轨线两端均受限制时的最优控制问题

本文用文献[4]中的方法,首先处理了轨线两端均受限制时的快速最优控制问题,得到控制最优性的必要条件以及在某种意义下的充分条件;还得到有关微分方程的边界条件,并说明其几何意义,即贯截条件.此外,又讨论了所用方法中乘子的性质及作用. 对于一般意义下的以及文献[4]中所讨论的最优控制问题,当轨线两端均受限时,也可象此处对快速系统那样进行处理,并得到相应的结果.同时,关于贯截条件及乘子的讨论,也仍然有效. 文中附有二个算例.     

轨綫两端均受限制时的最优控制问題

本文用文献[4]中的方法,首先处理了轨线两端均受限制时的快速最优控制问题,得到控制最优性的必要条件以及在某种意义下的充分条件;还得到有关微分方程的边界条件,并说明其几何意义,即贯截条件.此外,又讨论了所用方法中乘子的性质及作用. 对于一般意义下的以及文献[4]中所讨论的最优控制问题,当轨线两端均受限时,也可象此处对快速系统那样进行处理,并得到相应的结果.同时,关于贯截条件及乘子的讨论,也仍然有效. 文中附有二个算例.     

《关于透视变换的研究》一文商榷

1　引　　言在《关于透视变换的研究》(以下简称为文献[1 ])一文中提出 :“二点透视是经旋转平移方法得到的”,这种提法不符合二点透视投影等基本概念 ,但文中论证较难令人信服 .问题的关键在于对一些基本概念应该如何理解 .以下将说明对于一些概念我们与文献 [1 ]的不同理解 ,与作者及同行商榷 .2　透视投影和透视变换文献 [1 ]中的第 1句就提到 :“计算机图形学中的透视变换……”,严格地说 ,“透视投影”和“透视变换”不相同 .计算机图形学中关心的是透视投影 ,因为它要解决在二维表面上绘制三维形体的问题 .透视投影是已知投影中心和投…     

关于定量与定性微分对策

本文将文献[2,3,4,5,7]中的方法加以发展,用来解决一类定量和定性微分对策问题.对于定量对策,我们推出最优策略(u,v)所应满足的必要条件,即"双方极值原理".对于定性对策,也得到最优策略(u,v)的必要条件、且不必如文献[1]中那样限于"小范围".并确定了组成界栅(barrier)的轨线的方程. 还讨论了一些其他问题,如充分条件、目标集的更一般的形式、定性对策与能控性问题间的关系等. 可见,这种方法是一种可用来解决多种类型的最优控制和微分对策问题的有力工具. 文中附有二例.     

积分约束下多方线性微分对策的追捕问题

本文给出了多方线性微分追捕对策中完成追捕的充分条件.从推论可以得到文献[1]的结果.     

关于非线性时滞系统的鲁棒稳定性条件的讨论

1　引　言在《自动化学报》1 999年第 6期中 ,短文“非线性时滞系统的稳定性分析及鲁棒稳定性分析”[1 ] 用 Lyapunov函数方法分别讨论了确定性和不确定性非线性时滞系统的稳定性 .对于确定性系统得到了一种基于 LMI的渐近稳定充分条件 ,并研究了不确定性系统的鲁棒稳定性问题 .但由于该文对 Razumikhin定理的理解有误 ,有关鲁棒稳定性的结论 (定理 1、推论 1 )是不正确的 .对于 Razumikhin定理 ,文 [2 ]给出了一种所谓的改进型 Razumikhin定理 .但有人提出质疑 ,问题在于没有正确理解 Razumikhin定理 [3,4] .文 [1 ]虽然没有直接提到 R…     

关于线性特征系数的几个问题

本文研究了系统具有线性特征系数的条件。在指出文献[1]、[2]错误的同时,提出了系统具有全部线性特征系数的一个充分条件,并且证明了文献[1]的充分条件是这个充分条件的特殊情况。     

对《用常数阵实现对角优势的条件和算法》一文的商榷

该文[1]给出两个定理。其必要条件即λ_i>1/2是正确的,但该文所附文献[6]中的“实常阵补偿可获得对角优势的必要条件定理”早已指出。而其充分条件即λ_i>(m-1)/m则是错误的。问题在于,补偿后的矩阵(s)行优势的定义,即文中式(2.3)是错误的。必须在式后增加     

“用优选法解系统可靠性最优化问题的一个简捷算法”的注记

在一定的资源条件限制下,求部件的最优备份数,使系统的可靠度达最大,这类可靠性中的最优化问题已有广泛的研究.文献[1]对 k 阶串联系统提出了一个简捷算法.文中对算法的最优性未加证明,而认为所得之解必是最优的.事实上,这是不对的.下面的简单例子说明用文献[1]的简捷法算出的解并不是最优的.例:现有一个三级串联的系统,每级的可靠度、重量及价格如下表     

軌綫末端受限制时的最优控制问題

当轨线末端受有条件限制时,将使最优控制系统有关的微分方程的边界条件变得复杂.本文考虑了各种受限情形,提出了确定边界条件的方法,得到泛函改变量公式,讨论了控制最优性的充分条件以及在某些情形下的必要条件.     

Control constraints, abnormality, and improved performance by periodic control

Second-order conditions for steady-state optimality and nonoptimality in a periodic control problem are presented. The main result is a generalization of the π test, a second-order sufficient condition for improved performance by periodic control. Earlier results are generalized in two distinct ways: 1) the control constraint set is only assumed to be convex (and, hence, possibly nonopen) thus allowing the optimal steady-slate control to be an element of the control constraint set boundary; and 2) auxiliary normality conditions are eliminated. Proofs of the results are based upon second-order necessary, conditions for nonlinear programming and optimal control obtained recently in [43] and [44].     

On optimal parameter selection for stochastic Ito differential systems

In this paper necessary conditions for optimal parameter selection of stochastic Ito differential systems are developed. Our main result, a necessary condition for optimality, is presented in theorem 1. Its proof is based on some recent results of Fleming (1968, p. 210), The result is illustrated by its application to the problem of determination of the optimal feedback gain matrix for a noisy linear regulator.     

Variational optimality condition in the problem of control of initial boundary conditions for semilinear hyperbolic systems

Consideration is given to the problem of optimal control of a system of semilinear hyperbolic equations at finite-dimensional (pointwise) relations between initial boundary states of the system and control actions. In this case, the optimality condition in the form of a pointwise maximum principle is invalid. A nonclassical optimality condition of a variational type is proved. The sense of the obtained result is in that an optimal boundary or start control nearly at each point is a solution to a special problem of control of initial conditions for the system of ordinary differential equations constructed on the family of characteristics of the initial hyperbolic system. Constructions of the indicated optimality condition are illustrated by two examples. An iterative method based on the obtained result is stated. The method does not require additional assumptions about the differentiability of parameters of the control problem and convexity of the set of admissible controls necessary in using gradient methods.     

一类混杂系统的最优控制

研究了一类脉冲依赖于状态的混杂系统的最优控制问题.与传统的变分方法不同,通过将跳跃瞬间转化为一个新的待优化参数,得到了该混杂系统的必要最优性条件,从而将最优控制问题转化为一边界值问题,该边界值问题可由数值方法或解析方法解决.此外,利用广义微分的理论,将该必要最优性条件推广到Frechet微分形式.结论表明,在混杂动态系统运行的连续部分,最优解所满足的必要性条件和传统的连续系统相同.在混杂动态系统的脉冲点处,哈密尔顿函数满足连续性条件,协态变量则满足一定的跳跃条件.最后,通过两个实例分析,表明该方法是有效的.     

Necessary integral optimality conditions for quasi-singular controls in one control problem

An optimal control problem with variable structure described by a system of nonlinear integral Volterra-type equations is considered in the article. A necessary optimality condition is obtained in the form of a linearized maximum condition. A case of degeneracy of the linearized maximum principle is further studied. Integral necessary optimality conditions of quasi-singular controls are proved.     

Minimax control of maximal monotone differential inclusions in ℝN

Minimax optimal control problems driven by a maximal monotone operator and a multivalued control vector field are examined. First the existence of optimal controls is established. Then their variations are examined as well as the variations of the value of the problem as its data are perturbed (sensitivity analysis). Finally a necessary and sufficient condition for minimax optimality is obtained.     

Stochastic maximum principle for delayed doubly stochastic control systems and their applications

ABSTRACT

In this paper, we investigate the optimal control problems for delayed doubly stochastic control systems. We first discuss the existence and uniqueness of the delayed doubly stochastic differential equation by martingale representation theorem and contraction mapping principle. As a necessary condition of the optimal control, we deduce a stochastic maximum principle under some assumption. At the same time, a sufficient condition of optimality is obtained by using the duality method. At the end of the paper, we apply our stochastic maximum principle to a class of linear quadratic optimal control problem and obtain the explicit expression of the optimal control.     

Necessary condition for near optimal control of linear forward–backward stochastic differential equations

This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward–backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls and the control domain is not assumed to be convex. In the previous work (Theorem 3.1) of the second and third authors, some problem of near optimal control with the control dependent diffusion is addressed and our current paper can be viewed as some direct response to it. The necessary condition of the near-optimality is established within the framework of optimality variational principle developed by Yong and obtained by the convergence technique to treat the optimal control of FBSDEs in unbounded control domains by Wu. Some new estimates are given here to handle the near optimality. In addition, an illustrating example is discussed as well.