【作者】 邢东亚；

【导师】 石鸿雁；

【作者基本信息】 沈阳工业大学 ， 应用数学， 2012， 硕士

【摘要】 微分对策理论起源于军事并广泛应用于经济、工程、生物等各个领域。随着高新技术在军事中的广泛应用,使得微分对策问题的研究显得尤为重要。由于在实际的军事对抗中战机转瞬即逝,因此,寻求一种快速有效的解法,并且将智能方法与微分对策进行结合是微分对策理论未来发展的方向。本文针对微分对策的计算问题展开理论研究;针对微分对策在作战指挥中的某些问题展开了应用研究。主要内容包括:1、研究了微分对策数值解的求解方法。智能优化的发展为微分对策理论研究提供了一种有效的方法和技术途径。本文深入研究了混沌优化、人工鱼群算法的原理、实施步骤以及特点,针对人工鱼群算法运行速度慢和优化精度较差的缺点及混沌变量具有随机性、遍历性及规律性的特点,将混沌优化与人工鱼群相结合提出高效的混沌人工鱼群混合算法,通过对一些测试函数进行仿真实验,验证了该算法在寻优速度和计算精确度上均优于基本人工鱼群算法。同时在一定的假设条件下证明出混沌人工鱼群算法依概率收敛于全局最优值。2、研究了微分对策在作战指挥中的应用。基于Lanchester方程,着眼于最优火力分配问题研究。由于战争的多样性和复杂性,本文主要探讨在直瞄武器交战下单兵种对多兵种作战这类比较典型的战争模型,运用微分对策最大值最小值原理进行分析,得出最优分配策略,即多兵种一方应全力攻击单兵种一方;单兵种一方对多兵种一方的攻击顺序取决于双方的交战强度,应按交战强度从大到小顺序攻击,从而给出了军事对抗中兵力不占优势一方如何获取胜利的一种方法。3、结合特拉法尔海战历史战例,在军事想定的基础上建立适当的数学模型,利用本文提出的混沌人工鱼群算法,对模型进行求解,同时对得到的结果做出分析和研究,得出作战双方火力分配的最优决策。更多还原

【Abstract】 Differential games theory has been applied to economics, engineering, biology and allother fields. Especially in the world today, high technology in military affairs iswidespread usage, making the research of differential games problem more important. Thispaper directs at theoretical researches on the numerical calculation methods of differentialgame; also made researches on some problem of its application in attack, command andcontrol. Main contents include:1、Numerical calculation methods to differential game are researched. Development ofartificial intelligence provides an effective method and technological approach fordifferential game theoretical research. Principle, implementation steps and characteristicsof the chaos optimization and artificial fish-swarm algorithm are researched deeply. Due tolow speed and inadequate optimal efficiency of AFSA and chaotic variables with therandomness, regularity, an efficiency optimal hybrid algorithm (SCAFSA) whichcombines chaos optimization and artificial fish-swarm is proposed. The simulatingexperiment of test function verifies that this hybrid algorithm is stronger than AFSA inglobal optimization and the search efficiency is higher. Theoretically, this paper provesthat under certain circumstances the hybrid algorithm is convergent in probability to globaloptimum.2、Applications of differential game on operational commanding are researched.Based on Lanchester equation, the optimal fire allocation problem is focused on. Becausethe diversity and complexity of war, the article mainly discusses at straight war weaponsthe typical differential game model of one to many. Using the maximum and minimumprinciple in differential game, optimum allocation strategy is obtained. So the side withmore arms should attack the only arm with full power. The attack policy of single arm sidedepends on the descending order of battle intensity. And then the question of bad situationarm winning in military confront is solved. 3、In consideration of Battle of Trafalgar historical case, on the basis of the MilitaryScenario base appropriate mathematical model is set up, using SCAFSA which is proposedin the article. Then the results are analysed and researched properly, getting both sides inmilitary affairs optimizing decision of power distribution.更多还原