线性生成的完全模糊线性微分系统

基于模糊结构元方法, 定义了模糊数和模糊值函数的乘法运算, 研究了由对称模糊结构元线性生成的完全模糊线性微分系统的求解问题, 给出了系统解存在的充要条件, 得到了结构元线性生成的齐次、 非齐次的完全模糊线性微分系统求解方法．同时, 给出了这类模糊线性微分系统在经济、军事领域的实际应用．     

基于对角隐式Runge-Kutta公式的无约束优化方法

通过把一个无约束优化问题转化为一个等价的常微分方程,利用二阶半对角隐式Runge Kutta公式构造了求解无约束优化问题的LRKOPT算法。LRKOPT算法具有与IMPBOT方法相似的数值特性,但LRKOPT算法可以看成是最速下降方向与牛顿法方向的非线性组合,而IMPBOT方法为它们两者之间的线性组合。在目标函数为一致凸函数的假设条件下,证明了LRKOPT方法的具有全局收敛和局部超线性收敛性。数值结果表明LRKOPT方法具有很好的数值稳定性并且LRKOPT方法的计算效率优于IMPBOT方法。     

B-spline patches and transfinite interpolation method for PDE controlled simulation

This paper is to discuss an approach which combines B-spline patches and transfinite interpolation to establish a linear algebraic system for solving partial differential equations and modify the WEB-spline method developed by Klaus Hollig to derive this new idea.First of all,the authors replace the R-function method with transfinite interpolation to build a function which vanishes on boundaries. Secondly,the authors simulate the partial differential equation by directly applying differential operators to basis functions,which is similar to the RBF method rather than Hollig’s method.These new strategies then make the constructing of bases and the linear system much more straightforward.And as the interpolation is brought in,the design of schemes for solving practical PDEs can be more flexible. This new method is easy to carry out and suitable for simulations in the fields such as graphics to achieve rapid rendering.Especially when the specified precision is not very high,this method performs much faster than WEB-spline method.     

Missile robust gain scheduling autopilot design using full block multipliers

Reduction of conservatism is one of the key and difficult problems in missile robust gain scheduling autopilot design based on multipliers. This article presents a scheme of adopting linear parameter-varying (LPV) control approach with full block multipliers to design a missile robust gain scheduling autopilot in order to eliminate conservatism. A model matching design structure with a high demand on matching precision is constructed based on the missile linear fractional transformation (LFT) model. By applying full block S-procedure and elimination lemma, a convex feasibility problem with an infinite number of constraints is formulated to satisfy robust quadratic performance specifications. Then a grid method is adopted to transform the infinite-dimensional convex feasibility problem into a solvable finite-dimensional convex feasibility problem, based on which a gain scheduling controller with linear fractional dependence on the flight Mach number and altitude is derived. Static and dynamic simulation results show the effectiveness and feasibility of the proposed scheme.     

数值求解多延迟中立型系统的渐近稳定性

给出并证明了多延迟中立型系统渐近稳定的克分条件；分析了用线性多步法求解多延迟中立型系统数值解的稳定性，基于Lagrange插值，证明了数值求解多延迟中立型系境的线性多步法渐近稳定的充分必要条件是它是A-稳定的．     

自融资均值方差投资组合模型的旋转算法

将自融资投资组合问题用一个以极小化方差风险为目标的凸二次规划表示,用线性不等式组的一种旋转算法解其库恩塔克条件的线性部分并使互补松弛条件得以满足.     

水平穿越法在带有不耐烦顾客的呼叫中心中的建模及应用

研究了一种需求服从泊松分布的多座席呼叫中心服务系统的两个问题, 其中考虑了顾客的不耐烦行为. 第一个问题中只有单一排队队列, 顾客进入系统后由于不能立即接受服务或等待时间超过其期望等待时间会选择放弃排队. 第二个问题中有两个排队队列, 主排队队列是顾客呼入队列, 次排队队列是座席提供回拨服务的队列, 且这个队列的顾客来源于由于等待时间超过其期望等待时间放弃排队的主排队队列的顾客. 本文利用水平穿越法得到了稳态时第一个问题的顾客平均等待时间及顾客总的放弃概率及第二个问题中座席繁忙的概率. 该方法不仅具有直观清晰的物理意义, 而且能避免排队系统中冗长的推导过程, 有利于快速简单解决问题. 数值分析表明第一个问题中顾客平均等待时间是座席数的凸函数, 并且顾客的不耐烦程度越高则他们的平均等待时间越短. 同时坐席数的增加在初期能够显著提高接通率, 达到一定数量后效用开始递减. 而且在系统其它参数确定且系统需求流较大情况下, 顾客的放弃率大小对顾客总的放弃概率大小的影响几乎可以忽略.     

不确定系统实时保性能控制

研究了一类不确定离散系统在控制约束下的实时控制问题。在SDP凸优化理论的框架下,对这类不确定离散系统实施保性能控制,融合预测控制的优化思想,通过在线求解线性矩阵不等式技术,在满足控制约束的条件下,获得了滚动优化的保性能控制律,并使闭环系统稳定。     

求解常微分方程的一类线性多步方法

本文给出常微分方程y′=f(t,y)及″=f(t,y)的一类线性多步方法,它们的系数容易在计算机上生成。     

导弹追逃博弈微分对策建模与求解

针对导弹攻防对抗过程中拦截器追击具备较强机动能力弹头的追逃问题,建立了双方追逃微分对策模型并给出求解方法.一是给出导弹追逃质点动力学模型;二是基于微分对策理论,建立了导弹攻防对抗微分对策模型,模型以推力角为控制变量,高度,速度和经度角为状态变量,并考虑了地球重力和自转的影响;三是针对模型获得解析解的困难,给出高精度四阶Gauss-Lobatto多项式配点法来逼近非线性方程,通过离散化节点和配点上的状态量和控制量将微分方程组转换为代数约束;四是为采用配点法求解模型,给出了将双边最优对策问题转化为单边最优对策问题的具体方法.最后实例分析对本文研究进行了仿真验证.     

Synchronous Parallel Block Coordinate Descent Method for Nonsmooth Convex Function Minimization

This paper proposes a synchronous parallel block coordinate descent algorithm for minimizing a composite function, which consists of a smooth convex function plus a non-smooth but separable convex function. Due to the generalization of the proposed method, some existing synchronous parallel algorithms can be considered as special cases. To tackle high dimensional problems, the authors further develop a randomized variant, which randomly update some blocks of coordinates at each round of computation. Both proposed parallel algorithms are proven to have sub-linear convergence rate under rather mild assumptions. The numerical experiments on solving the large scale regularized logistic regression with 1 norm penalty show that the implementation is quite efficient. The authors conclude with explanation on the observed experimental results and discussion on the potential improvements.     

Determining the Optimal Solution Set for Linear Fractional Programming

1 .ＩＮＴＲＯＤＵＣＴＩＯＮＬｉｎｅａｒｆｒａｃｔｉｏｎａｌｐｒｏｇｒａｍｍｉｎｇｒｅｆｅｒｓｔｏｎｏｎｌｉｎｅａｒｐｒｏｇｒａｍｍｉｎｇｐｒｏｂｌｅｍｓｏｆｏｐｔｉｍｉｚｉｎｇｔｈｅｒａｔｉｏｏｆｔｗｏｌｉｎｅａｒｆｕｎｃｔｉｏｎｓｉｎｔｈｅｐｒｅｓｅｎｃｅｏｆｌｉｎｅａｒｃｏｎｓｔｒａｉｎｔｓ .Ｉｎｇｅｎｅｒａｌ,ｔｈｅｏｐｔｉｍａｌｓｏｌｕｔｉｏｎｏｆｔｈｅｍａｔｈｅｍａｔｉｃａｌｐｒｏｇｒａｍ ｍｉｎｇｆｏｒｍｅｄｉｎａｃｔｕａｌｂｕｓｉｎｅｓｓｍａｎａｇｅｍｅｎｔｓｉｔｕａｔｉｏｎｓｐｒ…     

连续体结构的模糊多目标拓扑优化设计方法研究

提出了连续体结构静力学和动力学多目标拓扑优化设计的模糊-目标规划方法。该方法利用目标规划方法将多目标优化问题转化为等效的单目标问题,并用模糊集理论中的非线性隶属函数来体现目标规划方法中目标函数期望值所具有的模糊性和不确定性。以结构静力学的刚度和动力学的特征值作为优化的两个目标函数,提出并建立了连续体结构拓扑优化设计的多目标优化模型。用移动渐进线方法(MMA)求解单目标优化问题,用序列线性规划方法(SLP)求解模糊-目标混合规划问题。通过典型的求解算例验证了所研究方法的有效性。     

基于协方差矩阵重构的单基地MIMO阵列无网格DOA估计方法

提出了一种单基地多输入多输出(multiple-input multiple-output, MIMO)阵列中的协方差矩阵重构的无网格波达方向(direction-of-arrival, DOA)估计方法。该方法通过降维处理将MIMO阵列等效为信噪比(signal-to-noise ratio, SNR)提升的均匀线列阵,将目标方位估计问题转化为混合范数最小化(mixed norm minimization, MixNM)稀疏信号重构问题。进一步给出了与该稀疏重构问题等价的基于网格的凸优化问题,并模型化为半定规划来求解。为了解决网格大小影响估计性能的问题,利用了等价均匀线列阵的托普利兹结构,模型化为半定规划问题来重构无噪声协方差矩阵,最后通过范德蒙分解来估计目标方位。与传统的基于MixNM方位估计方法相比,该方法减少了优化变量个数。与其他离网格方法相比,该方法估计精度不受网格大小的影响,且能够估计相干源目标。实验仿真验证了该方法的有效性。     

Observer-based robust predictive control of singular systems with time-delay and parameter uncertainties

The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain "min-max"optimization problems are converted into convex optimization problems solving by the linear matrix inequality (LMI), and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.     

RTFHM应用于DDE实时数值仿真及数值稳定性分析

几年前 ,有人分别从不同的角度构造了一类用常微分方程描述的动力学系统的实时仿真快速混合算法RTFHM ,将这类算法应用到延迟微分方程的实时数值仿真 ,并讨论了对线性常系数延迟微分方程测试模型的数值稳定性。数值试验结果表明 ,RTFHM对线性和非线性的非刚性延迟微分方程都是有效的。     

切向加速度与弦误差约束的CNC系统时间最优轨迹规划

针对计算机数控(CNC)系统给定参数化路径, 给出了一种求解时间最优轨迹规划问题的凸优化方法. 轨迹规划问题考虑切向加速度约束与弦误差约束. 通过建立两种约束下的状态容许空间, 分析约束对时间最优轨迹的影响. 通过非线性变量代换, 时间最优轨迹规划问题被表述为一个与时间无关的凸最优控制问题. 基于控制向量参数化(CVP)方法, 问题被进一步转化为易于求解的凸优化问题. 以路径参数对时间的二阶导数(参数加速度)为优化变量, 序列二次规划(SQP)方法获得问题数值解. 文末通过求解两个测试路径的时间最优轨迹规划问题, 验证方法的有效性.     

Well-Posedness of Fully Coupled Linear Forward-Backward Stochastic Differential Equations

This paper studies the well-posedness of fully coupled linear forward-backward stochastic differential equations(FBSDEs). The authors introduce two main methods-the method of continuation under monotonicity conditions and the unified approach-to ensure the existence and uniqueness of solutions of fully coupled linear FBSDEs. The authors show that the first method(the method of continuation under monotonicity conditions) can be deduced as a special case of the second method(the unified approach). An example is given to illustrate it in linear FBSDEs case. And then, a linear transformation method in virtue of the non-degeneracy of transformation matrix is introduced for cases that the linear FBSDEs can not be dealt with by the the method of continuation under monotonicity conditions and the unified approach directly. As a powerful supplement to the the method of continuation under monotonicity conditions and the unified approach, linear transformation method overall develops the well-posedness theory of fully coupled linear forward-backward stochastic differential equations which have potential applications in optimal control and partial differential equation theory.     

Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems

Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.     

A Continuous Minimization Method for Solving Optimal Control Problem

ＡＣｏｎｔｉｎｕｏｕｓＭｉｎｉｍｉｚａｔｉｏｎＭｅｔｈｏｄｆｏｒＳｏｌｖｉｎｇＯｐｔｉｍａｌＣｏｎｔｒｏｌＰｒｏｂｌｅｍＡＣｏｎｔｉｎｕｏｕｓＭｉｎｉｍｉｚａｔｉｏｎＭｅｔｈｏｄｆｏｒＳｏｌｖｉｎｇＯｐｔｉｍａｌＣｏｎｔｒｏｌＰｒｏｂｌｅｍ￥ＧＵＲｏ...