Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

An investigation of glasses for capillary chromatography

An investigation was conducted of various glasses, other than soda lime or borosilicate, for use in glass capillary gas chromatography. The work has uncovered some unique chromatographic qualities in the use of potash soda lead and fused silica glasses as materials for making glass capillary columns. The fused silica proved to be an ideal material for capillary column construction, being inherently more inert than glass containing metal oxides. It has been shown that through the use of thin wall capillary tubing of high flexibility many of the mechanical problems associated with glass capillary columns, such as fragility and column straightening, can be avoided.     

Stability theorems for infinitely constrained mathematical programs

The primary concern of this paper is to investigate stability conditions for the mathematical program: findx E ⁿ that maximizesf(x):g ^j(x)0 for somej J, wheref is a real scalarvalued function and eachg is a real vector-valued function of possibly infinite dimension. It should be noted that we allow, possibly infinitely many, disjunctive forms. In an earlier work, Evans and Gould established stability theorems wheng is a continuous finite-dimensional real-vector function andJ=1. It is pointed out that the results of this paper reduce to the Evans-Gould results under their assumptions. Furthermore, since we use a slightly more general definition of lower and upper semicontinuous point-to-set mappings, we can dispense with the continuity ofg (except in a few instances where it is implied by convexity assumptions).     

Back-and-forth shooting method for solving two-point boundary-value problems

The paper proposes a special iterative method for a nonlinear TPBVP of the form (t)=f(t, x(t),p(t)), (t)=g(t, x(t),p(t)), subject toh(x(0),p(0))=0,e(x(T),p(T))=0. Certain stability properties of the above differential equations are taken into consideration in the method, so that the integration directions associated with these equations respectively are opposite to each other, in contrast with the conventional shooting methods. Via an embedding and a Riccati-type transformation, the TPBVP is reduced to consecutive initial-value problems of ordinary differential equations. A preliminary numerical test is given by a simple example originating in an optimal control problem.     

既有铆接铁路钢桥剩余寿命的评估

为确保既有铆接铁路钢桥使用安全，探讨了评估既有铆接铁路钢桥疲劳剩余寿命的方法。以京九线赣江桥为例，介绍了基于断裂力学的既有铆接铁路钢桥剩余寿命评估的原理与方法。基于断裂力学的评估过程主要包括如下4个步骤：识别临界构件、计算临界裂纹尺寸、疲劳裂纹扩展模拟、确定探测间隔。根据赣江桥剩余寿命评估结果：若按保证桥梁的正常使用功能，超声波探测间隔为1a；若按保证主桁结构承载安全，则探测间隔为3a。     

在役桥梁结构延性系数的动力评价方法

以桥墩的基本振型函数为基础,推导出基于试验动力参数的在役桥梁结构延性系数的计算公式,并给出了结构非弹性地震力的求解方法。对室内钢模型桥利用冲击力锤法进行了模态试验和静力对比试验,实测参数与理论值相差仅2%,在此基础上利用给出的公式可以求得桥墩的变形增加系数为2.78。结果表明,在场地土条件未知的情况下,利用动力试验法对在役桥梁结构延性系数进行评价是可行的。     

我国罚金刑适用中存在的问题与对策

在人类刑罚史上，由残酷的肉刑到自由刑，又到罚金刑的过渡，是人类迈向文明的表现。我国新《刑法》扩大了罚金刑的适用范围，但同时亦带来了一些新的问题。这些问题和对策的探讨，对我国的刑事审判与立法的发展将有着重要的意义。     

科技视野下的"三农"问题

当前，“三农”问题已构成制约我国社会发展和实现现代化进程中的突出问题，这一问题的根本解决既需要从实践层面也需要从学术层面对其进行学理的分析。从科技与农业、科技与农民两个维度审视了“三农”问题，为解决我国“三农”问题提供一些有借鉴作用的建议和对策，对我国“三农”问题的解决将有着十分重要的理论意义和实践意义。     

二阶抛物问题的扩展混合元方法

对二阶抛物问题提出了一种新的混合元方法一扩展混合元方法．该方法能同时逼近未知函数、未知函数的梯度和流体的流量，较好地模拟了带有混合型边界条件的二阶抛物问题．通过数值分析进一步证明了未知函数、未知函数的梯度和流体的流量的最优L^2-误差估计。     

集成化物流中的定位运输路线安排问题(LRP)优化算法评述

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