一种基于半张量积的多层网络演化博弈方法

针对多层网络演化博弈,采用半张量积方法,遵循短视最优响应策略更新原则,将博弈动态过程进行公式化并研究其策略最优问题。首先,通过半张量积将多层网络演化博弈转化成代数公式的形式,建立相应的转化算法;其次,基于该公式,讨论了博弈的动态行为;最后,通过增加伪玩家到博弈中来研究策略最优问题,目的是设计自由控制序列来最大化伪玩家的平均收益,从而得到最优控制序列。并举例验证了研究结果的有效性。     

基于矩阵半张量积方法的改进数量化理论 (Ⅰ)

利用矩阵半张量积理论, 从两个方面对数量化理论(Ⅰ)进行改进: 一是改进模型, 提出一种定性数据通用预测模型; 二是扩展基准变量的维数, 建立一种多维预测方法. 首先, 基于混合逻辑半张量积表示, 研究一维基准变量预测问题, 提出一种新的 预测模型——伪混合逻辑函数模型, 它可描述定量基准变量与定性说明变量间的任一复杂解析关系; 并基于样品数据, 研究如何确定预测模型的结构矩阵. 然后, 研究多维基准变量预测问题, 提出一种伪混合逻辑函数向量预测模型, 并给出其结构矩阵的确定方法. 最后, 给出一个应用例子, 说明本文方法的有效性.     

Linearization of multi-valued nonlinear feedback shift registers

Nonlinear feedback shift registers (NFSRs) have been used in many stream ciphers for cryptographic security. The linearization of NFSRs is to describe their state transitions using some matrices. Such matrices are called their state transition matrices. Compared to extensive work on binary NFSRs, much less work has been done on multi-valued NFSRs. This paper uses a semi-tensor product approach to investigate the linearization of multi-valued NFSRs, by viewing them as logical networks. A new state transition matrix is found for a multi-valued NFSR, which can be simply computed from the truth table of its feedback function. The new state transition matrix is easier to compute and is more explicit than the existing results. Some properties of the state transition matrix are provided as well, which are helpful to theoretically analyze multi-valued NFSRs.     

Two-dimensional linear connected-k system with trinary states and its reliability

Existing studies about two-dimensional consecutivek-out-of-n:F system is dealt with two states(either component or system):working or failure.A new model for two-dimensional linear consecutive-k-out-of-n:F system is proposed,in which the components and systems can be at any of the three states:full working,derating working,and failure.Furthermore,two engineering concrete instances of the new system are given.By using the finite Markov chain imbedding approach,the system reliability is presented in a unified formula with the product of matrices for the case of independent and identically distributed component states which can be extended to the independent but non-identical case easily.Finally,an example is given to illustrate the effectiveness of the above approach and tractability of various problems.     

Reachability/controllability of high order mix-valued logical networks

This paper addresses the reachability/controllability of high order mix-valued logical control networks by using the semi-tensor product method, and presents some necessary and sufficient conditions for the reachability/controllability. The high order mix-valued logical network is converted into an algebraic form first, based on which the reachability/controllability of the system is then investigated, and several necessary and sufficient conditions are established. The study of several illustrative examples shows that our new method is very effective in dealing with the reachability/controllability of high order mix-valued logical control networks.     

具有时间窗的局内开放式车辆调度的竞争分析

基于k-卡车问题和局内运输问题，提出了具有时间窗的局内开放式车辆调度问题．该问题的优化目标为：在服务需求的发布为局内方式的条件下，如何最小化完成整个服务需求序列的时间跨度．建立了该问题的数学模型并对有关的概念和参数进行了定义和说明．研究了当车辆数为1时该问题的竞争分析的有关结果：给出并证明了对于该问题的竞争策略的竞争比下限；针对该局内问题，设计了两种不同的竞争策略，得到了相应的竞争比，并进行了理论证明．     

考虑撤单率的电商配送服务能力自建与外包博弈模型与求解

针对在线冷静期内产生消费者撤单行为情况下电商配送服务能力的自建与外包决策问题,引入撤单率,从是否进行合作的角度给出了完全合作博弈、完全非合作博弈和不完全非合作三种合作强度的动态博弈模型,并将其中两种情形划分为三阶段动态博弈过程,采用逆向递归法求解这两种情形下各子博弈均衡解,得到了在线购买环境下电商配送服务能力自建与外包的最优解集.进一步地,在第三种情形下设计了成本分担、利润分配以及风险规避三种子博弈模型,以增强模型的灵活性.数值算例与分析表明电商配送服务能力博弈中,电商决策者能够有效实现撤单行为与成本变动影响下动态博弈的帕累托优化.     

On the observability of free Boolean networks via the semi-tensor product method

This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on which and the algebraic form of Boolean networks,a kind of observabihty matrix is constructed.Second,by the observability matrix,a new necessary and sufficient condition is given for the observability of Boolean networks.Third,the concept of observabihty index for observable Boolean networks is defined,and an algorithm is established to calculate the observability index.Finally,a practical example of D.Melanogaster segmentation polarity gene networks is studied to support our new results.The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.     

耐用品动态古诺模型的长期产量解和短期产量解研究

依据耐用品的市场容量可变的特点,研究了两阶段情形下的两个耐用品企业同时博弈的动态古诺模型,分别得到即期利润最大化时和长期利润最大化时的不同的产量博弈模型及其各自所对应的产量解.通过比较与分析可知,长期产量解优于短期产量解.在此基础上,建立了分别以追求短期利润和长期利润为策略的新的博弈模型,由此可知两个企业依旧处于囚徒困境中,不得不以追求短期利润作为自己的选择.     

Graph theory methods for decomposition w.r.t. outputs of Boolean control networks

This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks (BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.     

非光滑两级优化问题的必要条件及其算法

利用集值分析、非光滑分析与优化理论,研究了两级优化问题的性质、结构,提出了处理这类问题的一个通用性结构化模型,并利用该模型导出了非凸非光滑条件下两级优化问题的微分包含型必要条件,最后给出了其求解的算法及算例．     

时滞对逻辑网络优化控制的影响

分析了包含两种个体的逻辑网络的时滞优化控制。其中第1种被称为机器的个体策略是固定的;第2种被称为人的个体具有自适应性,即能根据系统的整体状态做出策略的调整。以矩阵的半张量积作为逻辑分析的工具,分析了在状态时滞和输入时滞的影响下使人的收益最大的最优控制问题。理论分析显示状态时滞导致最优控制策略的周期长度增加,但人的最大收益值不会改变。最后提出仿真算法,其数值结果与理论结果一致。     

Observability of Boolean Control Networks with Time-Variant Delays in States

This paper gives an equivalent condition for the observability of Boolean control networks (BCNs) with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of the semi-tensor product of matrices. First, the BCN under consideration is split into a finite number of subsystems with no time delays. Second, the observability of the BCN is verified by testing the observability of the so-called observability constructed path (a special subsystem without time delays) based on graph theory. These results extend the recent related results on the observability of BCNs. Examples are shown to illustrate the effectiveness of the results.     

STABILITY OF SWITCHED POLYNOMIAL SYSTEMS

This paper investigates the stability of （switched） polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a （switched） polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.     

基于主模型CAD/CAE集成的卷绕锭轴结构参数优化

高速卷绕头是化纤长丝纺丝机的重要单元机,国内之前研究相对较少。采用虚拟产品开发技术进行高速卷绕头新产品开发的技术创新,提高卷绕头产品开发效率。与同类研究类似,在高速卷绕头产品的虚拟开发过程中,集成CAD/CAE系统存在若干技术瓶颈。基于CAD/CAE系统集成方法的对比分析,建立了主模型CAD/CAE集成框架,并在该框架下进行了高速卷绕头锭轴结构参数优化设计,其优化设计的动力性能分析结果验证了基于主模型CAD/CAE集成框架进行高速卷绕锭轴部件虚拟开发的有效性。

Abstract：

Researches based on the high speed winder, which is a key unit machine for filaments treatment, are relatively rare in China. The techniques of virtual product development （VPD） were applied to improve the new product development of the high speed winder, which would raise the product development efficiency of the high speed winder. Similarly to the research of this kind, in the procedure of developing the virtual product for the high speed winder, there were several key technical problems in the CAD/CAE integrated system. The contrast analysis of the CAD/CAE integrated methods was given; furthermore, the CAD/CAE integrated framework based on master model was built, in which the structural parameters of the high-speed winder chuck was optimized for design. The dynamic characteristics analysis for the optimization design was done; consequently, the result indicates that in the CAD/CAE integrated framework based on master model, the structural parameter optimization of high-speed winder chuck is available.     

基于鲁棒优化的无人机空战博弈决策

作为无人机空战过程中较大的不确定性因素,作战双方毁伤概率易受外界因素影响,可能在一定范围波动,针对这一问题将鲁棒优化思想引入无人机空战博弈模型中,结合纳什均衡求解的适应度函数的期望和方差,建立了变权重的自适应目标函数,设计了权重的分配方法。在确保策略解可行的同时,提高了毁伤概率变化因素下混合策略的鲁棒性。仿真实验结果表明,与原博弈模型相比,新模型纳什均衡解下的双方博弈收益受参数变化影响较小,可提供更可靠的策略参考。     

多人雪堆演化博弈在愿景驱动规则下的扩展平均丰度函数

随着博弈理论的深入研究,演化博弈模型在许多社会现象和经济问题的分析中得到了广泛应用.演化博弈模型将策略更新规则引入状态转移方程,得到相应的马尔可夫链,从而研究种群演化状态.当此马尔可夫链无吸收态时,采用平均丰度函数来研究种群演化状态.采用策略更新规则中的愿景驱动规则,通过分析马尔可夫链的平稳分布导出了扩展平均丰度函数.同时,通过将多人演化博弈模型应用于雪堆演化博弈中,得到了多人雪堆演化博弈模型的扩展平均丰度函数.采用数字分析的方式,计算分析了相应参数对平均丰度函数的影响,结合具体案例研究了参数变化如何影响企业在博弈中的行为.研究表明可以通过改变相关参数来提高合作者的占比,这一结论为在实际应用中如何调控相应参数以促进合作指出了方向.     

证券投资决策的微分对策方法研究

在证券价格存在有界不确定性的假设下,研究了基于最差情况的最优证券投资决策问题。首先建立了证券投资决策的微分对策模型,然后,证明了该微分对策模型存在唯一的值函数,最后,根据微分对策理论得出了值函数所满足的偏微分方程。