Foundations of Autonomous Systems: Verification and Synthesis

Designing autonomous systems like self-driving vehicles and robotic assistants requires absolute certainty that they will behave safely in unpredictable environments. This text-based course introduces you to the core principles of formal verification and controller synthesis, ensuring your autonomous designs meet strict safety and stability standards. You will transition from simply testing autonomous systems to mathematically proving their correctness. By understanding how to model system dynamics and express safety properties, you will gain the skills needed to design controllers that guarantee safe operation under diverse conditions. What you will learn: Understand foundational system dynamics and how to mathematically model autonomous behaviors; Apply Lyapunov stability theory to verify the long-term steady states of dynamic systems; Analyze reachability and use barrier certificates to guarantee safety-critical boundaries are never crossed; Explore formal model checking techniques to verify systems against regular and omega-regular temporal properties; Synthesize correct-by-construction controllers that automatically enforce desired safety policies; Examine modern safety challenges, including verifying systems that incorporate learning-enabled components and neural networks. The course begins with essential mathematical terminology and foundational system modeling before guiding you through stability analysis, formal verification algorithms, and controller synthesis techniques. This course is designed for aspiring robotics engineers, computer scientists, and systems developers looking for an accessible entry point into formal methods, requiring only a basic background in mathematics. Start reading today to master the mathematical foundations of safe autonomy.