反对称偏对称矩阵反问题的最小二乘解

该文研究了反对称偏对称矩阵反问题的最小二乘解,得到了该问题解的表达式以及该问题有解的充分必要条件.证明了其最佳逼近解的存在性和唯一性,建立了其最佳逼近解的表达式,并给出了求最佳逼近解的数值算法和算例.     

非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破

研究了具有非线性记忆项的Euler-Poisson-D arboux-Tricomi方程在次临界情况下解的爆破现象.利用泛函分析方法结合修正的Bessel方程推出了其柯西问题解的迭代框架和第一下界,然后通过迭代技巧,获得了其解的全局非存在性以及解的生命跨度上界估计.     

具有脉冲扰动的非线性时滞微分方程

本文研究一类脉冲非线性时滞微分方程解的性质，讨论了其解的整体存在性及非振动解的渐近性，也给出了其所有解振动的充分条件．     

多层规划和多目标规划的讨论

对任意给定的正整数 (n1,n2 ) ,构造了上下层决策变量分别是n1和n2 维的两层线性规划 ,其最优解不是相应双目标规划的有效解 ,进而构造出以任意给定的线性无关的向量d1,d2 为价格向量的两层规划 ,其最优解不是有效解 .这些讨论对现实问题的合理建模提供了理论依据 .此外 ,给出多层规划最优解是有效解的一个充分条件及判断其无效的方法 .     

中立型脉冲发展方程解的存在性和唯一性

本文研究了一类非线性中立型脉冲发展方程解的存在性和唯一性的问题.利用迭代分析方法结合半群理论的知识,得到了其解的表达式,并构造解的迭代序列,同时证明了其解的存在性和唯一性.通过研究发现其解的存在性和唯一性与脉冲时滞条件密不可分,利用迭代分析法求解此类问题具有一定的优越性.     

n维非线性中立型时超微分方程组解的振动性

本文首先研究了具有正负号系数的线性中立型时超微分不等式解的振动性。获得了其解振动的判定准则,然后应用该准则研究了非线性中立型时超微分方程和n维非线性中立型时超微分方程组解的振动性。获得其解振动的充分条件。     

推广的(G′/G)展开法与Zhiber-Shabat方程的精确解

利用推广的(G′/G)展开法,研究了Zhiber-Shabat方程的行波解,获得了其各种孤子解和周期波解,并且给出了由它得来的著名方程Liouville方程的精确解,丰富了解的范围.     

具有阻尼项的非线性KG方程的柯西问题

首先,介绍位势井及位势井族,并由定义证明其性质;其次,证明整体解的不变性;最后得到了整体解的存在定理,并得到了有限时间内解的爆破.     

一类广义Sylvester方程的反对称最小二乘解及其最佳逼近

本文利用矩阵的奇异值分解(SVD),给出了广义Sylvester矩阵方程AX YA=C反对称解存在的充分必要条件,导出了其反对称解和反对称最小二乘解的表达式,同时在解集合中得到了对给定矩阵的最佳逼近解.     

一类非线性分数阶微分方程的奇异边值问题

利用上下解方法及单调迭代技术讨论了一类非线性分数阶微分方程的奇异边值问题,给出了其解的存在及最小最大解的存在定理.     

年龄相关的半线性种群扩散系统的最优收获控制

研究年龄相关的半线性种群扩散系统的最优收获控制问题，证明了最优收获控制的存在性，得到了收获控制为最优的必要条件和由偏微分方程与变分不等式所构成的最优性组，由最优性组确定最优控制．     

年龄相关的种群扩散系统的最优分布控制

本文讨论年龄相关的种群扩散系统的最优分布控制 ,证明了最优分布控制的存在性 ,得到了分布控制为最优的充分必要条件及确定最优控制的最优性组 .     

与年龄相关的非线性种群系统的最优收获控制

讨论与年龄相关的一类非线性种群系统的最优收获控,运用泛函分析的Mazru's定理证明了最优收获控制的存在性,利用G-微分和Lions的变分不等式理论,导出了控制为最优的必要条件,得到了由积分-偏微分方程和变分不等式组成的最优性组,由最优性组确定最优控制.     

A linearization method inN-person nonzero-sum differential games

In the present treatment, a nonlinear system of anN-person nonzero-sum differential game is linearized with respect to the controls. It is shown that the optimal trajectory and the optimal costs of the linearized system lead, under certain conditions, to an approximation of the optimal trajectory and the optimal costs of the original nonlinear system.     

Optimal maintenance policy in a multistate deteriorating standby system

An optimal maintenance policy for a multistate deteriorating standby system is proposed in this study. Traditionally, a system could only presume two operational states: success or failure, and the maintenance policy is to determine the optimal number of standby components, subject to factors such as maintenance capability, cost of the standby items, etc., so as to minimize the operational cost. This study considers a more general production system in which progressive deterioration is incurred during the operating time, hence resulting in degrading performance. By modeling the system as a multistate deteriorating system, an optimal maintenance policy is obtained by determining the optimal number of standby components required in the system and the optimal state in which the replacement of deteriorating components shall be made.     

Optimal control in a macroeconomic problem

The Pontryagin maximum principle is used to develop an original algorithm for finding an optimal control in a macroeconomic problem. Numerical results are presented for the optimal control and optimal trajectory of the development of a regional economic system. For an optimal control satisfying a certain constraint, an invariant of a macroeconomic system is derived.     

An Optimal Control Problem of a Coupled Nonlinear Parabolic Population System

An optimal control problem for a coupled nonlinear parabolic population system is considered. The existence and uniqueness of the positive solution for the system is shown by the method of upper and lower solutions. An explicit prior bound of solutions to the system is given by considering an auxiliary coupled linear system. The existence of the optimal control is proved and the characterization of the optimal control is established.     

Chaos May Be an Optimal Plan

An interpretation of some chaotic systems as the result of optimal decisions is presented. First, a generalized discrete-time two-person game is introduced that may be solved by use of dynamic programming. Then, a specific game of this type is formulated whose optimal solution transforms an originally linear discrete-time system into a well-known discrete-time chaotic system. Finally, a particular continuous-time optimal control problem is formulated, whose optimal feedback solution transforms an originally linear continuous-time system into a well-known continuous-time chaotic system.     

基于随机动态规划的有限库存ATO系统优化控制

本文研究n维组件单一产品,有限库存的ATO系统。通过建立马尔可夫决策过程模型(MDP),构造优化算法,研究组件生产与库存的最优控制策略。最优策路可以表示为状态依赖型库存阈值,系统内任一组件的控制策略受其它组件库存状态的影响。利用最优控制理论动态规划方法和数值计算方法对最优控制策略的存在性、最优值的数值计算进行研究,建立更符合实际生产的ATO系统决策模型,进行相应的理论和实验验证,研究系统参数对最优策略的影响。     

Parametric Sensitivity Analysis of Perturbed PDE Optimal Control Problems with State and Control Constraints

We study parametric optimal control problems governed by a system of time-dependent partial differential equations (PDE) and subject to additional control and state constraints. An approach is presented to compute the optimal control functions and the so-called sensitivity differentials of the optimal solution with respect to perturbations. This information plays an important role in the analysis of optimal solutions as well as in real-time optimal control.The method of lines is used to transform the perturbed PDE system into a large system of ordinary differential equations. A subsequent discretization then transcribes parametric ODE optimal control problems into perturbed nonlinear programming problems (NLP), which can be solved efficiently by SQP methods.Second-order sufficient conditions can be checked numerically and we propose to apply an NLP-based approach for the robust computation of the sensitivity differentials of the optimal solutions with respect to the perturbation parameters. The numerical method is illustrated by the optimal control and sensitivity analysis of the Burgers equation.Communicated by H. J. Pesch