Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.     

On the relationship between the force ratio and the instantaneous casualty-exchange ratio for some lanchester-type models of warfare

A “local” condition of winning (in the sense that the force ratio is changing to the advantage of one of the combatants) is shown to apply to all deterministic Lanchester-type models with two force-level variables. This condition involves the comparison of only the force ratio and the instantaneous force-change ratio. For no replacements and withdrawals, a combatant is winning “instantaneously” when the force ratio exceeds the differential casualty-exchange ratio. General outcome-prediction relations are developed from this “local” condition and applied to a nonlinear model for Helmbold-type combat between two homogeneous forces with superimposed effects of supporting fires not subject to attrition. Conditions under which the effects of the supporting fires “cancel out” are given.     

On the treatment of force-level constraints in times-equential combat problems

The treatment of force-level constraints in time-sequential combat optimization problems is illustrated by further studying the fire-programming problem of Isbell and Marlow. By using the theory of state variable inequality constraints from modern optimal control theory, sharper results are obtained on necessary conditions of optimality for an optimal fire-distribution policy (in several cases justifying conjectures made in previous analysis). This leads to simplification of the determination of the domains of controllability for extremals leading to the various terminal states of combat. (Additionally, some new results for the determination of boundary conditions for the adjoint variables in optimal control problems with state variable inequality constraints have arisen from this work.) Some further extensions of previous analysis of the fire-programming problem are also given. These clarify some key points in the solution synthesis. Some important military principles for target selection and the valuation of combat resources are deduced from the solution. As a result of this work, more general time-sequential combat optimization problems can be handled, and a more systematic solution procedure is developed.     

步兵分队侦察模拟训练系统构建

针对步兵分队侦察训练存在地形受限、战斗情境失真、训练条件构设难等问题,本文在系统分析军事需求的基础上,采用软、硬结合的虚拟仿真技术对步兵分队侦察模拟训练系统框架、体系结构、物理结构、内外接口和应用模式进行了详细分析设计,并对关键技术进行了剖析,该系统方案设计已应用于步兵分队侦察模拟训练系统建设,并投入到院校教学训练中。实践表明,系统通过逼真的视、听一体化实现了高度沉浸式的训练,以现实地形和敌情的高度仿真与灵活组合,满足了步兵分队侦察技能训练对多样化战场环境、实战化目标设置的特殊要求,大大提升了步兵分队地形侦察、敌情侦察及综合对抗训练效益。     

Target selection in Lanchester combat: Linear-law attrition process

We develop the solution to a simple problem of target selection in Lanchester combat against two enemy force types each of which undergoes a “linear-law” attrition process. In addition to the Pontryagin maximum principle, the theory of singular extremals is required to solve this problem. Our major contribution is to show how to synthesize the optimal target selection policies from the basic optimality conditions. This solution synthesis methodology is applicable to more general dynamic (tactical) allocation problems. For constant attrition-rate coefficients we show that whether or not changes can occur in target priorities depends solely on how survivors are valued and is independent of the type of attrition process.     

Some simple victory-prediction conditions for lanchester-type combat between two homogeneous forces with supporting fires

This paper develops new “simple” victory-prediction conditions for a linear Lanchester-type model of combat between two homogeneous forces with superimposed effects of supporting fires not subject to attrition. These simple victory-prediction conditions involve only the initial conditions of battle and certain assumptions about the nature of temporal variations in the attrition-rate coefficients. They are developed for a fixed-force-ratio-breakpoint battle by studying the force-ratio equation for the linear combat model. An important consideration is shown to be required for developing such simple victory-prediction conditions: victory is not guaranteed in a fixed-force-ratio-breakpoint battle even when the force ratio is always changing to the advantage of one of the combatants. One must specify additional conditions to hold for the cumulative fire effectivenesses of the primary weapon systems in order to develop correct victory-prediction conditions. The inadequacy of previous victory-prediction results is explained by examining (for the linear combat model without the supporting fires) new “exact” victory-prediction conditions, which show that even the range of possible battle outcomes may be significantly different for variable-coefficient and constant-coefficients models.     

The rise and fall of counterproliferation policy

The US government initiated a Defense Counterproliferation Initiative to address the concern that, in the post-Cold War years, the proliferation of nuclear, biological, and chemical weapons would be widespread and create a significant challenge to the US military’s combat operations. In particular, non-nuclear states might use chemical or biological warfare agents against US forces with the belief that nuclear weapons would not be used against them in retaliation. Following the events of September 11, 2001, defense strategy and policy shifted to a wider view of the threat of adversarial use of “weapons of mass destruction” (WMD) and the term “counterproliferation” was replaced by “combating” or “countering WMD.” Over time, the Defense Department increasingly moved away from counterproliferation principles with the detrimental effect of losing capabilities that US forces still need for contemporary adversaries. This shift has been aggravated by other US government agencies’ use of “counterproliferation” in lieu of what would have been termed “nonproliferation” activities in the 1990s. The loss of clarity within the US government on these terms has led to the inability to focus the “whole of government” on this significant national security challenge. To alleviate this challenge, the US government needs a top-down initiative to refocus policy on the distinctly different aspects of WMD with respect to military combat operations, combating terrorism, and homeland security.     

Theoretical analysis of lanchester-type combat between two homogeneous forces with supporting fires

This paper studies combat between two homogeneous forces modelled with variable-coefficient Lanchester-type equations of modern warfare with supporting fires not subject to attrition. It shows that this linear differential-equation model for combat with supporting fires may be transformed into one without the supporting fires so that all the previous results for variable-coefficient Lanchester-type equations of modern warfare (without supporting fires) may be invoked. Consequently, new important results for representing the solution (i.e. force levels as functions of time) in terms of canonical Lanchester functions and also for predicting force annihilation are developed for this model with supporting fires. Important insights into the dynamics of combat between two homogeneous forces with such supporting fires are discussed.     

Effective attacks in the salvo combat model: Salvo sizes and quantities of targets

This article considers two related questions of tactics in the context of the salvo model for naval missile combat. For a given set of targets, how many missiles should be fired to produce an effective attack? For a given available salvo size, how many enemy targets should be fired at? In the deterministic version of the model I derive a simple optimality relationship between the number of missiles to fire and the number of targets to engage. In the stochastic model I employ the expected loss inflicted and the probability of enemy elimination as the main performance measures and use these to derive salvo sizes that are in some sense “optimal.” I find that the offensive firepower needed for an effective attack depends not only on a target's total strength but also on the relative balance between its active defensive power and passive staying power. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Kinetics in counterinsurgency: some influences on soldier combat performance in the 1st Australian Task Force in the Vietnam War

Counterinsurgency is often characterized by large numbers of small fire-fights interspersed with a few larger battles. Heavy firepower contributes to the outcome of the larger battles but the smaller contacts are often fought by infantry without heavy weapons support. Infantry combat performance in these fire-fights is therefore a key concern. It has been fashionable to discuss soldier combat performance in terms of ‘firers’, ‘non-firers’, and ‘posturers’, but we argue that other factors have a greater impact. We provide a detailed statistical analysis of a selection of combat factors, using combat data collected by the 1st Australian Task Force (1ATF) during the Vietnam War. An accepted measure of soldier lethality is the ‘shots per casualty’ ratio. Using this measure we are now able to describe the combat performance of the Australian infantry section in Vietnam in much greater detail than has hitherto been possible.     

Lanchester-type models of warfare and optimal control

The optimization of the dynamics of combat (optimal distribution of fire over enemy target types) is studied through a sequence of idealized models by use of the mathematical theory of optimal control. The models are for combat over a period of time described by Lanchester-type equations with a choice of tactics available to one side and subject to change with time. The structure of optimal fire distribution policies is discussed with reference to the influence of combatant objectives, termination conditions of the conflict, type of attrition process, and variable attrition-rate coefficients. Implications for intelligence, command and control systems, and human decision making are pointed out. The use of such optimal control models for guiding extensions to differential games is discussed.     

论“空海一体战”与中国国家安全

“空海一体战”是美国的一种新型作战理论,是在20世纪80年代“空地一体战”等诸多战法及兵种妥协基础上形成的一种新型军事战略,旨在通过空海军力量的配合,进行近域作战,以抵消对手的反进入/区域拒止能力,取得战争的主动权与控制权.“空海一体战”作为美国战略重心东移的重要角力点与支撑要素,在美国亚太战略中的作用举足轻重,对亚太周边国家尤其是中国的国家安全构成重大威胁,为此有必要对其理论渊源、发展目标、策略行动及障碍缺陷进行剖析与解构,为中国维护国家安全,构建良好的国家安全环境提供战略储备与智力支持.     

A Lanchester-type aggregated-force model of conventional ground combat

This article develops a Lanchester-type model of large-scale conventional ground combat between two opposing forces in a “sector”. It is shown that nonlinear Helmbold-type equations of warfare with operational losses may be used to represent the loss-rate curves that have been used in many aggregated-force models. These nonlinear differential equations are used to model the attrition of combat capability (as quantified by a so-called firepower index) in conjunction with a rate-of-advance equation that relates motion of the contact zone (or FEBA) between the opposing forces to the force ratio and tactical decisions of the combatants. This simplified auxiliary model is then used to develop some important insights into the dynamics of FEBA movement used in large-scale aggregated-force models. Different types of behavior for FEBA movement over time are shown to correspond to different ranges of values for the initial force ratio, for example, an attack will “stall out” for a range of initial force ratios above a specific threshold value, but it will “break out” for force ratios above a second specific threshold value. Such FEBA-movement predictions are essentially based on being able to forecast changes over time in the force ratio.     

浅析军旅诗词的战斗力

军旅诗词的战斗力,主要是通过提高我军战斗精神和打击敌军士气两个方面来实现的。从军事历史实践看,这种战斗力主要包括四个方面：讴歌正义,增强战斗意识;描绘蓝图,激发战斗豪情;不怕艰险,战斗作风顽强;情理交融,瓦解敌军意志。     

数字化步兵作战态势感知建模与仿真研究

通过分析数字化步兵的态势感知需求和信息获取来源以及信息传递方式，建立了数字化步兵单兵和连以下分队的态势感知模型，并进一步讨论了该模型的仿真实现途径。该模型可应用于数字化步兵作战仿真和单兵综合作战系统的效能仿真。     

多机协同目标与火力资源分配

在协同空战中,快速正确的空战决策是己方战机少受敌方伤害并取得战争胜利的前提。目标与火力资源分配是决策过程的重要部分。多机空战与单机空战相比有明显的不同,不同之处是面临多个敌方目标,根据我方资源最优分配作战对象和火力,基于遗传算法实现了两种算法的有人无人目标与火力资源分配。仿真结果表明,带有毁伤概率门限的算法既节省火力资源又快速有效。     

Bringing Military Conduct out of the Shadow of Law: Towards a Holistic Understanding of Rules of Engagement

In this article, I outline a holistic approach to the military concept of “Rules of Engagement” (ROE), which complements the legal aspects of ROE with considerations of operational and political requirements for the use of military force. Drawing upon two illustrative cases from the US military experience with the use of ROE, I demonstrate that ROE for any particular military operation should be formulated to balance optimally, if not harmonize fully, the legal, operational and political concerns related to the use of force. In this task, political decision-makers and military practitioners alike are confronted with unavoidable and real-life dilemmas. How these dilemmas are handled has significant implications for how legal requirements concerning accountability and concerns for civilian lives in military combat can be preserved through ROE.     

基于效果的炮兵火力打击控制示例

针对当代战争形态变化对炮兵战斗行动提出的诸多挑战,以我军炮兵战术理论为依据,借鉴美军"基于效果作战"理论,提出了一个具体的炮兵火力打击行动示例。通过运用"基于目标"与"基于效果"两种不同的作战思想对示例进行分析,既定性阐述了两种思想所制定作战方案的优劣,又根据对敌总体毁伤概率、炮兵生存概率、弹药消耗量和作战时间四个指标定量对比了两种作战思想下战斗结局的差异,从而论证了基于效果的炮兵火力打击控制思想的可行性和优异性,并通过模拟仿真,得出了一些有益于推动炮兵战术发展的普遍性结论。     

“Effing” the military: a political misunderstanding of management

The use of commercial business management techniques is widespread in all government departments, including the Ministry of Defence. This article examines the use of popular management techniques in the Armed Forces and argues that their application is misplaced. It looks at what the “effs” – “efficiency” and “effectiveness” – mean in the business world and to the Armed Forces. It compares the definitions both in business and the Armed Forces and finds that there are few, if any, situations where the same measurements can be applied. Whilst many management techniques are suited for business, the function of the Armed Forces and its output cannot be measured in the same way, complicated by the different metrics of “efficiency” in peace and in war. This difference may not be clearly understood by some politicians, or indeed by some senior military personnel. Using examples from some of the most popular management techniques such as “Lean” and “Agile” it is possible to see that their use might actually diminish the capabilities of the Armed Forces when it comes to performing their principal role – the use of force to achieve political objectives.     

Force deployment and the production of security: Why is the united states in NATO?

Standard economic concepts of production and cost minimization subject to a production constraint are used to derive the conditions of optimal deployment of home and forward military forces for the production of home security. United States' participation in the NATO alliance is then analyzed in the context of a two‐ally (U.S. and Western Europe) optimal force deployment model of NATO. Next, U.S. force‐basing policy is adduced as an enforcement mechanism for the “transatlantic contract.” Lastly, statistical evidence on burden sharing within Western Europe, and the effectiveness of the U.S. contract enforcement policy, is presented.