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  • Course Type: Elective
  • Specialization: Foundations of Autonomous Systems
  • Instructor: Dr. Majid Zamani, Associate Professor
  • Prior knowledge needed:

    This second course in the specialization focuses on modeling requirements. It is highly recommended that students take the first courses that focus on the core structure in any autonomous system before attempting this course. We anticipate that students possess a grasp of fundamental mathematical concepts equivalent to those covered in the first year of studies for STEM majors at a US college. Additionally, a familiarity with basic differential equations and linear algebra is expected. This encompasses key principles, including: 

    • Sets and Functions: Proficiency in understanding the properties of sets, along with a clear comprehension of function definitions and their associated properties.

    • Eigenvalues and Eigenvectors: A basic knowledge of eigenvalues and eigenvectors of matrices, coupled with an ability to perform matrix-vector multiplication. 

    • Systems of First Order Linear Differential Equations:  A basic knowledge in solving and analyzing systems of first-order linear differential equations.

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Learning Outcomes

  • Show different notions of stability over systems.

  • Construct regular and omega-regular expressions.

  • Describe regular and omega-regular languages, respectively, using regular and omega-regular expressions.

  • Understand non-deterministic finite and büchi automata.

  • Describe regular and omega-regular languages using, respectively, non-deterministic finite and büchi automata.

Course Grading Policy


Percentage of Grade

6 Assignments

60% (10% each)

3 Quizzes

20% (6.7% each)

Final Exam




Course Content

Duration: 2 hours 51 mins

In this course, we delve into the intricate world of high-level specifications, a cornerstone in the development of reliable and efficient systems. This module is tailored to provide students with a comprehensive understanding of how to express system behavior expectations using formal methods such as linear temporal logic and automata on finite and infinite strings. Through a series of detailed examples and practical applications, we will gain the skills necessary to define and analyze various types of system properties, ensuring robust and predictable system performance.

Duration: 3 hours 27 mins

This module introduces normed vector spaces and stability concepts in autonomous systems, including stability, asymptotic stability, and global asymptotic stability. It focuses on Lyapunov’s Stability Theorem for formal verification, applying it to various linear systems. Through examples, we will see how these concepts are crucial in analyzing and ensuring system stability.

Duration: 3 hours 11 mins

Module description forthcoming.

Duration: TBD

Module description forthcoming.

Duration: 1 hour 45 mins

Module description forthcoming.

Duration: 2 hours

This module contains materials for the final project. If you've upgraded to the for-credit version of this course, please make sure you review the additional for-credit materials in the Introductory module and anywhere else they may be found.

This is a "take home" final exam. You have 12 hours to solve them.  

There is only ONE attempt (submission) allowed for the final exam.

The final is identical to our regular assignment: the problems are multiple-choice question that require you to use the concepts you have learned so far to solve problems.  

We expect that the problems will cumulatively require 2 - 3 hours of work to finish and the remaining time will provide you the necessary flexibility.


  • Cross-listed Courses: Courses that are offered under two or more programs. Considered equivalent when evaluating progress toward degree requirements. You may not earn credit for more than one version of a cross-listed course.
  • Page Updates: This page is periodically updated. Course information on the Coursera platform supersedes the information on this page. Click the View on Coursera button above for the most up-to-date information.