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CSCI 5854: Foundations of Cyber-Physical Systems
Logistics
- Instructor:
Ashutosh Trivedi (ashutosh \dot trivedi \at colorado \dot edu)
- Course description:
Cyber-physical systems are characterized by a tight integration (a feedback loop) between the discrete control (the "cyber")
and the analog environment (the "physical"). This course provides an introduction to the state-of-the-art in model-based design
and verification of safety-critical cyber-physical systems (CPS).
This course has the following four parts:
- Part I: Discrete Dynamical Systems ( the "Cyber") .
mathematical modeling , requirement specification formalisms,
and verification techniques to reason with purely discrete systems.
- Part II: Continuous Dynamical Systems ( the "Physical") .
mathematical modeling (via Ordinary Differential Equations) and
analysis techniques (Reachability and Stability) for purely continuous systems.
- Part III: Hybrid Dynamical Systems (the "Cyber-Physical Systems")
models (Hybrid and Timed Automata), requirement
specification formalisms (MTL), and verification
techniques to reason with systems that integrate both discrete
and continuous behaviors.
- Part IV: Applications
We conclude the course by
exploring various case-studies highlighting applications of the ideas
presented in the course in designing and verifying cyber-physical
systems from various domains such as automotive systems, medical
devices, air-traffic management, and robotics.
- Requisites:
- Undergraduate level calculus and some exposure to CS theory.
- Background in Embedded Systems or Control Theory.
- Class Meeting Times: Monday (4:00pm—5:15pm) and
Wednesday (4:00pm—5:15pm)
- Office hours: after the class or by appointment.
- Venue :
- Class meeting location: ECCS 1B14
- Office Hour location: ECCS 121 D
Relevant Textbooks
No existing textbook is going to cover everything in the syllabus. We
will provide notes and pointers to the textbooks.
We will use a combination of the following textbooks:
Assignments
Grading
The overall grade will be based on a cumulative score computed by adding
together the grades from:
- Weekly assignments (50%)
- Weekly reading exercises
- Biweekly system modeling or verification assignments
- Some assignment may involve the use of
tools such as Matlab Simulink(tm)/Stateflow(tm) and other open
source tools.
- In-class quizzes (25%)
- We will have two in-class quizzes and will be announced two-weeks in advance.
- The final project (25%)
- The final project will be due at the end of the class.
- The project may involve
- modeling and designing a non-trivial CPS
using ideas introduced in the class,
- Reading papers on an advanced topic relevant to the class, or
- Working with a verification tool and evaluating it on a set
of benchmarks.
Topics Covered
- 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 (*)
- Requirement Specification Formalisms
- Specification Types: Safety, Liveness, Reactivity, Stability
- omega-automata and temporal logics (LTL and MTL)
- Verification Techniques
- Model Checking
- Deductive Verification: Lyapunov and Barrier Certificates
- Simulation-Based Verification: RRTs and S-Taliro.
- 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
-
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 |
January 17 |
Cyber-Physical Systems: Introduction
|
0 |
Part One: Discrete Dynamical Systems
| 2 |
Week 2 — January 22 |
Transition Systems and Extended Finite state machines
|
class notes |
| 3 |
Week 2 — January 24 |
Nondeterministic models.
|
class notes |
| 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)
|
|
Notes
-
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] colorado.edu.
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.
-
Religious Observances.
Campus policy regarding religious observances requires that faculty make every
effort to deal reasonably and fairly with all students who, because of religious
obligations, have conflicts with scheduled exams, assignments or required
attendance. In this class, you should notify your instructor of any conflict at
least two weeks in advance. See full details
here .
-
Classroom Behavior.
Students and faculty each have responsibility for maintaining an appropriate
learning environment. Those who fail to adhere to such behavioral standards may
be subject to discipline. Professional courtesy and sensitivity are especially
important with respect to individuals and topics dealing with differences of
race, color, culture, religion, creed, politics, veteran's status, sexual
orientation, gender, gender identity and gender expression, age, disability, and
nationalities. Class rosters are provided to the instructor with the student's
legal name. I will gladly honor your request to address you by an alternate name
or gender pronoun. Please advise me of this preference early in the semester so
that I may make appropriate changes to my records. For more information, see the
policies
on
classroom behavior and
the
student code.
-
Discrimination and Harassment.
The University of Colorado Boulder (CU Boulder) is committed to maintaining a
positive learning, working, and living environment. CU Boulder will not tolerate
acts of sexual misconduct, discrimination, harassment or related retaliation
against or by any employee or student. CU's Sexual Misconduct Policy prohibits
sexual assault, sexual exploitation, sexual harassment, intimate partner abuse
(dating or domestic violence), stalking or related retaliation. CU Boulder's
Discrimination and Harassment Policy prohibits discrimination, harassment or
related retaliation based on race, color, national origin, sex, pregnancy, age,
disability, creed, religion, sexual orientation, gender identity, gender
expression, veteran status, political affiliation or political
philosophy. Individuals who believe they have been subject to misconduct under
either policy should contact the Office of Institutional Equity and Compliance
(OIEC) at 303-492-2127. Information about the OIEC, the above referenced
policies, and the campus resources available to assist individuals regarding
sexual misconduct, discrimination, harassment or related retaliation can be
found at
the OIEC website.
-
Honor Code.
All students enrolled in a University of Colorado Boulder course are responsible
for knowing and adhering to
the academic
integrity policy of the
institution. Violations of the policy may include: plagiarism, cheating,
fabrication, lying, bribery, threat, unauthorized access, clicker fraud,
resubmission, and aiding academic dishonesty. All incidents of academic
misconduct will be reported to the Honor Code Council (honor@colorado.edu;
303-735-2273). Students who are found responsible for violating the academic
integrity policy will be subject to nonacademic sanctions from the Honor Code
Council as well as academic sanctions from the faculty member. Additional
information regarding the academic integrity policy can be found at
honorcode.colorado.edu.
- The web-page of a previous offering of the course is
available
here and here .