基于统计线性化的随机非线性微分对策逼近最优策略

针对二人零和随机非线性微分对策问题, 利用统计线性化技术并提出一种新的逼近策略控制方法. 通过求解具有统计线性化参数的Riccati微分方程得到逼近控制策略, 该Riccati微分方程与一般线性系统的Riccati微分方程具有明显的区别; 同时对控制量受约束情形的控制策略也进行了求解; 最后通过仿真验证了所得结论的正确性.     

基于LQ微分对策的最优规避策略与决策算法

针对信息化条件下飞行器通过"智能"机动方式来规避拦截这一问题,基于LQ微分对策方法对最优规避参数的决策问题进行了研究.首先,将微分对策引入LQ最优控制算法,建立了飞行器规避拦截问题的数学模型;其次,提出了将Hamil-ton-Yaceobi伴随向量与共轭法相结合的共轭决策方法,简化了微分对策的求解,并得到了最优规避参数的解析解;给出了规避策略中不同参数对规避效果的不同灵敏度,并给出了最优规避参数的决策算法;最后,针对不同的对抗情形,进行了数字仿真,检验了本文微分对策模型的合理性和算法的有效性.     

最优保留遗传算法及其收敛性分析

最优保留ＧＡ（ＥＧＡ）是目前ＧＡ收敛性研究中比较典型的一类。在已有研究成果的基础上给出了ＥＧＡ更一般的规范化定义,指明了ＥＧＡ全局收敛的本质及其两种实现方式,并分别对它们进行了收敛性分析。最后提出一种变形的全局收敛的ＥＧＡ。     

基于微分博弈的移动目标防御最优策略

目前,针对移动目标防御最优策略研究大多采用经典单/多阶段博弈和Markov博弈模型,无法在连续实时网络攻防对抗中进行灵活决策.为实现实时选取最优移动目标防御策略,在研究节点级传染病模型与微分博弈理论的基础上,提出了一种移动目标防御微分博弈模型,对网络空间重要节点构造安全状态演化方程与攻防收益目标函数,并设计开环纳什均衡求解算法以得出最优防御策略.仿真结果表明,该方法可有效对网络攻击进行实时防御,并且可针对网络关键节点制定相应移动目标防御策略.     

一类自适应蚁群算法及其收敛性分析

为了克服蚁群算法易陷入局部最小点的缺点,同时提高算法的收敛速度,提出一类自适应蚁群算法.该算法利用自适应改变信息激素的挥发系数改善传统蚁群算法的全局搜索能力和收敛速度.通过马尔科夫过程对算法的全局收敛性进行分析,得出该类蚁群算法全局收敛性条件.并构造出该类算法的一种信息激素更新策略,证明了这种算法全局收敛性.利用提出的算法对典型的TSP问题进行仿真研究,结果表明比典型蚁群算法在收敛速度和解的性能上都有较大改善.     

多组对策系统非劣Nash策略的最优均衡解算法

多组对策系统中求解组与组之间的非劣Nash策略至关重要.如何针对一般问题解析求出非劣Nash策略还没有有效的方法.本文阐述了一种利用组与组之间的非劣反应集构造求解非劣Nash策略的迭代算法.为此首先引进多组对策系统组内部合作对策的最优均衡值和最优均衡解的概念,然后通过证明最优均衡解是组内部隐含某一权重向量的合作对策的非劣解,得到求解合作对策的单目标规划问题.进一步说明在组内部该问题的解不仅是非劣解而且对所有局中人都优于不合作时的Nash平衡策略.最后给出了验证该算法有效性的一个实际例子.     

微分对策理论及其应用研究的新进展

微分对策理论是控制论和对策论的重要分支,在军事对策和经济学研究领域具有非常广泛而重要的应用．对此简述了半个世纪以来微分对策理论和应用发展的历史,介绍了近年来微分对策理论发展的最新研究成果,并对微分对策理论发展的几个热点问题作了简要评述．     

线性二次微分对策鞍点策略的小波分析法

研究线性二次微分对策鞍点策略的数值求解问题,基于小波多尺度多分辨逼近特性,提出一种求解新方法。该方法将原问题转化为代数问题,算法简捷明了,适合于计算机求解。数值例子表明该方法是合理而可行的。     

一类自适应蚁群算法的收敛性分析

为了提高基本蚁群算法的全局求解能力,对基本蚁群算法进行了改进,提出了一种基于信息素挥发因子自适应变化的蚁群算法,并证明了当迭代次数充分大时算法能以概率1收敛到全局最优解,通过对TSP仿真实验表明改进后的蚁群算法在求解最优解时存在优势。     

具不定二次项的一般代数RICCATI方程解的存在性问题

讨论具有不定二次项的一般代数RICCATI方程(GARE)的实对称镇定解的存在性问题,利用GARE相应的微分方程解的性质,建立了GARE实对称镇定解存在性的充分条件.     

不完全信息下开发商Markov博弈均衡的最优策略

房地产开发商对于资源的争夺存在零和博弈的特点,在信息不对称条件下对开发商经济博弈模型的研究具有重要价值。该研究考虑到市场上存在开发商Cartel联盟的情形,以Markov博弈模型为核心,针对不完全信息下的Cartel联盟与竞争者的Markov博弈均衡进行研究,得到了博弈双方的最优策略及演算方法。最后,利用实例对该模型的有效性和可行性进行了说明。     

Stochastic games on a graph

Stochastic games on a graph are considered under the assumption that the phase space of a system and the space of values of the control actions of both players are complete separable metric spaces. The sufficient conditions for the existence of the optimal stationary nonrandomized Markovian strategies for both players are obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 13–144, September–October, 1999.     

A linear differential game with a fixed termination time and restrictions on resources

A linear game with a fixed termination time and integral restrictions on player controls is considered. The pursuer constructs his control with knowledge of the control of the evader, and the evader uses information on all previous actions of his opponent at each instant of time. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 178–183, July–August, 2000.     

New Algorithms for Solving Simple Stochastic Games

We present new algorithms for determining optimal strategies for two-player games with proba- bilistic moves and reachability winning conditions. Such games, known as simple stochastic games, were extensively studied by A.Condon [Anne Condon. The complexity of stochastic games. Information and Computation, 96(2):203–224, 1992, Anne Condon. On algorithms for simple stochastic games. In Jin-Yi Cai, editor, Advances in Computational Complexity Theory, volume 13 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 51–73. AMS, 1993]. Many interesting problems, including parity games and hence also mu-calculus model checking, can be reduced to simple stochastic games. It is an open problem, whether simple stochastic games can be solved in polynomial time. Our algorithms determine the optimal expected payoffs in the game. We use geometric interpre- tation of the search space as a subset of the hyper-cube [0,1]^N. The main idea is to divide this set into convex subregions in which linear optimization methods can be used. We show how one can proceed from one subregion to the other so that, eventually, a region containing the optinal payoffs will be found. The total number of subregions is exponential in the size of the game but, in practice, the algorithms need to visit only few of them to find a solution. We believe that our new algorithms could provide new insights into the difficult problem of deter- mining algorithmic complexity of simple stochastic games and other, equivallent problems.     

Game problems for systems with discontinuous dynamics

Differential games with discontinuous dynamics and a fixed termination time are considered. The operators describing the structure of a game are determined under certain conditions. The results obtained are illustrated by a model example. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 183–187, July–August, 2000.     

Counterexamples to convergence theorem of maximum-entropy clustering algorithm

In this paper, we surveyed the development of maximum-entropy clustering algorithm, pointed out that the maximum-entropy clustering algorithm is not new in essence, and constructed two examples to show that the iterative sequence given by the maximum-entropy clustering algorithm may not converge to a local minimum of its objective function, but a saddle point. Based on these results, our paper shows that the convergence theorem of maximum-entropy clustering algorithm put forward by Kenneth Rose et al. does not hold in general cases.     

A proof of the convergence theorem of maximum-entropy clustering algorithm

In this paper, we point out that the counterexample constructed by Yu et al.is incorrect by using scientific computing software Sage.This means that the example cannot negate the convergence theorem of maximum entropy clustering algorithm.Furthermore, we construct an example to negate Theorem 1 in Yu's paper, and we propose Proposition 3 to prove that the limit of the iterative sequence is a local minimum of the objective function while v varies and u remains stable.Finally, we give a theoretical proof of t...