Tour d'Horizon: Optimal Control

This chapter presents the fundamentals of optimal control theory. In the first section we give a short historical survey, introducing the reader to the main ideas and notions. Subsequently we introduce the standard problem of optimal control theory.

We state Pontryagin's Maximum Principle, distinguishing between the cases without and with mixed path or pure state inequality constraints. The Hamilton–Jacobi–Bellman equation is used to give an informal proof of the Maximum Principle. Then the Maximum Principle is extended to the case of an infinite planning horizon. This is followed by the presentation of a onedimensional optimal control model, and we give an economic interpretation of the Maximum Principle.