinary Differential Equations.

    3. Synchronous Discrete Models: Finite State Machines

    4. Asynchronous Models: Network of Automata and Synchronization.

    5. Timed and Hybrid Models.

  2. Property Specifications

    1. Specification Types: Safety, Liveness, Reactivity, Stability.

    2. omega-automata and temporal logics.

  3. Verification Techniques

    1. Model Checking

    2. Deductive Verification: Lyapunov and Barrier Certificates

    3. Simulation-Based Verification: RRTs and S-Taliro.

  4. Application Examples

    1. Real-Time Scheduling.

    2. Air Traffic Management.

    3. Automotive Systems.

    4. Excitable Cells: Heart Tissue.

    5. Anesthesia Control.

    6. Insulin Infusion Control.

Note: Some of these topics will be explored through student projects.


Note that no existing textbook is going to cover everything in the syllabus. We will provide notes and pointers to textbooks.

A few books including Rajeev Alur's book or Lee and Seshia's book come close to covering more than 60% in significant detail and other parts in less detail.

Main Textbooks

Course Work

Course work will involve:

  • Weekly assignment problems given out each week.

    • Some assignments may involve the use of tools such as Matlab Simulink(tm)/Stateflow(tm) and other open source tools.

  • Course Project due at the end of the class. Projects may involve:

    • Modeling and Designing a nontrivial CPS using the ideas taught in the class,

    • Reading papers on a advanced topic relevant to the class, or

    • Working with a verification tool and evaluating it on a set of benchmarks.


There will be two in-class ‘‘midterm’’ quizzes that will test the material learned. Midterms will be announced two weeks in advance, and held in class.


The final grade will be calculated by adding up grades for various parts of the class:

  1. Assignments: 50%

  2. Project: 25%

  3. Quizzes: 25%

Collaboration Policy

The collaboration policy is rather simple:

  • Inspiration is free: you may discuss homework assignments with anyone. You are especially encouraged to discuss solutions with your instructor and your classmates.

  • Plagiarism is forbidden: the assignments that you turn in should be written entirely on your own. While writing the assignment you are not allowed to consult any source other than the textbook(s) for the class, your own class notes or the lecture notes for the class. Copying/consulting from the solution of another classmate constitutes a violation of the course's collaboration policy and the honor code.

  • Do not search for a solution on-line: You may not actively search for a solution to the problem from the internet. This includes posting to newsgroup or asking experts at other universities.

  • When in doubt, ask: If you have doubts about this policy or would like to discuss specific cases, please ask the instructor.

Honor Code

We will expect strict adherence to our our honor code. Please read and understand the code thoroughly. If in doubt, ask the instructor. At the end of the day, honor code violators hurt themselves by sacrificing their integrity and risking hard-earned reputation for a few measly grade points.