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Majid Zamani
This course will provide different techniques on the verification of autonomous systems against stability, regular, or omega-regular properties. Such techniques include Lyapunov theories, reachability analysis, barrier certificates, and model checking. Finally, it will introduce several techniques on designing controllers enforcing properties of interest over the original autonomous systems.
Read more
This course will provide different techniques on the verification of autonomous systems against stability, regular, or omega-regular properties. Such techniques include Lyapunov theories, reachability analysis, barrier certificates, and model checking. Finally, it will introduce several techniques on designing controllers enforcing properties of interest over the original autonomous systems.
Read more
This course will provide different techniques on the verification of autonomous systems against stability, regular, or omega-regular properties. Such techniques include Lyapunov theories, reachability analysis, barrier certificates, and model checking. Finally, it will introduce several techniques on designing controllers enforcing properties of interest over the original autonomous systems.
This course can be taken for academic credit as part of CU Boulder’s Masters of Science in Computer Science (MS-CS) degrees offered on the Coursera platform. This fully accredited graduate degree offer targeted courses, short 8-week sessions, and pay-as-you-go tuition. Admission is based on performance in three preliminary courses, not academic history. CU degrees on Coursera are ideal for recent graduates or working professionals. Learn more:
MS in Computer Science: https://coursera.org/degrees/ms-computer-science-boulder
Register for this course and see more details by visiting:
OpenCourser.com/course/a63mr7/verification
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Syllabus
Course Introduction
Welcome to the beginning of our exploration into formal verification and synthesis within the model-based design framework. In this introductory module, we will guide you through the key processes of specification, design, verification, and refinement of systems. We will delve into the vital role of formal methods in guaranteeing the correctness of systems. Through captivating examples, we will demonstrate the importance of formal verification, especially in safety-critical and life-critical applications. This module lays the foundation for the more advanced topics we will address throughout the course.
Read more
Syllabus
Course Introduction
Welcome to the beginning of our exploration into formal verification and synthesis within the model-based design framework. In this introductory module, we will guide you through the key processes of specification, design, verification, and refinement of systems. We will delve into the vital role of formal methods in guaranteeing the correctness of systems. Through captivating examples, we will demonstrate the importance of formal verification, especially in safety-critical and life-critical applications. This module lays the foundation for the more advanced topics we will address throughout the course.
Read more
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what should give you pause and
possible dealbreakers
Provides techniques for verifying and designing autonomous systems, which are increasingly used in various industries, research, and applications
Covers advanced techniques such as Lyapunov theories, reachability analysis, barrier certificates, model checking, and controller design, which are essential for ensuring the safety and correctness of autonomous systems
Taught by Majid Zamani, a renowned researcher in the field of formal verification, with extensive experience in developing techniques for autonomous systems
Part of CU Boulder's Master of Science in Computer Science degree program, indicating its academic rigor and relevance to industry standards
Requires no specific academic background or history, making it accessible to a wide range of learners interested in formal verification and autonomous systems
May require students to purchase additional materials or software, which could be a financial consideration
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Reviews summary
Rigorous formal methods for autonomous systems
According to learners, this course provides a deep and rigorous exploration into the verification and synthesis of autonomous systems. Students frequently highlight its well-structured content and strong theoretical foundations, especially praising insightful lectures on topics like model checking and Lyapunov theories. While highly valuable, the course is consistently described as challenging due to its fast pace and assumed advanced prerequisites in mathematics and logic. Some noted areas for improvement include assignment clarity and forum support responsiveness. Overall, it's highly recommended for those seeking a profound, academic understanding of this specialized field.
Instructor provides clear explanations for complex technical concepts.
"The lectures on model checking were particularly insightful, and the practical examples helped solidify complex concepts. The instructor's explanations are clear..."
"The explanations of Lyapunov theories and barrier certificates were exceptionally clear."
"I found the theoretical foundations very strong, which is crucial for this topic, and the instructor feedback was timely."
Provides thorough, high-level exploration of complex topics.
"This course is incredibly well-structured and provides a deep dive into formal verification techniques."
"Excellent content! I especially appreciated the modules on abstraction and refinement. The course truly fills a gap in online education..."
"This course provided a fantastic introduction to a complex field. The explanations of Lyapunov theories and barrier certificates were exceptionally clear."
Some assignments lack clarity; forum support can be inconsistent.
"I found some of the assignment instructions could be a bit clearer, and they sometimes felt disconnected from the lecture examples."
"The forum support was also inconsistent, which made debugging assignments harder."
"I struggled with the rapid pace and the assumed prior knowledge, and the forum support was inconsistent."
Course requires strong foundational knowledge and significant time.
"The material is inherently challenging. Highly recommend for anyone serious about autonomous systems."
"It's demanding, requiring a strong background in discrete mathematics and logic, but it's worth the effort."
"I struggled with the rapid pace and the assumed prior knowledge. I felt a more gradual introduction... would have been beneficial."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Verification and Synthesis of Autonomous Systems with these
activities:
Lyapunov theory for stability
Show steps
Understand the theoretical foundations of stability analysis using Lyapunov theory and prepare for future modules on verification and synthesis.
Browse courses on
Stability analysis
Show steps
-
Review the basics of Lyapunov theory and stability
-
Practice applying Lyapunov functions to analyze the stability of nonlinear systems
-
Solve problems involving the construction and validation of Lyapunov functions
Compile Resources on Verification and Synthesis
Show steps
Stay organized and enhance your learning experience by assembling a compilation of valuable resources, including articles, videos, and tools related to verification and synthesis.
Browse courses on
Verification
Show steps
-
Conduct research to gather relevant resources.
-
Organize the resources logically for easy access and reference.
Attend a Verification and Synthesis Workshop
Show steps
Immerse yourself in the field by attending a workshop dedicated to verification and synthesis, gaining valuable insights and broadening your knowledge.
Browse courses on
Verification
Show steps
-
Research and identify relevant workshops.
-
Attend the workshop and actively participate.
11 other activities
Expand to see all activities and additional details
Show all 14 activities
Reachability analysis tutorial
Show steps
Enhance your understanding of reachability analysis techniques to prepare for the verification of finite systems.
Browse courses on
Reachability Analysis
Show steps
-
Find and follow an online tutorial on reachability analysis
-
Work through examples of reachability analysis on simple systems
-
Apply reachability analysis to a small-scale system of your own design
Review Lyapunov Theory and Its Applications
Show steps
Review key principles of Lyapunov theory to strengthen your theoretical understanding of stability analysis.
Show steps
-
Read Introduction and Chapter 2 of the book.
-
Summarize the main principles and theorems of Lyapunov theory.
Discussion on model checking
Show steps
Engage in discussions with peers to clarify concepts and deepen your understanding of model checking.
Browse courses on
Model Checking
Show steps
-
Join an online discussion forum or study group
-
Participate in discussions on model checking topics
-
Ask questions and share your insights
Practice Reachability Analysis
Show steps
Engage in regular practice of reachability analysis techniques to enhance your proficiency in formal verification.
Browse courses on
Reachability Analysis
Show steps
-
Solve reachability problems on finite automata.
-
Use model checking tools to verify reachability properties.
Robotics workshop
Show steps
Gain hands-on experience with robotics by attending a workshop that covers design, building, and programming.
Browse courses on
Robotics
Show steps
-
Find a robotics workshop that aligns with your interests
-
Register for the workshop
-
Attend the workshop and actively participate in the activities
Design an Omega-Regular Property
Show steps
Develop an understanding of omega-regular properties by designing your own, strengthening your grasp of formal specification techniques.
Browse courses on
Formal Specification
Show steps
-
Identify a system behavior to be specified.
-
Use LTL or Buchi automata to represent the omega-regular property.
Simulate a controller for an autonomous system
Show steps
Reinforce your understanding of the design and implementation of controllers for autonomous systems by creating a simulation.
Browse courses on
Controller design
Show steps
-
Choose an autonomous system model to work with
-
Design a controller for the system
-
Create a simulation environment to test the controller
-
Run simulations to evaluate the controller's performance
-
Analyze the results and refine the controller as needed
Apply Barrier Certificates
Show steps
Reinforce your understanding of barrier certificates through dedicated practice, solidifying your ability to apply them in formal verification.
Show steps
-
Construct barrier certificates for simple dynamical systems.
-
Verify safety properties using barrier certificates.
Autonomous systems design competition
Show steps
Put your skills to the test by participating in a design competition that challenges you to create innovative autonomous systems.
Browse courses on
Autonomous Systems
Show steps
-
Find a suitable competition to participate in
-
Gather a team and brainstorm ideas
-
Design and build an autonomous system that meets the competition requirements
-
Test and refine your system
-
Submit your system to the competition
Design a Controller for Verification
Show steps
Apply the principles of controller design to develop a controller that meets specific properties, deepening your understanding of formal verification techniques.
Browse courses on
Controller design
Show steps
-
Define a control system and the desired properties.
-
Use formal methods to design a controller.
Contribute to an Open-Source Verification Tool
Show steps
Gain practical experience and contribute to the community by participating in the development of an open-source verification tool, deepening your understanding of the field.
Browse courses on
Open Source
Show steps
-
Identify a suitable open-source verification tool.
-
Make contributions to the tool's codebase or documentation.
Lyapunov theory for stability
Show steps
Understand the theoretical foundations of stability analysis using Lyapunov theory and prepare for future modules on verification and synthesis.
Browse courses on
Stability analysis
Show steps
Show steps
Show steps
- Review the basics of Lyapunov theory and stability
- Practice applying Lyapunov functions to analyze the stability of nonlinear systems
- Solve problems involving the construction and validation of Lyapunov functions
Compile Resources on Verification and Synthesis
Show steps
Stay organized and enhance your learning experience by assembling a compilation of valuable resources, including articles, videos, and tools related to verification and synthesis.
Browse courses on
Verification
Show steps
Show steps
Show steps
- Conduct research to gather relevant resources.
- Organize the resources logically for easy access and reference.
Attend a Verification and Synthesis Workshop
Show steps
Immerse yourself in the field by attending a workshop dedicated to verification and synthesis, gaining valuable insights and broadening your knowledge.
Browse courses on
Verification
Show steps
Show steps
Show steps
- Research and identify relevant workshops.
- Attend the workshop and actively participate.
11 other activities
Expand to see all activities and additional details
Show all 14 activities
Reachability analysis tutorial
Show steps
Enhance your understanding of reachability analysis techniques to prepare for the verification of finite systems.
Browse courses on
Reachability Analysis
Show steps
Show steps
Show steps
- Find and follow an online tutorial on reachability analysis
- Work through examples of reachability analysis on simple systems
- Apply reachability analysis to a small-scale system of your own design
Review Lyapunov Theory and Its Applications
Show steps
Review key principles of Lyapunov theory to strengthen your theoretical understanding of stability analysis.
Show steps
Show steps
Show steps
- Read Introduction and Chapter 2 of the book.
- Summarize the main principles and theorems of Lyapunov theory.
Discussion on model checking
Show steps
Engage in discussions with peers to clarify concepts and deepen your understanding of model checking.
Browse courses on
Model Checking
Show steps
Show steps
Show steps
- Join an online discussion forum or study group
- Participate in discussions on model checking topics
- Ask questions and share your insights
Practice Reachability Analysis
Show steps
Engage in regular practice of reachability analysis techniques to enhance your proficiency in formal verification.
Browse courses on
Reachability Analysis
Show steps
Show steps
Show steps
- Solve reachability problems on finite automata.
- Use model checking tools to verify reachability properties.
Robotics workshop
Show steps
Gain hands-on experience with robotics by attending a workshop that covers design, building, and programming.
Browse courses on
Robotics
Show steps
Show steps
Show steps
- Find a robotics workshop that aligns with your interests
- Register for the workshop
- Attend the workshop and actively participate in the activities
Design an Omega-Regular Property
Show steps
Develop an understanding of omega-regular properties by designing your own, strengthening your grasp of formal specification techniques.
Browse courses on
Formal Specification
Show steps
Show steps
Show steps
- Identify a system behavior to be specified.
- Use LTL or Buchi automata to represent the omega-regular property.
Simulate a controller for an autonomous system
Show steps
Reinforce your understanding of the design and implementation of controllers for autonomous systems by creating a simulation.
Browse courses on
Controller design
Show steps
Show steps
Show steps
- Choose an autonomous system model to work with
- Design a controller for the system
- Create a simulation environment to test the controller
- Run simulations to evaluate the controller's performance
- Analyze the results and refine the controller as needed
Apply Barrier Certificates
Show steps
Reinforce your understanding of barrier certificates through dedicated practice, solidifying your ability to apply them in formal verification.
Show steps
Show steps
Show steps
- Construct barrier certificates for simple dynamical systems.
- Verify safety properties using barrier certificates.
Autonomous systems design competition
Show steps
Put your skills to the test by participating in a design competition that challenges you to create innovative autonomous systems.
Browse courses on
Autonomous Systems
Show steps
Show steps
Show steps
- Find a suitable competition to participate in
- Gather a team and brainstorm ideas
- Design and build an autonomous system that meets the competition requirements
- Test and refine your system
- Submit your system to the competition
Design a Controller for Verification
Show steps
Apply the principles of controller design to develop a controller that meets specific properties, deepening your understanding of formal verification techniques.
Browse courses on
Controller design
Show steps
Show steps
Show steps
- Define a control system and the desired properties.
- Use formal methods to design a controller.
Contribute to an Open-Source Verification Tool
Show steps
Gain practical experience and contribute to the community by participating in the development of an open-source verification tool, deepening your understanding of the field.
Browse courses on
Open Source
Show steps
Show steps
Show steps
- Identify a suitable open-source verification tool.
- Make contributions to the tool's codebase or documentation.
Career center
Learners who complete Verification and Synthesis of Autonomous Systems will develop knowledge and skills
that may be useful to these careers:
For more career information including salaries, visit:
OpenCourser.com/course/a63mr7/verification
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OpenCourser.com/course/a63mr7/verification
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Effort
10 hours to complete
Level
Intermediate
Via
Coursera
Institution
University of Colorado Boulder
Instructor
Majid Zamani
Language
English
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