The Maximum Principle of Pontryagin in control and in optimal control. Handouts for the course taught at the Universitat Politcnica de Catalunya. Department of Mathematics and Statistics Queen’s University.[online] Available: http://www.mast.queensu.ca/ a

These notes provide an introduction to Pontryagin’s Maximum Principle. Optimal con-trol, and in particular the Maximum Principle, is one of the real triumphs of mathematical control theory. Certain of the developments stemming from the Maximum Principle are now a part of the standard tool box of users of control theory. While the Maximum Principle has proved to be extremely valuable in applications, here our emphasis is on understanding the Maximum Principle, where it comes from, and what light it sheds on the subject of control theory in general. For this reason, readers looking for many instances of applications of the Maximum Principle will not find what we say here too rewarding. Such applications can be found in many other places in the literature. What is more difficult to obtain, however, is an appreciation for the Maximum Principle. It is true that the original presentation of Pontryagin, Boltyanskĭi, Gamkrelidze, and Mishchenko [1986] is still an excellent one in many respects. However, it is probably the case that one can benefit by focusing exclusively on understanding the ideas behind the Maximum Principle, and this is what we try to do here. Let us outline the structure of our presentation