Some properties of nonlinear Lanchester equations with an application in military

Abstract

There have been many research literature on traditional direct fire combat modelling. Recently, network centric warfare (NCW) is an active research topic, in which information plays more important role than in the traditional warfare. It can be easily agreed that the use of information affects the combat results greatly. However, it is not straightforward to measure the effect of the information, thus decision making involving the impact of information during combat is a non-trivial task. In this study, we propose a simple model for NCW modified from the original Lanchester differential equation, which can be used as a basic model for analysing characteristics of NCW. We derive some useful properties of the model in a special case. In order to solve the optimal fire allocation decision under this model in general case, we propose an algorithm based on reinforcement learning, followed by numerical examples.