基于时滞兰彻斯特战斗模型的现代攻防对抗

针对现代攻防对抗研究的复杂性,在分析已有的现代战争模型的基础上,充分考虑时间因素在作战中的影响,建立了反映双方对抗态势的时滞兰彻斯特战斗模型,并借助Matlab-Simulink工具箱,对模型进行了数值仿真实验。仿真结果表明：时间因素在现代攻防对抗中占据越来越重要的地位。最后依据所得结论,分别探讨了攻防双方为取得最佳战绩应当采取的对策,为武器装备发展规划、现代作战决策与军事练兵提供一定的理论指导。     

基于改进兰彻斯特平方律的空战进程预测研究

在战斗进程预测方面,兰彻斯特方程起着重要作用。分析了兰彻斯特平方律模型,得出了战役优势参数和参战双方战斗单位数量的关系;在考虑预警机支援的情况下,分别对兰彻斯特平方律和多元兰彻斯特平方律模型进行了改进,并得出了相应的改进后的战役优势参数形式;最后将改进后的模型分别应用于单一机型和多种机型参战的空战进程预测,仿真结果表明,预警机是取得战役优势的关键因素。     

基于时滞兰彻斯特战斗模型的现代攻防对抗?

针对现代攻防对抗研究的复杂性,在分析已有的现代战争模型的基础上,充分考虑时间因素在作战中的影响,建立了反映双方对抗态势的时滞兰彻斯特战斗模型,并借助Matlab?Simulink工具箱,对模型进行了数值仿真实验。仿真结果表明：时间因素在现代攻防对抗中占据越来越重要的地位。最后依据所得结论,分别探讨了攻防双方为取得最佳战绩应当采取的对策,为武器装备发展规划、现代作战决策与军事练兵提供一定的理论指导。     

基于改进战役优势参数的作战飞机优化配置

空军在现代战争中起着不可替代的作用,而作战飞机是空中力量的重要组成部分.在考虑信息支援和预警机的情况下,改进了多元兰彻斯特方程,并进一步导出了改进的战役优势参数.以战役优势参数为目标函数,建立了作战飞机在装备数量和采购经费限制条件下的优化配置模型,最后通过算例验证了模型的有效性.     

基于SD的信息化防御作战中兰彻斯特方程

在对信息化条件下的防御作战进程分析的基础上,增加信息因素和兵力补充速度对经典的兰彻斯特方程进行改进。通过引入系统动力学方法,构建了信息化条件下的防御作战进程的系统动力学模型,利用系统动力学方法来对改进的兰彻斯特方程进行求解。仿真结果证明了系统动力学在解决复杂兰彻斯特方程中的优越性。     

装备战损量的兰彻斯特方程预计方法*

针对装备战损量预计这一未来作战装备保障必须解决的核心问题,运用兰彻斯特方程探讨解决途径。从分析影响装备战损的因素出发,综合讨论目前预计装备战损量的方法,提出基于指数多元兰彻斯特方程的装备战损量预计模型和模型中毁伤能力系数的确定方法,得到了装备战损量的兰彻斯特方程预计方法,并举例验证。该方法将经验计算与模拟计算相结合,用较简单的确定性解析方程描述所考虑因素对装备战损量的客观约束关系,较好地满足了未来信息化条件下作战装备战损量预计的需要。     

蓝彻斯特方程与作战研究

本文对蓝彻斯特方程在战斗中的指导意义、它与集中兵力的优化问题以及它在现代战争的应用作了一些粗浅的探讨。     

反映作战协同的兵力损耗微分方程

基于现代战争作战体系对抗中作战单位损耗相关性,在兰彻斯特平方律基础上引入协同系数概念,加入相关性指标.建立了反映作战协同的兵力损耗微分方程.以作战双方各有两个作战单位参战的具体模型为例进行分析,给出了随战斗时间演变的作战双方兵力变化值,绘出了相应兵力损耗曲线.分析结果表明,在作战双方初始战斗力不等的情况下,协同水平的高低有可能成为决定战斗结果的关键因素.该兵力损耗模型对于研究现代协同作战具有一定意义.     

应用兰彻斯特法进行体系对抗效能评估

在考虑整体效能、强调体系对抗时,单一方法的应用存在其固有的局限性,兰彻斯特法综合应用了多种分析方法,能对对抗双方的效能进行准确的评估.建立了矩阵形式的多元兰彻斯特方程,引用算例,以任务完成率作为效能指标,比较分析了对抗双方处于平方律和线性律两种作战方式下的效能.     

诱饵干扰下无人机集群攻击阈值控制方法

针对诱饵干扰下无人机集群作战中的计算量爆炸,攻击阈值控制解算困难问题,给出了一种基于兰彻斯特方程和最优控制模型的无人机集群作战攻击阈值控制方法。从机载雷达的性能出发,建立作战双方兵力损耗的微分方程,从而构建改进兰彻斯特方程;以兰彻斯特方程为最优控制的状态方程,以无人机攻击阈值为控制变量,建立弹药约束下无人机集群空战的最优控制模型,并且证明一方剩余兵力的最大化等价于另一方剩余兵力的最小化;最后采用直接凸优化法对最优控制问题进行求解,并进行仿真验证。     

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.     

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。     

“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.     

一种基于随机映射的战斗效能模型

利用随机映射概念提出了一种新的战斗毁伤模型形式———Lanchester战斗网络模型。模型是由一个阶递减的随机映射序列组成的随机有向二部图,它明确、形式地描述了战争整体行为与局部作用之间的关系。理论分析和计算获得的结论表明,模型描述的整体作战效能符合Lanchester平方律,其网络拓扑结构是非同质的,出度和入度分布服从指数幂律。应用模型定量对比了“对称”与“非对称”战斗中全局信息因素对战斗系统整体效能的影响。初步讨论了网络模型研究在战争建模理论、实证和计算方法论上的意义。     

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.     

着眼信息化条件下作战需求充分发挥军队律师职能作用

信息化条件下作战对战争各要素提出了更多更高的要求,法律支持与保障作用凸显、不可或缺。作为军事行动法律保障的专业力量,军队律师唯有积极应对战场环境透明化、军事打击快速化、作战行动精确化的作战特点,坚持运用为主,做好平战转化,紧贴作战需求,提供及时、精准的全程化和全方位法律保障,才能充分发挥其职能作用,运用法律武器确保作战意图的最终达成。     

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.     

导弹作战体系作战能力评估方法研究*

对导弹作战体系作战能力评估问题进行了建模与仿真研究.分析了导弹作战体系的基本构成,建立了基于指数法和兰彻斯特战斗方程的导弹作战体系作战能力评估模型;仿真分析了发现和预警概率、指挥控制系统作战能力对导弹作战体系作战能力的影响,得到了一些有价值的数值仿真结论.