Introduction The problem of maximizing the utility of multiple objectives given limited resources is a common problem in homeland security applications. Examples abide. Consider, for example, the assignment of (a limited resource of) security officers at an airport whose objectives might be twofold: to survey the greatest number of passengers, as well as to minimize the waiting time of passengers. Another example might be the allocation of unmanned aerial systems (UAS) in search and rescue missions in the event of a disaster. The number of UAS might be limited and their objectives might be: (i) to maximize the surveillance of a given area through their scanning detectors; (ii) to maintain close proximity to each other to maintain communication links and so that more than one might be called on; and (iii) to avoid collision with each other. Other examples of allocation of resources in security applications include the routing of police cars in a large city to maximize the surveillance of an area, and yet to stay in reasonable proximity of each other in case they are called on by an agent. The purpose of this chapter is to explain a general methodology for addressing these types of problems where multiple objectives are sought and where a limited number of resources is available. The main idea of the proposed approach will be to first determine the multiple objectives and assess the trade-offs among them in a meaningful way using advances in utility theory (Abbas, 2009b, 2013), and then to use multi-objective control theoretic procedures to derive the control strategies that maximize the multiple objectives (Stipanović, Melikyan, & Hovakimyan, 2010). As we shall see, this approach will enable a closed-form expression for the decision strategies, a method to control multiple agents achieving the objectives, and a simple implementation of the control. The feasibility of this approach is made possible by capturing the different objectives (such as surveillance and collision avoidance) using new constructs, called Archimedean multiattribute utility copulas (Abbas, 2009b; Abbas & Sun, n.d.), that have the flexibility to model a large variety of trade-offs among multiple objectives. The control strategies are then obtained through the optimization procedure, which provides explicit solutions and thus requires minimal computational time when implemented. The only computation needed is related to updating feedback information, which may be the position of a target being followed.
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