A cyber-physical system is a collection of interconnected computing devices interacting with the physical world. The computing devices together constitute a cyber system that regulates the behavior of the physical world. The cyber system closely monitors the physical world through sensors, computes required control laws based on the current state of the physical world, and applies the computed control law to the physical world through actuators. The sensors, the controllers, and the actuators are developed on top of an embedded platform. Thus, the cyber component of a cyber-physical system is often termed as an embedded control system.
Developing an embedded control system requires the understanding of the physical world with which the system has to interact. The understanding of the physical world is captured in a faithful model that is used for synthesizing feedback control laws using control theoretic methods. Implementing the feedback control law on the embedded computing platform requires addressing the challenges of embedded computing, for example, the availability of limited resources in terms of computing power and memory, stringent timing requirements, and so on. Moreover, most cyber-physical systems are safety-critical. Thus, it is essential that the correctness of such systems is established through the use of formal verification techniques.
The course will cover the modeling, implementation and verification issues related to developing a cyber-physical system. Through the discussion of the implementation of an embedded control system, the course will cover the basic design principles of an embedded system.
The course does not have any formal prerequisites. The students are expected to have mathematical maturity of the level of an undergraduate degree in engineering. However, some familiarity with finite state machines and ordinary differential equations, and programming experience will be helpful.
Homework Assignments - 15%
Mid-Semester Examination - 20%
End-Semester Examination - 30%
Project - 35%
Our department follows this anti-cheating policy strictly.
Homework
Homework 1 (Deadline: September 12, 2025)
Homework 2 (Deadline: October 10, 2025)
Homework 3 (Deadline: November 7, 2025)
Project
Project Registration (Deadline: August 8, 2025)
Project Presentation Submission (October 31, 2025)
Project Presentation Question Submission (Deadline: November 7, 2025)
Project Presentation Response Submission (Deadline: November 14, 2025)
Mid-Semester Examination
TBD
Final Examination
TBD
| Lecture | Date | Topic | References |
| 1 | July 31, 2025 (Thursday) | Introduction to the course | [LS15 - Ch 1] |
| 2 | August 4, 2025 (Monday) | Modeling Dynamic Behaviors - Continuous Dynamics | [LS15 - Ch 2] |
| 3 | August 7, 2025 (Thursday) | Basics of Feedback Control Theory | [AM09] |
| 4 | August 11, 2025 (Monday) | Modeling Dynamic Behaviors - Discrete Dynamics | [LS15 - Ch 3] |
| 5 | August 14, 2025 (Thursday) | Hybrid Systems | [LS15 - Ch 4] |
| 6 | August 18, 2025 (Monday) | Timed Systems | [BK08 - Ch 8] |
| 7 | August 21, 2025 (Thursday) | Composition of State Machines | [LS15 - Ch 5] |
| 8 | August 25, 2025 (Monday) | Concurrent Models of Computation | [LS15 - Ch 6] |
| 9 | August 28, 2025 (Thursday) | Sensors and Actuators | [LS15 - Ch 7] |
| 10 | September 1, 2025 (Monday) | Embedded Processors | [LS15 - Ch 8] |
| 11 | Swptember 4, 2025 (Thursday) | Memory Architectures | [LS15 - Ch 9] |
| 12 | September 8, 2025 (Monday) | Input and Output | [LS15 - Ch 10] |
| 13 | September 11, 2025 (Thursday) | Multitasking | [LS15 - Ch 11] |
| 14 | September 15, 2025 (Monday) | Scheduling | [LS15 - Ch 12] |
| -- | September 18, 2025 (Thursday) | Mid-Semester Examination | |
| -- | September 22, 2025 (Monday) | Mid-Semester Examination | |
| 15 | September 25, 2025 (Thursday) | Scheduling | [LS15 - Ch 12] |
| -- | September 29, 2025 (Monday) | Mid-Semester Recess | |
| -- | October 2, 2025 (Thursday) | Mid-Semester Recess | |
| 16 | October 6, 2025 (Monday) | Invariants and Temporal Logic | [LS15 - Ch 13] |
| 17 | October 9, 2025 (Thursday) | Invariants and Temporal Logic | [LS15 - Ch 13] |
| 18 | October 13, 2025 (Monday) | Equivalence and Refinement | [LS15 - Ch 14] |
| 19 | October 16, 2025 (Thursday) | Reachability Analysis and Model Checking | [LS15 - Ch 15] |
| -- | October 20, 2025 (Monday) | Holiday: Diwali | |
| 20 | October 23, 2025 (Thursday) | Quantitative Analysis | [LS15 - Ch 16] |
| 21 | October 27, 2025 (Monday) | Signal Temporal Logic | [SS23] |
| 22 | October 30, 2025 (Thursday) | Specification Guided Controller Synthesis Using RL | [SS23] |
| 23 | November 3, 2025 (Monday) | Project Presentation | |
| 24 | November 6, 2025 (Thursday) | Project Presentation | |
| 25 | November 10, 2025 (Monday) | Project Presentation | |
| 26 | November 13, 2025 (Thursday) | Project Presentation | |
[AD94] Rajeev Alur, David L. Dill: A Theory of Timed Automata. Theor. Comput. Sci. 126(2): 183-235 (1994).
[AM09] K. J. Astrom and R. M. Murray. Feedback Systems: An Introduction for Scientists and Engineers. Prince- ton University Press, 2009. http://www.cds.caltech.edu/~murray/amwiki/index.php/Main_Page.
[BK08] C. Baier and J.-P. Katoen. Principles of Model Checking. The MIT Press, 2008.
[Harel87] D. Harel. Statecharts: A Visual Formalism for Complex Systems. Science of Computer Programming 8 (1987) 231-274.
[LS15] Edward A. Lee and Sanjit A. Seshia, Introduction to Embedded Systems, A Cyber-Physical Systems Approach, Second Edition, http://LeeSeshia.org, ISBN 978-1-312-42740-2, 2015.
[Ras05] Jean-Francois Raskin. An Introduction to Hybrid Automata. Handbook of Networked and Embedded Control Systems, pages 491-517, 2005.
[SS23] Nikhil.K. Singh and Indranil Saha. STL-Based Synthesis of Feedback Controllers Using Reinforcement Learning. AAAI 2023.