Network-Enabled Missile Deflection: Games and Correlation Equilibrium

The problem of deploying countermeasures (CM) against antiship missiles is investigated from a network centric perspective in which multiple ships coordinate to defend against a known missile threat. Using the paradigm of network enabled operations (NEOPS), the problem is formulated as a transient stochastic game with communication where the appropriate strategy takes the form of an optimal stationary correlated equilibrium. Under this strategy, ships cooperate through real-time communication to satisfy both local and collective interests. The use of communication results in a performance improvement over the noncommunicating, Nash equilibrium scenario. This framework allows us to develop a theoretical foundation for NEOPS and captures the trade-off between information exchange and performance, while generalizing the standard Nash equilibrium solution for the missile deflection game given in [1], The NEOPS equilibrium strategy is characterized as the solution to an optimization problem with linear objective and bilinear constraints, which can be solved calculating successive improvements starting from an initial noncooperative (Nash) solution. The communication overhead required to implement this strategy is associated with the mutual information between individual action probability distributions at equilibrium. Numerical results illustrate the trade-off between communication and performance.     

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。     

多导弹编队齐射攻击分散化协同制导方法

针对多导弹编队齐射攻击在时间上的协同要求,将攻击时间可控制导律(ITCG)与一致性分散化协调算法相结合,提出一种多导弹编队齐射攻击的分散化协同制导方法.编队内各导弹采用相邻局部通信,编队之间则通过各编队通信拓扑生成树的根节点进行通信.设计了导弹编队内和编队间的分散化协调策略,实现多导弹编队齐射攻击的分散化协调.推导了攻...     

航空公司市场竞争定价博弈模型

利用产品差异化理论和博弈理论，在传统的豪泰林定价模型基础上，建立了航空公司市场竞争定价博弈模型，分析了旅客类型以及航空公司需求情况，证明了在旅客对价格极其敏感的情况下，这种博弈不存在纯战略均衡。     

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。     

基于分布式模型预测控制的多UAV协同区域搜索

针对多无人机(UAV)协同区域搜索问题展开研究。提出了一种基于分布式模型预测控制(DMPC)的多UAV分布式优化搜索方法。首先基于传统的搜索图模型,建立了多UAV协同搜索的问题描述和状态空间模型,然后在DMPC框架下,将集中式多UAV在线优化决策问题转化为各架UAV的小规模分布式优化问题,采用基于纳什最优和粒子群优化(PSO)相结合的算法实现对每个子系统优化问题的迭代求解。仿真结果表明:DMPC方法能够有效地降低多UAV协同搜索决策问题的求解规模,是一种可行的方法。     

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。     

应用博奕理论的多目标分布式气动优化设计

应用博奕理论研究了最优气动外形优化设计方法。采用的基本的优化器为基于控制理论的约束优化设计方法,通过引入标量伴随变量来执行约束条件,进而将上面的方法和对策论结合起来处理多目标翼型优化设计问题,根据各种不同的气动标准(可以是互为冲突的)来优化翼型形状。在对称Nash策略中,每一个“player”都力图优化自己的目标,而Nash平衡则提供了多个目标之间的一种解。不同的翼型分裂和设计算例表明了本文虚拟和真实Nash竞争策略在多目标翼型优化设计中的能力。成功的设计结果表明了本文方法的有效性。     

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.     

蜂群对抗决策故障下的容错博弈控制

针对大规模分簇蜂群无人机的任务分配问题,考虑对抗场景下某些无人机由于受到敌方攻击或操控,决策规则遭到篡改,进而导致群决策行为与期望的均衡点产生偏差的决策故障。在演化矩阵博弈的框架下,运用多群体复制子动态方程对蜂群无人机和故障建模,基于李雅普诺夫函数对故障发生前后均衡点的局部渐近稳定性及其吸引域进行了分析,从而建立了自容错条件,并设计了基于激励的簇间协同容错博弈控制方法,对群决策行为偏差进行补偿,使得蜂群任务分配状态在故障下仍能达到期望的均衡点,获得理想的分工收益。     

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.     

风场中无动力滑翔弹可攻击区研究

基于无动力滑翔弹气动力特性与动力学模型、中/末制导律与控制系统的飞行仿真模型,以及风场模型等,在一定的释放条件下,通过不同风场(即不同风向与风速的组合),计算了大量的可攻击区。利用VC 与Matlab飞行仿真软件,较为直观地比较了无风与不同风场中的无动力滑翔弹可攻击区及相应的六自由度(6DOF)飞行轨迹。大量的数据表明风场改变了无动力滑翔弹的可攻击区的形状及大小。因此,风场是影响无动力滑翔弹命中率与可攻击区的重要因素。当计算无动力滑翔弹的可攻击区时,随机风场必须考虑,这在实战中很有参考价值和工程实用价值。     

Coverage area analysis for decentralized detection in Weibullclutter

The performance of a decentralized constant false-alarm rate (CFAR) detection system with data fusion in homogeneous non-Gaussian background is analyzed in terms of ground area covered. The advantages of using a distributed radar system and the differences between the system behavior in Rayleigh clutter and in Weibull clutter are stressed. Notably, the increasing benefit of cooperative decision making when clutter becomes spikier is pointed out     

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。     

Three-dimensional cooperative guidance laws against stationary and maneuvering targets

This paper presents the cooperative strategies for salvo attack of multiple missiles based on the classical proportional navigation(PN) algorithm.The three-dimensional(3-D) guidance laws are developed in a quite simple formulation that consists of a PN component for target capture and a coordination component for simultaneous arrival.The centralized algorithms come into effect when the global information of time-to-go estimation is obtained, whereas the decentralized algorithms have better performance when each missile can only collect information from neighbors.Numerical simulations demonstrate that the proposed coordination algorithms are feasible to perform the cooperative engagement of multiple missiles against both stationary and maneuvering targets.The effectiveness of the 3-D guidance laws is also discussed.     

A unified approach to the design of decentralized detection systems

A unified approach to the design of decentralized detection networks with arbitrary topologies is proposed and analyzed. In this approach, a decentralized detection system of arbitrary topology is represented by a communication matrix that specifies the interconnection structure of the detection network. This matrix is used to derive the general decision rule using the person-by-person-optimal (PBPO) solution methodology. It is shown that the PBPO decision rule is a likelihood ratio test for statistically independent observations. The threshold of the test is shown to be a function of the decision input vector of the detector under consideration. This unified approach is used to obtain the PBPO decision rules of decentralized detection systems with various topologies. Various results in the literature are verified. In addition, the PBPO decision rules for a decentralized detection system with peer communication are presented. Numerical examples are presented for illustration     

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。     

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.     

Stochastic game approach to air operations

A command and control (C/sup 2/) problem for military air operations is addressed. Specifically, we consider C/sup 2/ problems for air vehicles against ground-based targets and defensive systems. The problem is viewed as a stochastic game. We restrict our attention to the C/sup 2/ level where the problem may consist of a few unmanned combat air vehicles (UCAVs) or aircraft (or possibly teams of vehicles), less than say, a half-dozen enemy surface-to-air missile air defense units (SAMs), a few enemy assets (viewed as targets from our standpoint), and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some targets are mapped out and possible SAM sites that are unavoidably part of the situation are known. One may then employ a discrete stochastic game problem formulation to determine which of these SAMs should optimally be engaged (if any), and by what series of air vehicle operations. We provide analysis, numerical implementation, and simulation for full state-feedback and measurement feedback control within this C/sup 2/ context. Sensitivity to parameter uncertainty is discussed. Some insight into the structure of optimal and near-optimal strategies for C/sup 2/ is obtained. The analysis is extended to the case of observations which may be affected by adversarial inputs. A heuristic based on risk-sensitive control is applied, and it is found that this produces improved results over more standard approaches.