Abstract
We propose the basis for a rigorous approach to modeling combat, specifically under conditions of complexity and uncertainty. The proposed basis is a tensorial generalization of earlier Lanchester-type equations, inspired by the contemporary debate in defence and military circles around how to best utilize information and communications systems in military operations, including the distributed C4ISR system (Command, Control, Communications, Computing, Intelligence, Surveillance and Reconnaissance). Despite attracting considerable interest and spawning several efforts to develop sound theoretical frameworks for informing force design decision-making, the development of good frameworks for analytically modeling combat remains anything but decided. Using a simple combat scenario, we first develop a tensor generalization of the Lanchester square law, and then extend it to also include the Lanchester linear law, which represents the effect of suppressive fire. We also add on-off control inputs, and discuss the results of a simple simulation of the final model using our small scenario.
Highlights
Since at least the time of the Military Enlightenment, military organizations have invested considerable effort into developing theories of war and battle
What research to conduct, how to conduct operations, and what operations to conduct in the first place. Many such efforts at the development of theories of war and battle have been oriented around the idea of achieving something like a complete and correct theory by which future outcomes might be predicted and thereby the means of determining the means to guarantee, or at least maximize the chances of, obtaining the outcome one desires. This has remained a dominant theme in military thinking ever since the foundational works of early theorists such as Jomini [1], through adoptions into military domains other than land battles in the late 19th century and early 20th Century with military educators such as Mahan [2], into the middle of the 20th Century with increasingly technologically-oriented theorists such as Fuller [3] [4] and Hart [5], and into modern and even more heavily technologically focussed instantiations such as Network Centric Warfare (NCW) [6] and Effects-Based Operations (EBO) [7]
Classical attempts at mathematically modeling military conflict occurred within this overarching tradition of military thinking, and they manifest the same basic goal of yielding mathematical theories that are numerically predictive with respect to battle outcomes
Summary
Since at least the time of the Military Enlightenment, military organizations have invested considerable effort into developing theories of war and battle.
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