Kirk describes optimal control thus:

The objective of optimal control theory is to determine the control signals that will cause a process to satisfy the physical constraints and at the same time minimize (or maximize) some performance criterion.

He then requires three things for the formulation of an optimal control problem:

1. A mathematical model of the process we wish to control;
2. A statement of the constraints on the system & controls; and
3. Specification of a performance criterion.

I’ll get into a discussion of these terms next post.