Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in both science and engineering. Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved.
The report is mainly based on the first four chapters of Calculus of Variations and Optimal Control Theory - A Concise Introduction by Daniel Liberzon. The Zermelo’s river crossing problem solved in the last chapter is inspired by Patrick Suhm’s YouTube video Time Optimal River Crossing Tutorial Based On Pontryagins Maximum Principle.
