A Primer on Pontryagin's Principle in Optimal Control

EDITORIAL REVIEW:

This book provides a guided tour in introducing optimal control theory from a practitioner's point of view. As in the first edition, Ross takes the contrarian view that it is not necessary to prove Pontryagin's Principle before using it. Using the same philosophy, the second edition expands the ideas over four chapters:

• In Chapter 1, basic principles related to problem formulation via a structured approach are introduced:
1. What is a state variable?
2. What is a control variable?
3. What is state space? And so on.
• In Chapter 2, Pontryagin's Principle is introduced using intuitive ideas from everyday life: Like the process of "measuring" a sandwich and how it relates to costates. A vast number of illustrations are used to explain the concepts without going into the minutia of obscure mathematics. Mnemonics are introduced to help a beginner remember the collection of conditions that constitute Pontryagin's Principle.
• In Chapter 3, several examples are worked out in detail to illustrate a step-by-step process in applying Pontryagin's Principle. Included in this example is Kalman's linear-quadratic optimal control problem.
• In Chapter 4, a large number of problems from applied mathematics to management science are solved to illustrate how Pontryagin's Principle is used across the disciplines. Included in this chapter are test problems and solutions.

The style of the book is easygoing and engaging. The classical calculus of variations is an unnecessary prerequisite for understanding optimal control theory. Ross uses original references to weave an entertaining historical account of various events. Students, particularly beginners, will embark on a minimum-time trajectory to applying Pontryagin's Principle.