CSCI 5854: Foundations of Cyber-Physical Systems

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Relevant Textbooks



The overall grade will be based on a cumulative score computed by adding together the grades from:

Topics Covered

  1. Mathematical Models of Systems and Their Properties
    • Synchronous Discrete Models: (Extended) Finite State Machines (FSMs)
    • Asynchronous Models: Network of FSMs and Synchronization
    • Continuous Time Models: Ordinary Differential Equations
    • Hybrid Models: Timed Automata, Multi-mode Systems, and Hybrid Automata
    • Probabilistic Models: Markov Decision Processes and Probabilistic Timed Automata (*)
  2. Requirement Specification Formalisms
    • Specification Types: Safety, Liveness, Reactivity, Stability
    • omega-automata and temporal logics (LTL and MTL)
  3. Verification Techniques
    • Model Checking
    • Deductive Verification: Lyapunov and Barrier Certificates
    • Simulation-Based Verification: RRTs and S-Taliro.
  4. Verification Tools
    • NuXMV model checker for discrete systems
    • UPPAAL model checker for timed systems
    • PRISM model checker for probabilistic systems (*)
    • S-TaLiRo: temporal logic falsification tool
    • Flow-star : a verification tool for hybrid systems
  5. Applications (*)
    • Real-Time Scheduling
    • Medical Devices (Artificial Pacemaker and Artificial Pancreas)
    • Robot Motion and Path Planning
    • Automotive Systems
Topics marked with (*) will be explored via student projects and presentations.

Schedule and Lecture Notes

The schedule of lectures shown below is subject to change. We will post lecture notes or provide pointers to the texbook. We will strive to post all material well in advance. Please take a look through them, and come prepared for class.
# Date Description Chapter
1 Week 1 —January 17 Cyber-Physical Systems: Introduction Alur (Chapter 1)

Part One: Discrete Dynamical Systems

2 Week 2 — January 22 Transition Systems and Extended Finite state machines (An informal introduction) Alur (Chapter 2)
3 Week 2 — January 24 Nondeterministic models. Alur (Chapter 2)
4 Week 3 — January 29 Composition, Events and Communication between models. class notes
5 Week 3 — January 31 Safety Verification: Overview of Model Checking
6 Week 4 — February 5 Demo of NuXMV. Introduction to SAT/SMT solvers
7 Week 4 — February 7 Bounded model checking for reachability
8 Week 5 — February 12 Beyond Safety: Liveness
9 Week 5 — February 14 Temporal Logic and omega automata
10 Week 6 — February 19 Model-Checking Temporal Logic
11 Week 6 — February 21 In-Class Quiz I

Part Two: Continuous Dynamical Systems

12 Week 7 — February 26 Continuous systems. Ordinary Differential Equations
13 Week 7 — February 28 Basic theory of ODEs. Existence and Uniqueness
14 Week 8 — March 5 Simulation of ODEs in Simulink(tm)
15 Week 8 — March 7 Linear ODEs and introduction to feedback control
16 Week 9 — March 12 Linear systems: reachability and stability
17 Week 9 — March 14 Eigenvalues, pole placement, introduction to PID control
18 Week 10 — March 19 Stability Analysis: Lyapunov Functions and Barrier Certificates
19 Week 10 — March 21 In-class Quiz II
21 Week 11 — March 26-30 No Class — Spring Break

Part Three: Hybrid Dynamical Systems

20 Week 12 — April 2 Hybrid Systems: Basic introduction and examples
22 Week 12 — April 4 Hybrid automata: Theoretical Results
23 Week 13 — April 9 Hybrid Automata: Simulations using Simulink/Stateflow
24 Week 13 — April 11 Hybrid Automata: Metric Temporal Logic, Robustness, and Falsification
25 Week 14 — April 16 Hybrid Automata: Bounded Model Checking, Flowpipe construction, Flowstar tool demo
26 Week 14 — April 18 Timed Automata: Theory and tool demo
28 Week 15 — April 23 Probabilistic Modeling: Verification and PRISM tool demo

Part Four: Applications

29 Week 15 — April 25 Applications I (TBA)
30 Week 16 — April 30 Applications II (TBA)
31 Week 16 — May 2 Applications III (TBA)


  1. Accommodation Statement. If you qualify for accommodations because of a disability, please submit to me a letter from Disability Services in a timely manner (for exam accommodations provide your letter at least one week prior to the exam) so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities. Contact Disability Services at 303-492-8671 or by e-mail at dsinfo [AT] If you have a temporary medical condition or injury, see Temporary Injuries under Quick Links at the Disability Services website and discuss your needs with me.
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