Optimal control of counter-terrorism tactics
L. Bayon, P. Fortuny Ayuso, P. J. Garcia-Nieto, J. M. Grau, M. M. Ruiz
TL;DR
The paper addresses optimizing counter-terrorism tactics by formulating a two-control, fire-and-water model in an infinite-horizon, time-autonomous optimal control framework. It advances a numerical algorithm that blends Pontryagin's Minimum Principle, shooting methods, and cyclic descent of coordinates, enabling efficient solutions and convergence guarantees, plus a priori steady-state computation using a steady-state CCD adaptation. Key findings include the existence of two steady-states separated by a switching point $x^S$ (with $v=0$ below $x^S$), explicit high- and low-value steady-state values, and a parametric sensitivity analysis showing greater influence of fire-efficiency $\gamma$ than water-efficiency $\beta$ on steady-states; a convexified cost functional is proposed to ensure local (and, under conditions, global) optimality. The methods offer practical guidance for policy design by allowing rapid exploration of how parameter changes affect steady-state outcomes and corresponding costs, without solving the full dynamic problem each time.
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.