  The maximum surveillance of a target which is holding course is considered,
wherein an observer vehicle aims to maximize the time that a faster target
remains within a fixed-range of the observer. This entails two coupled phases:
an approach phase and observation phase. In the approach phase, the observer
strives to make contact with the faster target, such that in the observation
phase, the observer is able to maximize the time where the target remains
within range. Using Pontryagin's Minimum Principle, the optimal control laws
for the observer are found in closed-form. Example scenarios highlight various
aspects of the engagement.
