We formulate a search-trajectory optimization problem, with multiple searchers looking for multiple targets in continuous time and space, as a parameterdistributed optimal control model. The problem minimizes the probability that all of the searchers fail to detect any of the targets during a planning horizon. We construct discretization schemes and prove that they lead to consistent approximations in the sense of E. Polak.

We implement and solve a search-trajectory optimization problem originally formulated in our companion paper, with multiple searchers looking for multiple targets in continuous time and space. The problem minimizes the probability that all of the searchers fail to detect any of the targets during a planning horizon. We develop an implementable algorithm that converges to stationary points of the original infinitedimensional problem. Numerical tests illustrate the approach in a naval scenario with up to three searchers protecting a capital ship from ten attackers in go-fast boats.

We present a validation of a centralized feedback control law for robotic or partially robotic water craft whose task is to defend a harbor from an intruding fleet of water craft. Our work was motivated by the need to provide harbor defenses against hostile, possibly suicidal intruders, preferably using unmanned craft to limit potential casualties. Our feedback control law is a sample‐data receding horizon control law, which requires the solution of a complex max‐min problem at the start of each sample time. In developing this control law, we had to deal with three challenges. The first was to develop a max‐min problem that captures realistically the nature of the defense‐intrusion game. The second was to ensure the solution of this max‐min problem can be accomplished in a small fraction of the sample time that would be needed to control a possibly fast moving craft. The third, to which this article is dedicated, was to validate the effectiveness of our control law first through computer simulations pitting a computer against a computer or a computer against a human, then through the use of model hovercraft in a laboratory, and finally on the Chesapeake Bay, using Yard Patrol boats. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 247–259, 2016