Foundations of Optimal Control, Guidance, and Estimation

Designing systems that can navigate, stabilize, and optimize their paths autonomously is at the heart of modern aerospace, robotics, and automation. This written course demystifies the complex mathematics behind control, guidance, and estimation, making it accessible to beginners. You will transition from understanding basic system dynamics to formulating and solving optimal control problems, implementing state estimators, and designing robust guidance laws. What you'll learn: - Understand the foundational concepts of state-space modeling and system dynamics. - Formulate optimal control problems using the Calculus of Variations and Pontryagin's Minimum Principle. - Apply dynamic programming and the Hamilton-Jacobi-Bellman equation to find optimal strategies. - Design state estimators and Kalman filters to reconstruct hidden system states from noisy data. - Implement classic guidance laws, such as proportional navigation, used in autonomous path planning. - Explore modern computational approaches and numerical methods for solving complex trajectory optimization problems. The course begins with essential definitions and linear system theory before progressing to optimization techniques, estimation algorithms, and real-world guidance applications. This course is designed for engineering students, hobbyists, and developers new to control theory, requiring only basic calculus and linear algebra. Start your journey into autonomous systems and control theory today.