MATH 641 Optimal Control Theory
Examples of problems: electro-dynamical systems leading to time optimal control problems, spacecraft navigation leading to fuel optimal control problems. Proof of Pontryagin's maximum principle. Existence of optimal controls for linear systems with convex constraints on the control function. Derivation of Lagrange, Euler-Lagrange, and Hamilton equations of classical variational calculus from Pontryagin's principle. Method of first integrals and Hamilton-Jacobi generating function. Application to problems in celestial mechanics. Prerequisites: 540 and 624.