Optimal Control Theory: Basics

This lecture covers the fundamentals of optimal control theory, focusing on optimal control problems (OCPs). Topics include defining OCPs, admissible controls, dynamical systems, existence of solutions, performance criteria, physical constraints, and the equivalence of performance criteria. The lecture also delves into the calculus of variations, Gâteaux derivative, weak and strong minima, and geometric conditions of optimality. The principle of optimality, interpretation of adjoint variables, and OCPs with terminal equality constraints are discussed, along with the necessary conditions of optimality and the principle of optimality. The lecture concludes with an overview of necessary conditions and extensions to input and state constraints.