Leveraging lectures and coding assignments, this course provides the theoretical foundations and practical application of optimal control and optimal state estimation algorithms for dynamical systems. Foundational topics include Calculus of Variation, Pontryagin’s Minimum Principle, Dynamic Programing (which serve as a basis for modern Reinforcement Learning), and Nonlinear Observer Design. Practical applications include synthesis of Linear Quadratic Regulators (LQR), Model Predictive Controllers (MPC) and Extended Kalman Filters (EKF) which serve as standard algorithms in the fields of robotics, aerospace, and electro-mechanical systems. This course will require both analytical derivation exercises on theoretical concepts, as well as hands-on code development as training for practical algorithm implementation. Working knowledge in vector calculus, ordinary differential equations, and linear algebra is required. Continuous Control Systems (EN.525.609 or equivalent), helpful but not required. Working knowledge in MATLAB and Python required.