Optimal control of counter-terrorism tactics

TL;DR

This paper develops an optimal control framework combining Pontryagin's Minimum Principle, shooting method, and cyclic descent to analyze and optimize counter-terrorism tactics, providing a way to identify steady states and improve solution optimality.

Contribution

It introduces a novel algorithm integrating multiple techniques for optimal control in counter-terrorism, including a priori steady state analysis and an improved functional for local optimality.

Findings

Efficient algorithm for counter-terrorism control problems

Ability to determine steady state solutions beforehand

Numerical examples demonstrating method effectiveness

Abstract

This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of coordinates. We also present a result that allows us to know a priori the steady state solutions. Using this technique we are able to choose parameters that reach a specific solution, of which there are two. Numerical examples are presented to illustrate the possibilities of the method. Finally, we study the sufficient conditions for optimality and suggest an improvement on the functional which also guarantees local optimality.