Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare

This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” áttrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It introduces a canonical auxiliary parity-condition problem for the determination of a single parity-condition parameter (“the enemy force equivalent of a friendly force of unit strength”) and new exponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive.     

Attrition models of the Ardennes campaign

This paper revisits the modeling by Bracken [3] of the Ardennes campaign of World War II using the Lanchester equations. It revises and extends that analysis in a number of ways: (1) It more accurately fits the model parameters using linear regression; (2) it considers the data from the entire campaign; and (3) it adds in air sortie data. In contrast to previous results, it concludes by showing that neither the Lanchester linear or Lanchester square laws fit the data. A new form of the Lanchester equations emerges with a physical interpretation. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 1–22, 1998     

Fitting Lanchester equations to the battles of Kursk and Ardennes

Lanchester equations and their extensions are widely used to calculate attrition in models of warfare. This paper examines how Lanchester models fit detailed daily data on the battles of Kursk and Ardennes. The data on Kursk, often called the greatest tank battle in history, was only recently made available. A new approach is used to find the optimal parameter values and gain an understanding of how well various parameter combinations explain the battles. It turns out that a variety of Lanchester models fit the data about as well. This explains why previous studies on Ardennes, using different minimization techniques and data formulations, have found disparate optimal fits. We also find that none of the basic Lanchester laws (i.e., square, linear, and logarithmic) fit the data particularly well or consistently perform better than the others. This means that it does not matter which of these laws you use, for with the right coefficients you will get about the same result. Furthermore, no constant attrition coefficient Lanchester law fits very well. The failure to find a good‐fitting Lanchester model suggests that it may be beneficial to look for new ways to model highly aggregated attrition. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

The two-on-one stochastic duel

The one-on-one stochastic duel is extended to the general two-on-one duel for the first time. The state equations, win probabilities, mean value, and variance functions are derived. The case where one side has Erlang (2) firing times and the other is negative exponential is compared with the corresponding “Stochastic Lanchester” and Lanchester models to demonstrate their nonequivalence.     

基于信息-决策影响因素的兰彻斯特作战模型?

为有效评估信息因素和决策因素对现代作战进程的影响,改进了传统的兰彻斯特方程作战模型,通过引入信息获取能力指数和筹划决策能力指数,建立了基于信息-决策影响因素的兰彻斯特作战模型,并分3种假设情况进行了仿真。仿真结果表明,该作战模型一定程度上反映了信息因素和决策因素对作战的影响,体现了现代作战的基本致胜机理。     

基于兰切斯特方程的网络中心战模型

为了更全面、客观地评价信息优势和决策优势对网络中心战进程的影响,在分析经典兰切斯特方程的基础上,引入信息?决策概率,提出了基于兰切斯特方程的网络中心战模型,仿真实验表明该模型能够有效地描述信息?决策概率在网络中心战进程中发挥的作用,为研究分析网络中心作战过程提供了理论参考。     

一类带时滞的非线性兰彻斯特战斗模型的分析

基于非线性兰彻斯特方程的一般形式和现代战争的特点,考虑到时间因素在现代战争中的巨大作用,建立并讨论了一类带时滞的非线性兰彻斯特战斗模型。通过定性分析,得到了模型的平衡点及其稳定性,证明了原模型解的存在唯一性,并给出了解的存在区域。战例分析结果表明该模型能用来描述现代战争。因此,该模型对研究现代战争的战斗进程、武器发展规划、现代军事练兵等都具有一定的参考价值。     

战役优势参数及其应用研究

数学分析方法在军事行动计划中扮演着越来越显著的角色。对以兰彻斯特作战模型为基础的描述诸兵种合成作战的矩阵微分方程，以及由方程的控制矩阵和状态变量初值，在不解方程的情况下导出的战役优势参数进行了研究；以空战为例讨论了预测战役结局、辅助军事决策、优化兵力部署和规划火力分配等战役优势参数的主要应用；给出了对战役优势参数和数学模型的评价。     

Lanchester方程与火力指数的内在联系

本文从Lanchester 方程出发,利用正矩阵的特性,将矩阵特征向量与火力指数有机地联系起来。通过例子进一步说明火力指数是Lanchester 方程中威力系数概念的推广;它不仅与武器本身有关,而且依赖于整个战斗的武器配系。当某些种类的武器被摧毁,战斗格局发生一定变化时,火力指数也会发生变化。火力指数还决定于火力分配原则。     

Target selection in lanchester combat: Heterogeneous forces and time-dependent attrition-rate coefficients

We develop solutions to two fire distribution problems for a homogeneous force in Lanchester combat against heterogeneous enemy forces. The combat continues over a period of time with a choice of tactics available to the homogeneous force and subject to change with time. In these idealized combat situations the lethality of each force's fire (as expressed by the Lanchester attrition-rate coefficient) depends upon time. Optimal fire distribution rules are developed through the combination of Lanchester-type equations for combat attrition and deterministic optimal control theory (Pontryagin maximum principle). Additionally, the theory of state variable inequality constraints is used to treat the nonnegativity of force levels. The synthesis of optimal fire distribution policies was facilitated by exploiting special mathematical structures in these problems.     

基于时滞的现代空防对抗兰彻斯特方程模型

针对现代战争中空防对抗过程的复杂,分析了现代作战条件下空袭与防空作战的主要特点,建立了基于时滞的现代空防对抗兰彻斯特方程模型,给出了该模型参数的求取方法,并进行了算例仿真分析,得到了有价值的仿真结果,为现代空防与防空作战提供了指导。     

兰切斯特方程在水雷战模型中的应用与分析

根据对抗模拟的特点,以兰切斯特方程为基础建立了水雷战的解析数学模型,并进行了仿真,得到了被封锁方的兵力组合优化曲线,以定量分析的方法阐明了该模型在战役全局和战术局部上对水雷战对抗双方的指导意义。     

应用新型Lanchester方程的非对称空战进程预测

针对未来空战中可能出现的非对称空战问题进行研究,在设定的非对称空战背景下构建新型Lanchester方程对问题进行建模分析,得到单一机种和多兵种非对称空战模型,并通过仿真试验验证了模型的有效性,对非对称空战指挥决策提供了一定的帮助。     

陆军诸兵种合同作战兰切斯特方程的弹药消耗预测研究

描述了诸兵种合同作战的兰切斯特方程及其矩阵解,提出了一种通过兵力损耗换算弹药损耗的新思路,分析和确定了用该方法预测弹药消耗的相关参数,最后运用Matlab进行仿真计算,预测出了武器装备战损情况和弹药消耗情况。     

战场数字化条件下的单兵数字化系统——“数字化战场与单兵数字化系统”系列论文之二

本文首先讨论了战场数字化条件下单兵数字化系统的概念和内涵，用Ｌａｎｃｈｅｓｔｅｒ模型分析了单兵系统的作战效能，然后以此为基础研究了单兵系统的基本功能单元和实现其整体功能的组成结构。     

机群对地攻击分析动力学模型的建立及仿真分析

根据兰彻斯特作战动态方程的研究方法建立了机群对地攻击效果的分析动力学模型,并通过仿真分析、讨论了影响对地攻击效果的可能因素,如:目标分配形式,目标发现概率,攻击结果侦察概率以及假目标等.     

战场态势转化指挥策略分析

介绍了战场态势的转化规律,构建了考虑时变武器正常发挥因子、增援和非战斗减员的兰切斯特方程,运用此方程定量分析了能促成战场态势由劣转优的两种指挥策略,最后提出了一些作战研究建议.     

海战中信息支援的影响分析

进入信息时代,信息成为作战取胜的第一要素,信息的作用与运行流程的掌握也就成为现代作战分析与决策的重要任务。以信息在作战应用中的特点进行分类为基础,建立了新的作战信息指标体系;想定了具体的典型海战对抗模式,通过构建基于信息支援的兰彻斯特方程模型,经作战仿真模拟,定量描述了在现代海战中信息支援能力的增强对作战能力的提升的显著程度;信息支援能力的提高使敌方损耗呈指数曲线上升。     

空防对抗武器装备对比优势评估模型

针对战役对抗准备和兵力部署的需要,根据兰切斯特动态方程,从作战能力入手,建立了空防对抗武器装备对比优势评估模型,提出了一种异类武器装备对比优势的定量计算方法。给出了应用该方法的具体步骤,通过算例分析,验证了模型的合理性,该模型对其他武器装备的对比优势评估具有一定的参考价值。     

基于网络中心战背景的Lanchester导弹战斗模型

在对网络中心战进行简要介绍基础上,分析了信息网络与导弹作战效能发挥程度的关系。依据此关系,建立了具有网络中心战背景的Lanchester导弹战斗模型并对此模型进行了讨论。最后以海湾战争中美军导弹攻击策略对此模型进行了初步验证。结果表明该模型能较准确反映信息战体系对抗特点,具有较高可信度。