Foundations of Risk-Aware and Robust Nonlinear Planning

Modern autonomous systems must operate safely in unpredictable, real-world environments. To build truly reliable robots and vehicles, engineers must move beyond simple linear models and learn how to plan paths that systematically account for physical uncertainty and risk. This text-based course introduces the core mathematical concepts and optimization techniques needed to verify the safety and control of nonlinear dynamical systems under uncertainty. You will transition from basic probability concepts to advanced convex optimization formulations, preparing you to analyze and secure real-world robotic systems. What you'll learn: - Understand the foundational mathematics of nonlinear dynamical systems and uncertainty modeling. - Learn how to formulate safety verification problems using robust and risk-aware planning frameworks. - Explore the theory of measures, moments, and nonnegative polynomials for system analysis. - Configure semidefinite programming and convex optimization models to solve complex control problems. - Apply modern optimization concepts and Python-based CVXPY modeling patterns to translate theory into structured formulations. - Analyze risk bounds and safety guarantees for autonomous vehicles and robotic systems. This course begins with essential terminology, probability basics, and foundational definitions of dynamical systems. From there, you will progress through the mathematics of nonnegative polynomials, semidefinite programming, and practical formulation strategies for robust control. Designed for engineering students, robotics enthusiasts, and developers with a basic background in calculus and linear algebra, this course requires no prior experience with advanced optimization. Start reading today to master the mathematical foundations of risk-aware robotic planning.