随机广义耦合微分Riccati方程解的存在性（英文）

本文研究利用奇异值分解方法,获得了随机广义耦合微分Riccati方程解的存在性.另外,作为应用,我们将解的存在性结论应用到了,带马尔可夫跳的线性随机奇异系统最优控制问题,并得到有限时区上的最优控制问题中最优控制的显式表示形式.     

Thompson型广义g-奇异值交错不等式

Ｔｈｏｍｐｓｏｎ型广义ｇ－奇异值交错不等式伍俊良（重庆大学工商管理学院，６３００４４）关键词ｇ－奇异值，交错不等式．分类号ＡＭＳ（１９９１）１５Ａ１８／ＣＣＬＯ１５１．２１Ｒ．Ｃ．Ｔｈｏｍｐｓｏｎ在［１］中得到一个著名的奇异值交错不等式，即定理设Ａ...     

一类半线性椭圆型方程的不适定边值问题的最小极值解

本研究Banach空间L^p(Ω）中一类半线性椭圆型方程的不适定边值问题。运用度量广义逆与Schauder不动点定理证得该问题的最小极值解的存在性，应用Banach空间几何与Sobolev空间的方法，给出小极值解的等价条件。本结果，可应用于奇异最优控制问题。     

广义时间最优控制问题的近似最优解

本文考虑受控系统为Ｖｏｌｔｅｒｒａ积分系统的某种广义时间最优控制问题，导出了近似最优控制的充要条件和存在性结果，并在此基础上给出了一个四步法，可求得广义时间最优控制问题的近似最优解．     

一类非线性奇异最优控制问题的离散解法

本文研究非线性奇异最优控制问题的离散解法。利用在每个“小”时间区间上的积分形式来刻画奇异最优控制的特征,并构造了求解问题的差分方程,同时建立预估、校正格式给出了最优控制近似解的计算方法。     

无限群分次环的Smash Product的理想交性质

Ｇ是群，Ｒ是Ｇ－分次环．本文将有限群Ｇ分次环Ｒ与Ｇ的ｓｍａｓｈｐｒｏｄｕｃｔＲ＃Ｇ￣＊的理想交性质推广到无限群的情形．证明了：Ｇ是无限群，Ｒ是非奇异Ｇ－分次环．Ｒ与Ｇ的广义ｓｍａｓｈｐｒｏｄｕｃｔＲ＃Ｇ￣＊有理想交性质的充要条件，对任意０≠ａ＿ｅ∈Ｒ＿ｅ．     

矩阵的广义奇异值的若干不等式

本文引进广义奇异值概念，获得了若干广义奇异值不等式及交错定理．     

一类线性奇异摄动最优控制问题的渐近解

研究了一类线性奇异摄动最优控制问题的空间对照结构,讨论了初始点固定,终端自由的情形.首先根据变分法得到了一阶最优性条件,其次运用退化最优控制问题的解证明了异宿轨道的存在性,从而结合奇异摄动理论证明了原问题空间对照结构解的存在性.进一步根据解的结构,利用边界层函数法构造了奇异摄动最优控制问题一致有效的形式渐近解.最后,通...     

随机最优控制的二阶必要条件综述

文章介绍作者(含合作)近期在随机最优控制的二阶必要条件方面的工作.首先,在凸控制约束情况下给出经典意义下随机奇异最优控制的逐点型二阶必要条件.其次,利用针状变分获得具有非凸控制约束的Pontryagin最大值原理意义下随机奇异最优控制的逐点型二阶必要条件.最后利用变分分析的工具进一步改进非凸控制约束情形的结果,并将其推广到具有状态约束的情形.     

带磁场的广义Zakharov模型的奇异解

该文研究了带磁场的广义Zakharov模型的奇异解.得到了带磁场的广义Zakharov模型奇异解存在的充分条件,以及奇异解的下界速率.     

Optimal control of the viscous generalized Camassa–Holm equation

In this paper, we study the optimal control problem for the viscous generalized Camassa–Holm equation. We deduce the existence and uniqueness of weak solution to the viscous generalized Camassa–Holm equation in a short interval by using Galerkin method. Then, by using optimal control theories and distributed parameter system control theories, the optimal control of the viscous generalized Camassa–Holm equation under boundary condition is given and the existence of optimal solution to the viscous generalized Camassa–Holm equation is proved.     

OPTIMAL CONTROL OF MARKOVIAN SWITCHING SYSTEMS WITH APPLICATIONS TO PORTFOLIO DECISIONS UNDER INFLATION

This article is concerned with a class of control systems with Markovian switching,in which an ltd formula for Markov-modulated processes is derived.Moreover,an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman(HJB) equation with Markovian switching is characterized.Then,through the generalized HJB equation,we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation.Thus,we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds.Finally,for the CRRA utility function,we explicitly give the optimal consumption and portfolio policies.Numerical examples are included to illustrate the obtained results.     

Optimal control problems in hybrid systems with active singularities

The optimal control problem for systems with controlled unilateral phase constraints is considered. The definition of the generalized solutions is introduced, the transformation method for the original optimal control problem within the class of generalized solution to a standard optimal control problem is proposed, and the necessary optimality conditions are found.     

Weak maximum principle for optimal control problems of nonsmooth systems

In this paper, by considering vector-valued maximum type functions satisfying Lipschitz condition, and optimal control systems with continuous-time which is governed by systems of ordinary differential equation, we derive results similar to Pontryagin’s maximum principle and properties concerning the generalized Jacobian set for optimal control problems of these systems.     

Pointwise error estimates for a generalized Oseen problem and an application to an optimal control problem

We derive pointwise error estimates for a generalized Oseen when it is approximated by a low order Taylor‐Hood finite element scheme in two dimensions. The analysis is based on estimates for regularized Green's functions associated with a generalized Oseen problem on weighted Sobolev spaces and weighted interpolation results. We apply the maximum norm results to obtain convergence in an optimal control problem governed by a generalized Oseen equation and present a numerical example that allows us to show the behavior of the error.     

Method of Characteristics for Optimal Control Problems and Conservation Laws

In this paper, notions of global generalized solutions of Cauchy problems for the Hamilton–Jacobi–Bellman equation and for a quasilinear equation (a conservation law) are introduced in terms of characteristics of the Hamilton–Jacobi equation. Theorems on the existence and uniqueness of generalized solutions are proved. Representative formulas for generalized solutions are obtained and a relation between generalized solutions of the mentioned problems is justified. These results tie nonlinear scalar optimal control problems and one-dimensional stationary conservation laws.     

广义LQ最优控制问题的极小化序列

将经典LQ问题的评价泛函中关于控制变量的二次型推广为一类偶次多项式,证明了这类广义LQ无约束最优控制问题的一个等价扩张逼近可由一列半径递增的球约束最优控制问题加以实现.进而利用P0ntryagin极值原理建立相应的球约束最优控制问题的二次规划,并通过Canonical倒向微分流及不动点定理,求解常微分方程边值问题,得到球约束最优控制问题的最优值.随着约束球半径趋于无穷大,形成原广义LQ最优控制问题的一个极小化序列,从而得到原问题的最优值.     

具非线性控制变量的非自治松驰系统时间最优追踪控制问题中的若干结果

本文讨论了一类广义非自治离散松驰系统的时间最优控制问题，将R^n中点曲线的目标约束推广为凸集值函数的超曲线约束．在证明了松驰系统与原系统可达集相等的基础上，得到了最优控制的存在性．由凸集分离定理及终端时间闺值函数方程，我们获得了最大值原理及最优控制时间的确定方法．较之Hamilton方法，本文的条件更一般．离散松驰系统的相关结论可以用于分散控制．     

On an Augmented Lagrangian SQP Method for a Class of Optimal Control Problems in Banach Spaces

An augmented Lagrangian SQP method is discussed for a class of nonlinear optimal control problems in Banach spaces with constraints on the control. The convergence of the method is investigated by its equivalence with the generalized Newton method for the optimality system of the augmented optimal control problem. The method is shown to be quadratically convergent, if the optimality system of the standard non-augmented SQP method is strongly regular in the sense of Robinson. This result is applied to a test problem for the heat equation with Stefan-Boltzmann boundary condition. The numerical tests confirm the theoretical results.     

Optimal projection equations for reduced-order modelling,estimation, and control of linear systems with multiplicative white noise

The optimal projection equations for quadratically optimal reduced-order modelling, estimation, and control are generalized to include the effects of state, control, and measurement dependent noise.