Introduction

The methods of dynamic optimization are rocket science – and more. Quite literally when NASA or the European Space Agency plan space missions, they use the methods described in this book to determine when to launch, how much fuel to carry, and how fast and how long to fire thrusters. That's exciting, but it's old news. Engineers have appreciated the power of this branch of mathematics for decades.What is news is the extent to which these methods are now contributing to business, economics, public health, and public safety.

The common attribute across these diverse domains, from medicine to robotics, is the need to control or modify the behavior of dynamical systems to achieve desired goals, typically maximizing (or minimizing) a performance index. The mathematics of optimal control theorymake this possible. In particular, the discovery of the Maximum Principlefor optimal paths of a system is what led the way to successful designs of trajectories for space missions like Sputnik and the Apollo program and myriad applications here on earth.