Decentralized algorithms for netcentric force protection against antiship missiles

We model a decentralized network of decision makers charged with optimally deploying hardkill and/or softkill weapons (countermeasures (CMs)) to defend a task group from antiship missiles. Each platform (decision maker) observes missile threats using a combination of shipboard sensor measurement data and data from other ships, but acts independently when controlling its own weapon systems to cooperatively pursue the defensive objectives of the task group in a decentralized fashion. The main results are a formulation of the missile deflection problem as a stochastic shortest path Markovian game with constraints, a characterization of the Nash equilibrium solution, and a decentralized algorithm for computing the Nash equilibrium when the stochastic game is collaborative. Numerical examples are given to demonstrate the equilibrium policies and illustrate their sensitivity to the missile dynamics.     

An optimal one-way cooperative strategy for two defenders against an attacking missile

This paper investigates a cooperative strategy for protecting an aerial target.The problem is solved as a game among four players(a target,two defenders,and a missile).In this scenario,the target launches two defenders(defender-1 and defender-2)simultaneously,to establish a oneway cooperation system(OCS)against an attacking missile.A new optimal evasion strategy for the target is also derived.During the engagement,the target takes into account the reaction of the attacking missile,and guides defender-1 to the interception point by receiving information from defender-1.Depending on the control effort of the target,defender-2 can choose appropriate launch conditions and use very limited maneuvering capability to intercept the missile.For adversaries with first-order dynamics,simulation results show that the OCS allows two defenders to intercept the missile.During the engagement,even if one defender or communication channel is broken,the OCS still allows an interception to be made,thus increasing the target’s survivability.     

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.     

Effectiveness of the Nash strategies in competitive multi-team target assignment problems

The Nash strategy in game theory has often been criticized as being ineffective in competitive multi-team target assignment problems, especially when compared with other simplistic strategies such as the random or greedy targeting strategies. This criticism arises from the fact that the Nash strategies may yield unpredictable results when paired with non-Nash strategies in non-zero sum games. In addition, the Nash equilibrium is generally more difficult to compute than strategies which do not attempt to anticipate the strategy of the other side. The authors seek to show that in multi-team target assignment problems the Nash strategy is superior to such simplistic strategies while also remaining computationally feasible. To demonstrate this point, an attrition model was considered, consisting of two teams of nonhomogeneous fighting units simultaneously targeting each other and compare the outcomes when various combinations of four targeting strategies are used on each side. The four strategies are: 1) the random strategy where each unit selects its target randomly, 2) the unit greedy strategy where each unit chooses the target that optimizes its own performance only, 3) the team optimal strategy where the units coordinate their choice of targets so as to optimize the overall team performance while ignoring the possible strategy choices by the other team, and 4) the team Nash strategy, calculated under the assumption that the other team is also using a Nash strategy. Because the computational requirements for calculating the team Nash strategies may become unfeasibly large, an efficient method was discussed for approximating the Nash strategies using a neighborhood search algorithm called unit level team resource allocation (ULTRA). The results were compared for all 16 possible combinations of these four targeting strategies and show that for each team the Nash strategy outperforms all other strategies irrespective of the strategy employed by the other team     

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。     

Optimal guidance against active defense ballistic missiles via differential game strategies

The optimal guidance problem for an interceptor against a ballistic missile with active defense is investigated in this paper. A class of optimal guidance schemes are proposed based on linear quadratic differential game method and numerical solution of Riccati differential equation. By choosing proper parameters, the proposed guidance schemes are able to drive the interceptor to the target and away from the defender simultaneously. Additionally, fuel cost, control saturation, chattering phenomenon and parameters selection were taken into account. Satisfaction of the proposed guidance schemes of the saddle point condition is proven theoretically. Finally, nonlinear numerical examples are included to demonstrate the effectiveness and performance of the developed guidance approaches. Comparison of control performance between different guidance schemes are presented and analysis.     

基于深度学习的突防控制博弈对象匹配方法CSCD

针对基于博弈理论设计应对多枚拦截弹的协同突防控制方案时需要确定博弈对象的问题,提出了一种基于长短时记忆(LSTM)网络的拦截弹攻击对象匹配方法。基于传统防空导弹飞行时序与流程构建拦截弹飞行轨迹库,以轨迹库为训练样本对LSTM网络进行训练,并以此为基础构建航迹预测模型与对象匹配模型,实现对拦截弹攻击对象的识别。仿真结果表明,该方法能够有效识别拦截弹拦截目标,为后续的巡航弹突防研究提供支撑。     

基于Hotelling模型的双寡头市场定价博弈分析

文章在三阶段Hotelling模型的基础上研究了双寡头市场的定价博弈问题。在第一阶段两个寡头企业同时选择价格策略;在第二阶段两寡头企业确定价格大小及相应的定价概率;在第三阶段由消费者选择企业。由博弈分析的结果得出,使用高价和打折相互结合的混合策略为双寡头市场定价博弈的唯一纳什均衡策略,此时博弈双方获得最大利润,即高低价混合策略才是理论推导的最佳策略。文章在最后还从正反两方面给出了这个结论实证上的支持。     

基于混合战略均衡双寡头航空公司定价博弈研究

利用产品差异化理论和博弈理论,建立了双寡头航空公司市场竞争定价的不完全信息静态博弈模型,假定双方经营相同航线、选择相同机型、面临相同旅客,而在产品价格和服务水平方面存在差异性,在文献【1】中证明了这种博弈不存在纯策略均衡,按照纳什均衡解存在性理论,对混合战略均衡进行求证,得出结论：双方价格和服务水平的大小关系一致时,其市场份额和期望利润的关系与之相同;双方两因素关系随机变化时,其市场份额及期望利润同其变化程度有关,即结果不确定。     

基于Nash均衡与进化计算的协调航迹规划

在对策论框架下研究多无人飞行器的协调航迹规划问题,提出了一种基于Nash平衡和进化计算的航迹规划算法.协调航迹规划是一个多目标合作优化问题,也是一个非合作对策问题.飞行器编队的分布结构提供了一种隐性偏好信息,有助于找到飞行器编队的最优协调航迹和最优飞行代价分配.本文算法使用特定的航迹个体表示方法和进化算子,按照层次方法处理各种航迹约束.不同飞行器间的协同和竞争关系定义在航迹评价函数里.仿真结果验证了基于博弈论航迹规划算法的可行性和优越性.     

基于博弈论的顶岗实习策略分析

顶岗实习是工学结合的重要形式,以博弈论的角度,顶岗实习方案决策是职业院校与企业的博弈过程,且主要为二人零和完全信息静态博弈;建立了博弈模型,给出了纳什均衡,确定了可行策略的条件;提出了对不同企业类型的策略设计要点。     

基于DQN的反舰导弹火力分配方法研究

反舰导弹作为海上作战的主战武器，由于其精度高、射程远、威力大等特性长期以来一直被当作舰艇编队的主要防御对象。针对反舰导弹打击舰艇编队的火力分配问题，我们提出了一种基于深度Q值网络求解反舰导弹火力分配策略的算法。不同于现有的基于领域知识的方法，深度Q值网络无需依赖任何先验信息，就能够通过与模拟器的交互自动求解最佳的攻击策略。该算法使用深度神经网络拟合Q值函数，解决了传统强化学习中的状态空间过大无法遍历的问题。实验结果表明，在各种不同的舰队防御配置下，深度Q值网络求解得到的攻击策略均获得了最佳的毁伤效果。     

Quick identification of guidance law for an incoming missile using multiple-model mechanism

A guidance law parameter identification model based on Gated Recurrent Unit (GRU) neural network is established. The scenario of the model is that an incoming missile (called missile) attacks a target aircraft (called aircraft) using Proportional Navigation (PN) guidance law. The parameter identification is viewed as a regression problem in this paper rather than a classification problem, which means the assumption that the parameter is in a finite set of possible results is discarded. To increase the training speed of the neural network and obtain the nonlinear mapping relationship between kinematic information and the guidance law parameter of the incoming missile, an output processing method called Multiple-Model Mechanism (MMM) is proposed. Compared with a conventional GRU neural network, the model established in this paper can deal with data of any length through an encoding layer in front of the input layer. The effectiveness of the proposed Multiple-Model Mechanism and the performance of the guidance law parameter identification model are demonstrated using numerical simulation.     

Optimal trajectory and downlink power control for multi-type UAV aerial base stations

Unmanned Aerial Vehicles (UAVs) enabled Aerial Base Stations (UABSs) have been studied widely in future communications. However, there are a series of challenges such as interference management, trajectory design and resource allocation in the scenarios of multi-UAV networks. Besides, different performances among UABSs increase complexity and bring many challenges. In this paper, the joint downlink transmission power control and trajectory design problem in multi-type UABSs communication network is investigated. In order to satisfy the signal to interference plus noise power ratio of users, each UABS needs to adjust its position and transmission power. Based on the interactions among multiple communication links, a non-cooperative Mean-Field-Type Game (MFTG) is proposed to model the joint optimization problem. Then, a Nash equilibrium solution is solved by two steps: first, the users in the given area are clustered to get the initial deployment of the UABSs; second, the Mean-Field Q (MFQ)-learning algorithm is proposed to solve the discrete MFTG problem. Finally, the effectiveness of the approach is verified through the simulations, which simplifies the solution process and effectively reduces the energy consumption of each UABS.     

关于多目标气动优化设计中伴随方法与对策理论的耦合研究(英文)

本文研究了多目标气动优化设计中伴随方法和对策理论的耦合问题,给出了伴随方法在每个对策策略中的具体应用和数值方法。在合作对策中伴随方法被并行地执行以共同得到Pareto阵面上的最优解;相反在Nash对策中伴随方法在Nash策略的最后被耦合起来以互相竞争的形式得到各自目标的最优解;而在Stackel-berg对策中伴随方法被分层耦合进"领头人"和"跟随者"的策略中以求解他们相互依赖的平衡解。文末的优化算例表明了本文耦合算法及其数值过程在求解多目标气动优化设计问题中的有效性。     

反舰导弹末端突防对策与仿真

以反舰导弹为背景，设计了一种末端控制方案，给出了反舰导弹，舰艇和拦截器的简化模型，建立了导弹，舰艇和拦截器的快速仿真算法，开发了一套基于网络的导弹-舰艇-拦截器以及突防效果分析的仿真演示系统。     

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.     

拦截机动目标的模糊导引律研究

使用模糊方法研究了三维实际追逃问题的最小能量导引律问题。首先,通过对一些状态变量的定义域进行在线模糊分区,一方面,将非线性模型变为模糊T-S线性模型;另一方面,又能方便地处理目标的任意机动而引起的目标运动方向的变化。其次,利用RH（Receding Hori-zon）控制方法和伴随技术,在目标作对抗性机动条件下,获得了一个有效拦截的导引律。数值仿真结果表明,由这种导引律导引的导弹能够精确拦截任意机动的目标。     

分布式进化算法及其在翼型气动反设计中的应用

构造了一种新型基于基因算法与博弈论的并行分级多目标优化方法，并应用于多段翼型气动反设计。此方法基于二进制编码的基因算法和博弈论，优化变量被分配给不同的博弈者，因而总体优化问题转变为分裂空间中的局部优化问题。文中给出了一个多段翼型形状，位置可压位流的反设计问题的求解算例，引入了基于非结构网格的分级结构。与传统基因算法数值算例的对比表明了本文构造的并行分级算法具有较高的计算效率，可广泛应用于多目标优化问题。     

岛礁环境下空舰导弹搜索航向优选

针对空舰导弹打击岛礁区水面舰艇目标问题,由岛礁与目标的相对位置关系,将导弹搜索航向划分为 4个区域,界定了降低岛礁影响的区域;从岛目距离、弹载雷达搜索扇面、开机距离、最小间隔角等方面,研究了空舰导弹搜索航向计算方法。通过仿真实验,分析了不同最大间隔角和岛目距离情况下的空舰导弹搜索航向优选方法。