Optimal Exact Control

Abstract

In optimal control problems, we choose the ‘best’ controls from the set of all admissible controls. In our case, the set of admissible controls consists of the set of all controls that steer the system to the desired terminal state at the given terminal time. In general, these exact controls are not uniquely determined. Therefore we can choose from the set of admissible controls an exact control that is optimal in the sense that it minimizes an objective function that models our preferences. This leads to an optimal control problem where the prescribed end conditions can be regarded as equality constraints. Often, the control costs that are given by the norm of the control function are an interesting objective function.