Introduction and Summary

In an optimal control problem, we are given a dynamical system whose behavior may be influenced or regulated by a suitable choice of some of the system’s variables, which are called control—or action or decision—variables. The controls that can be applied at any given time are chosen according to “rules” known as control policies. In addition, we are given a function called a performance criterion (or performance index), defined on the set of control policies, which measures or evaluates in some sense the system’s response to the control policies being used. Then the optimal control problem is to determine a control policy that optimizes (i.e., either minimizes or maximizes) the performance criterion.