企业债务与破产对策模型

本文从多人合作对策理论出发,讨论企业破产时尚留资产价值抵不上债务总数时,如何在债权人间进行合理分配的问题,并将此问题转化为一个相应的多人合作对策模型,较详细地讨论了使用对策的τ值法解作为破产对策问题合理分配方法的计算过程。本文讨论的方法可以推广至一般企业、工厂破产时的资产分配中去。     

求解最小费用最大流问题的一种方法

介绍了最大流问题的多解，提出了通过调整圈来求解最小费用最大流的方法。     

航线网络中基于最小费用流的航线选择问题

针对航线网络中航线选择优化问题,分析了空中交通航线网络结构和空中交通流的特点,给出了空中交通航线网络的数学描述,考虑从求解最小费用流问题的角度寻求最优航线,建立了航线网络中求解最小费用流问题的数学模型。借鉴了连续时间网络最小费用流问题中结点到达费用的概念,并结合简单算例的求解验证了航线网络中用最小费用流方法选择航线的可行性,具有良好的计算性能。     

具有学习效应的单机可控加工时间排序问题研究

在经典排序问题中，工件的加工时间往往是一个常数，但在现代生产过程中，工件的加工时间受许多因素的影响。因此，研究工件具有学习效应的单机可控加工时间排序问题，其中工件的加工时间是其所在位置的函数，且与加工时间的控制变量有关。目标是求出最优的加工时间控制变量和最优的排序使得目标函数最小，目标函数包括极小化时间表长与控制费用的和、极小化总完工时间与控制费用的和、极小化总完工时间偏差和与控制费用和。证明他们都能转化为指派问题，从而多项式时间可解。并给出数值例子来说明问题是如何求解的。     

带有时间与探测约束的“到达-回避”博弈

针对飞行器具有运行时间约束以及所携带探测器具有有限探测范围的现实情况，在传统生命线对策问题的基础上提出了一类考虑时间约束与探测约束的新型“到达-回避”定性微分对策博弈。通过分析对策问题所有可能的中性终端集以及问题对应的哈密顿方程，给出了防御者与进攻者最优博弈策略形式。利用所得到的策略和攻防双方的约束条件，得到了原问题对应界栅的精确解，并通过数值仿真验证了界栅的正确性。所得到的界栅可将博弈空间分为攻防双方的获胜区域，并可用于快速判断博弈问题最终结果，为飞行器攻防博弈双方的策略制定提供理论依据。     

关于E．O．Q．公式的一点改进

经济订购批量公式（E．0．Q．公式）是管理学中很重要的一个公式，但其假设条件中却有“存储空间无限大”这一条件不符合的实际条件这一问题，针对此问题提出了改进方案：扩大投资，建设新的存储空间，存储物品。针对这种方案建立了总平均费用存储模型，并讨论模型的适用条件，得出其在总平均费用最小条件下的最优解。     

不允许缺货时存储空间存在限制的存储模型研究

针对经济订购批量公式假设中存储空间无限大这一条件不符合实际这一问题,提出了改进方案：租用场地,存储物品。针对这种方案建立了总平均费用存储模型,给出了在总平均费用最小意义下的最优存储决策。并给出实例验证其可行性。     

联合策略的数学模型及其最优化解

本文建立了联合策略的数学模型，首先给出在引进联合策略后，Ｎ人多次对策的数学模型的特殊代数表示式，其次建立了求解Ｍ方（ｒ＋１）个联合策略的数学模型。进而讨论了联合策略的最优化解。联合策略，Ｎ人多次对策，数学模型     

基于模糊理论的微分对策制导律

在现代战场环境下，导弹制导所需信息经常受到各种干扰，有时甚至是不确定的。而基于精确模型的微分对策制导律的实时实现面临着许多困难。为解决这个问题，尝试将模糊理论与微分策制导律相结合，采用多级模糊控制规则，以导弹怀收音机格半为例，给出了模型的建立方法，并探讨了这种模糊微分对策制导律实现的可行性和优点，为将来发展基于微分对策理论的智能制导律提供了一定的思路。     

两种多天线GNSS动态定姿方法的比较

针对移动载体对姿态的需求,对两种多天线GNSS动态定姿方法,即直接法和最小二乘迭代法进行了研究.分析了定姿的原理,给出了姿态解算模型.基于车载四天线GNSS的实测数据,分别用两种方法进行了姿态解算,并用同一运动平台高精度惯导给出的姿态作为参考值,对两种定姿方法的精度和可靠性进行了分析和比较.     

非对称机动能力多无人机智能协同攻防对抗

协同攻防对抗是未来军用无人机的重要作战场景。针对不同机动能力无人机群体间的攻防对抗问题，建立了多无人机协同攻防演化模型，基于多智能体强化学习理论，研究了多无人机协同攻防的自主决策方法，提出了基于执行-评判（Actor-Critic）算法的集中式评判和分布式执行的算法结构，保证算法稳定收敛的同时，提升执行效率。无人机的评判模块使用全局信息评价决策优劣引导策略学习，而执行时只需要依赖局部感知信息进行自主决策，提高了多机攻防对抗的效能。仿真结果表明，所提的多无人机强化学习方法具备较强的自进化属性，赋予了无人机一定智能，即稳定的自主学习能力，通过不断演化，能自主学习提升协同对抗的决策效能。     

Satellite proximate interception vector guidance based on differential games

This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire (CW) equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exo-atmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations.     

An Adaptive Weighted Differential Game Guidance Law

For intercepting modern high maneuverable targets, a novel adaptive weighted differential game guidance law based on the game theory of mixed strategy is proposed, combining two guidance laws which are derived from the perfect and imperfect information pattern, respectively. The weights vary according to the estimated error of the target’s acceleration, the guidance law is generated by directly using the estimation of target’s acceleration when the estimated error is small, and a differential game guidance law with adaptive penalty coefficient is implemented when the estimated error is large. The adaptive penalty coefficients are not constants and they can be adjusted with current target maneuverability. The superior homing performance of the new guidance law is verified by computer simulations.     

Linear Quadratic Differential Game Strategies with Two-pursuit Versus Single-evader

In order to intercept the future targets that are characterized by high maneuverability, multiple interceptors may be launched and aimed at single target. The scenario of two missiles P and Q intercepting a single target is modeled as a two-pursuit single-evader non-zero-sum linear quadratic differential game. The intercept space is decomposed into three subspaces which are mutually disjoint and their union covers the entire intercept space. The effect of adding the second interceptor arises in the intercept space of both P and Q (PQ-intercept space). A guidance law is derived from the Nash equilibrium strategy set (NESS) of the game. Simulation studies are focused on the PQ-intercept space. It is indicated that 1) increasing the target’s maneuverability will enlarge PQ-intercept space; 2) the handover conditions will be released if the initial zero-effort-miss (ZEM) of both interceptors has opposite sign; 3) overvaluation of the target’s maneuverability by choosing a small weight coefficient will generate robust performance with respect to the target maneuvering command switch time and decrease the fuel requirement; and 4) cooperation between interceptors increases the interception probability.     

Cooperative differential games guidance laws for multiple attackers against an active defense target

This paper is concerned with a scenario of multiple attackers trying to intercept a target with active defense. Three types of agents are considered in the guidance: The multiple attackers, the target and the defender, where the attackers aim to pursuit the target from different directions and evade from the defender simultaneously. The guidance engagement is formulated in the framework of a zero-sum two-person differential game between the two opposing teams, such that the measurements on the m...     

飞机除冰资源申请过程航空公司的博弈研究

以博弈论方法为分析工具,分析飞机除冰资源申请过程航空公司的博弈行为及其经济绩效。以航空公司合作组织中各博弈方的资源转让策略为研究对象,引入了合作博弈思想和违约惩罚机制,讨论航空公司合作组织的最优稳定策略,设计了基于Agent效用的成员协商算法;最后,运用协商算法结合Shapley值解分析的方法对除冰费用分摊的的合理性进行仿真,结果对比显示,此方法实现了分配的公平和有效。     

团队精神中的博弈分析

“负和博弈”和“零和博弈”是一种不合作博弈;而“正和博弈”是一种合作性博弈。在一个团队中,要取得良好的效果,不应采取对抗性博弈,而应制造非对抗性博弈,在竞争合作中寻找到辩证的结合点。     

Linear-quadratic and norm-bounded differential game combined guidance strategy against active defense aircraft in three-player engagement

A new type of guidance strategy, combining linear quadratic and norm-bounded game theory, is proposed for the scenario of an attacker against active defense aircraft in three-player engagement. The problem involves three players, an attacker, a defender and a target. The differential game theory and the solution of Hamiltonian equation are utilized to obtain the combined guidance strategy for each player with arbitrary-order dynamics. The game process is divided into 4 phases, C1-C4, according to the switching time. The linear quadratic differential game guidance scheme is employed to reduce the fuel cost in the game parts of C1 and C3. The norm-bounded game guidance strategy is adopted to satisfy the constraint of control input in the game stages C2 and C4. Furthermore, zero-effort miss distance is introduced to meet the constraints of game space and defender’s killing radius in the guidance strategy, which guarantees that the attacker is able to avoid the interception of the defender and hit the target with lower fuel cost and maximum acceleration. And it is proved that the proposed guidance strategy satisfies the Nash equilibrium condition. Finally, the feasibility and superiority of combined guidance strategy are respectively illustrated by nonlinear numerical simulation and verified by comparing with linear quadratic and norm-bounded differential game guidance strategies.     

基于微分对策的导弹攻击策略

利用建立的垂直平面内交战双方攻击模型,应用微分对策理论,得到导弹的最优攻击策略,对比微分对策导引律与比例导引律在多种仿真环境下的结果,说明在近距离交战中,基于微分对策理论的导引律设计具有更大的优越性。