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 - 30%
Our department follows this anti-cheating policy strictly.
Homework
Homework 1 (Deadline: September 13, 2024)
Homework 2 (Deadline: October 11, 2024)
Homework 3 (Deadline: November 1, 2024)
Project
Project Registration (Deadline: August 9, 2024)
Book Chapter Submission (Deadline: October 25, 2024)
Project Submission (Deadline: October 25, 2024)
Project Presentation (October 28 - November 14, 2024)
Final Submission (Deadline: November 15, 2024)
Mid-Semester Examination
September 21, 2024 (Saturday) 6:00 pm to 8:00 pm at L18, L19, and L20 OROS
Final Examination
TBD
| Lecture | Date | Topic | References |
| 1 | August 1, 2023 (Thursday) | Introduction to the course | [LS15 - Ch 1] |
| 2 | August 5, 2023 (Monday) | Modeling Dynamic Behaviors - Continuous Dynamics | [LS15 - Ch 2] |
| 3 | August 8, 2023 (Thursday) | Basics of Feedback Control Theory | [AM09] |
| 4 | August 12, 2023 (Monday) | Modeling Dynamic Behaviors - Discrete Dynamics | [LS15 - Ch 3] |
| -- | August 15, 2023 (Thursday) | Holiday: Independence Day | |
| 5 | August 19, 2023 (Monday) | Hybrid Systems | [LS15 - Ch 4] |
| 6 | August 22, 2023 (Thursday) | Timed Systems | [BK08 - Ch 8] |
| -- | August 26, 2023 (Monday) | Holiday: Janmashtami | |
| 7 | August 29, 2023 (Thursday) | Composition of State Machines | [LS15 - Ch 5] |
| 8 | September 2, 2023 (Monday) | Sensors and Actuators | [LS15 - Ch 7] |
| 9 | Swptember 5, 2023 (Thursday) | Embedded Processors | [LS15 - Ch 8] |
| 10 | September 9, 2023 (Monday) | Memory Architectures | [LS15 - Ch 9] |
| 11 | September 12, 2023 (Thursday) | Multitasking | [LS15 - Ch 11] |
| -- | September 16, 2023 (Monday) | Holiday: Milad-un-Nabi or Id-e-Milad | |
| -- | September 19, 2023 (Thursday) | Mid-Semester Examination | |
| 12 | September 23, 2023 (Monday) | Scheduling | [LS15 - Ch 12] |
| 13 | September 26, 2023 (Thursday) | Scheduling | [LS15 - Ch 12] |
| 14 | September 30, 2023 (Monday) | Invariants and Temporal Logic | [LS15 - Ch 13] |
| 15 | October 3, 2023 (Thursday) | Invariants and Temporal Logic | [LS15 - Ch 13] |
| -- | October 7, 2023 (Monday) | Mid-Semester Recess | |
| -- | October 10, 2023 (Thursday) | Mid-Semester Recess | |
| 16 | October 14, 2023 (Monday) | Equivalence and Refinement | [LS15 - Ch 14] |
| 17 | October 17, 2023 (Thursday) | Reachability Analysis and Model Checking | [LS15 - Ch 15] |
| 18 | October 21, 2023 (Monday) | Quantitative Analysis | [LS15 - Ch 16] |
| 19 | October 24, 2023 (Thursday) | Specification Guided Controller Synthesis Using RL | [SS23] |
| 20 | October 28, 2023 (Monday) | Project Presentation | |
| -- | October 31, 2023 (Thursday) | Holiday: Diwali | |
| 21 | November 4, 2023 (Monday) | Project Presentation | |
| 22 | November 7, 2023 (Thursday) | Project Presentation | |
| 23 | November 11, 2023 (Monday) | Project Presentation | |
| 24 | November 14, 2023 (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.