An examination of the effects of the criterion functional on optimal fire-support policies

This paper examines the dependence of the structure of optimal time-sequential fire-support policies on the quantification of military objectives by considering four specific problems, each corresponding to a different quantification of objectives (i.e. criterion functional). We consider the optimal time-sequential allocation of supporting fires during the “approach to contact” of friendly infantry against enemy defensive positions. The combat dynamics are modelled by deterministic Lanchester-type equations of warfare, and the optimal fire-support policy for each one-sided combat optimization problem is developed via optimal control theory. The problems are all nonconvex, and local optima are a particular difficulty in one of them. For the same combat dynamics, the splitting of supporting fires between two enemy forces in any optimal policy (i.e. the optimality of singular subarcs) is shown to depend only on whether the terminal payoff reflects the objective of attaining an “overall” military advantage or a “local” one. Additionally, switching times for changes in the ranking of target priorities are shown to be different (sometimes significantly) when the decision criterion is the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths of the combatants' total infantry losses. Thus, the optimal fire-support policy for this attack scenario is shown to be significantly influenced by the quantification of military objectives.     

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.     

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.     

基于动态贝叶斯网的炮兵战斗效果评估建模仿真

依据炮兵火力作战的特点规律,分析炮兵战斗效果评估的内容、程序、建模过程和影响因素,运用动态Bayesian网建立炮兵战斗效果评估模型,运用主成分分析方法确定评估专家权重,运用Poly Tree的消息传递算法进行评估网络推理分析,最后结合案例仿真验证。结果表明,该研究解决了情报信息不确定性、模糊性和动态性等影响战斗效果精确评估问题。     

“simple-approximate” battle-outcome-prediction conditions for variable-coefficient lanchester-type equations of modern warfare

This article considers combat between two homogeneous forces modeled by variable- coefficient Lanchester-type equations of modern warfare and develops new “simple-approximate” battle-outcome-prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). These battle-outcome-prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition-rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable-coefficient Lanchester-type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.     

信息化条件下单炮多发同时弹着研究

信息化条件下,炮兵火力打击的强度对炮兵火力打击效果的影响呈指数函数递增,集中火力依然是炮兵战斗的首要原则,也是提高火力打击效果的首要手段,炮兵火力打击的速度与强度结合创造决定性效果.分析了信息化条件下单炮多发同时弹着的目的和用途,给出了实现多发同时弹着的约束条件,讨论了弹道计算模型和同时弹着方案的确定方法,并以某155mm自行火炮为例进行了多发同时弹着的计算与分析,论证了单炮实施多发同时弹着的可行性.     

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.     

On the isbell and marlow fire programming problem

A complete solution is derived to the Isbell and Marlow fire programming problem. The original work of Isbell and Marlow has been extended by determining the regions of the initial state space from which optimal paths lead to each of the terminal states of combat. The solution process has involved determining the domain of controllability for each of the terminal states of combat and the determination of dispersal surfaces. This solution process suggests a solution procedure applicable to a wider class of tactical allocation problems, terminal control attrition differential games. The structure of optimal target engagement policies in “fights to the finish” is discussed.     

基于ExtendSim的高炮群作战效能仿真分析

构建了高炮部队抗空袭作战仿真流程,并在特定作战条件下基于ExtendSim建立了高炮群雷达诸元法抗击敌空袭目标的作战仿真模型,对火控雷达组网工作模式下的扇形和线性配置的高炮群作战效能进行了仿真分析,结果表明在火控雷达组网模式下,高炮群整体探测范围增大,作战反应时间延长,提高了部队作战效能。     

多指标下的炮兵火力最优分配

为了提高炮兵火力打击效能,提出了小生境遗传算法与模糊多目标决策相结合的混合算法,建立了多指标下的炮兵火力分配模型,并阐述了混合算法设计,给出了应用举例,结果表明,与传统的单指标下的炮兵火力最优分配相比,该方法更符合战场实际情况。     

某高炮火控系统射击诸元采集装置设计

在高炮火控系统射击校正中,射击诸元需要以数字量形式送入校射系统作为输入信号使用,而高炮火控系统射击诸元大都是采用三相轴角信号形式的模拟信号。为了解决这一问题,设计了一种高炮火控系统射击诸元采集装置实现射击诸元模拟量向数字量形式的转换。首先分析了射击诸元的采集与测量原理,设计了SCOTT变压、采样保持、A/D转换、正峰值脉冲产生、数据处理与控制等硬件功能电路,阐述了采集装置的总体工作过程,在此基础上进行了软件程序设计。该射击诸元采集装置的研制为高炮火控系统射击诸元的采集以及校射工作提供了一种实用的方法。     

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.     

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.     

炮兵作战指挥训练手段与训练质量相关性分析

为了探索炮兵作战指挥训练手段与训练质量之间的关系,在向有关专家咨询的基础上,运用模糊数学方法对现有炮兵作战指挥训练手段进行模糊综合评价及模糊聚类分析。从分析中可以得到不同训练手段对训练质量各因素影响程度不同;利用组合数学模型对炮兵作战指挥训练手段的优化组合,提供了数据支持,实现优劣互补;通过建立模糊相关矩阵,为炮兵作战指挥训练手段比例分配提供依据。     

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.     

炮兵指挥决策中优选作战方案的神经网络模型

优选作战方案是炮兵指挥决策的重要内容.如何从炮兵众多的作战方案中确定其价值,并根据作战任务需要选出最佳方案,是炮兵指挥员及其参谋人员的-项重要任务.根据神经网络中联想记忆的-般模型和迭代解法对炮兵作战方案进行分析和排序,并可运用计算机进行处理,为炮兵指挥员的决策行为提供依据.     

Theoretical analysis of the general linear model for lanchester - type combat between two homogeneous forces

This paper studies Lanchester-type combat between two homogeneous forces modeled by the so-called general linear model with continuous replacements/withdrawals. It demonstrates that this model can be transformed into a simpler canonical form, which is also shown to arise from fixed-force-level-breakpoint battles modeled by Lanchester-type equations for modern warfare. Analytical expressions for the force levels for the general variable coefficient linear model with continuous replacements/withdrawals are constructed out of so-called general Lanchester functions for the model without replacements/withdrawals, for which all solutions are shown to be nonoscillatory in the strict sense. These force-level results are unfortunately so complicated and opaque that the constant-coefficient version of the model must be studied before any insights into the dynamics of combat may be analytically obtained. Thus, fairly complete results are given for the general linear model with constant attrition-rate coefficients and constant rates of replacement/withdrawal. However, the expressions for the force levels are still so complicated that we have not been able to develop battle-outcome prediction conditions directly from them alone but have had to establish general results on the qualitative behavior of solutions. A significant result (and one that greatly complicates the prediction of battle outcome) is that all solutions to the model with replacements/withdrawals are no longer necessarily nonoscillatory in the strict sense, i.e., both sides force levels can take on negative values if the force-on-force attrition equations are not “turned off” at the right time. Thus, this paper shows that the addition of continuous replacements/withdrawals to a Lanchester-type model may significantly change the qualitative behavior of the force-level trajectories. Battle-outcome prediction conditions are nevertheless given, and important insights into the dynamics of combat are briefly indicated.     

炮兵作战决策方案优选的方法

炮兵作战方案的选择,是炮兵作战指挥决策的关键环节,其合理与否,直接关系到炮兵作战效能的发挥和作战的成败.根据炮兵作战的实际,阐述了炮兵作战方案优选的依据,给出了运用层次分析法确定影响作战方案选择的各因素权重的方法步骤,在对优选依据的建模要素进行分析的基础上,构建了每个要素的效用函数计算模型,并给出了评估方案的计算方法,提供了模型应用的一般步骤.     

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。     

基于效果的炮兵行动C2系统动力学建模与仿真

一体化联合作战参战军兵种多、指挥控制(C2)与协调复杂。围绕炮兵行动特点要求,运用系统动力学理论建立联合作战炮兵行动指挥控制的系统动力学模型,研究常规打击和基于效果作战两种指挥控制模式下炮兵行动所产生的不同结果及其原因,并给合作战想定仿真验证,得出较为可靠的结论,为解决联合作战炮兵行动精确指挥控制与协调提供一种有效途径