一类推广的奇异型最佳随机控制问题

§1.引言设 W_t,t≥0为概率空间(Ω,(?),P)上的标准 Wiener 过程,{(?)_t}为由之所产生的上升σ-域族,以(?)表所有{(?)_t}适应左连续0初值有限变差过程的全体.对每个ξ={ξ_t,t≥0}∈(?),熟知有正规分解ξ_t=ξ_t~ -ξ_t~-,而(?)_t(?)ξ_t~ ξ_t~-为ξ_t 的全变差过程,当然ξ_t~ 及ξ_t~-皆为(?)中的单调非降过程。     

从停止问题到折扣费用问题

本文借助一类停止问题,研究了奇异型折扣费用问题,得出了最佳控制的存在性及结构形式.其模型为设(Ω,(?),P)为某概率空间,w_t,t≥0为其上 Wiener 过程,(?)_t=σ(w_s,0≤s≤t).以(?)表(?)_t,适应左连续0初值有限变差过程的全体.对(?)ξ={ξ,t≥0}∈(?),     

一类随机微分方程的解法

设(Ω,,p)是一个完备的概率空间,(_t)_(t≤T)是的非降子σ代数族,W=(W_t,_t),t≤T 是 Wiener 过程。a(t,x),b(t,x)均是关于[0,T]×R 可测函数,并且假定 a(t,ξ_t)∈L_W~1[0,T],b(t,ξ_t)∈L_W~2[0,T](参考[5])。称 p—a.s 连续的随机过程ξ=(ξ_t,_t),t≤T 为随机微分方程     

一类平稳的奇异性随机控制问题的研究

§1.引言 关于奇异型随机控制问题,已有很多文章进行研究,如文献[1]—[3]等。在某种意义上来说,文献[2]的结果比文献[1]更为一般。具体描述如下: 设W_t,t≥0为概率空间(Ω,(?),P)上标准Wiener过程。(?)_t为由此过程所生成的上升σ-域族。以(?)表(?)_t适应左连续零初值有限变差过程的全体。对,有正规分解表全变差过程。我们所说的控制全包含在集中。文献[2]研究的平稳模型是:     

马氏过程的可加泛函与停时变换(Ⅱ)

定义4.1 设 X=(Ω(?),(?)_t,X_t,θ_t,P~x,T)是以(E_Δ,(?)_Δ)为状态空间的随机过程,称(Ω,(?))上的随机变量族 M={M_t,0≤t≤∞}为 X 的可乘泛函,如果(1)M_t∈(?)_t,((?)t≥0);(2)M_(s+t)=M_t(M_s(?)θ_t),((?) s、t≥0);(3)0≤M_t≤1,((?)t≥0).若 t(?)M_t 右连续(连续),则称 M 是右连续(连续)可乘泛函。对 X 的可乘泛函 M=     

具有保留费用及按比例费用的受控扩散——脉冲过程的最佳控制问题

关于脉冲控制的原始模型最初由 Bernsoussan 和 Lions 提出,并且研究了该模型在有限直线上费用固定时的情形,Richard 将该模型进行了推广,研究了无限直线上的问题,Richard 的模型简述如下:设 W_t,t≥0为一标准 Wiener 过程,(?)为由之而产生的上升σ-域的完备化,其中的每一个控制 v 即指确定一列上升的(?)停时0≤τ_1≤τ_2≤……及(?)τ_i可测随机变量ξ_i,i=1,2…,令 V=(τ_1,ξ_1;…;τ_i,ξ_i;…),而其最佳控制问题就是求一个控制(?)使对任何初值 x 成立:     

Richard模型的平均期望费用问题

设 W_t,t≥0为(Ω,■,P)上标准 Wiener 过程,■为由之所生成的上升 σ-域族,以τ_i,i≥1表任一个(?)单调上升停时列,对每个τ_i 确定一个F_(τi)可测随机变量ξ_i,我们称任一这样的对列 v={(τ_i,ξ_i),i≥1}为一脉冲过程,以 V 表脉冲过程,(以下称脉冲控制)的全体,设 h 和 B 为 R 上满足某些条件的非负实函数,再设σ,μ为任何实常数且|σ|>0.本文求得一个常数λ>0使对任一实数 x 皆有一个十分明确具体的控制 v~*={(τ_i~*,ξ_i~*),i≥1)∈V 满足lim~T→∞(1/T)E[integral from 0 to T h(x+μt+σW_t+sum τ_i~*相似文献   

Richard模型最佳控制的存在性及其费用的函数结构

§0.导言.Richard 提出的是一个以一维齐次扩散过程为状态模型的最佳控制问题——有折扣费用的无限水平线问题,具体描述如下:设 W_t,t≥0为概率空间(Q,(?),p)上的一维 Wiener 过程,(?)=σ(W_(?),(?)≤t).0=τ_0≤τ_1≤…为一列上升的(?)停时.(?)表τ_n 前σ-域.对每个τi     

Schrdinger方程的广义Dirichlet问题

在本文中,{B(t),t≥0}是 d(d≥1)维标准 Brown 运动,(?)_t=σ{B(s),s≤t},P_x 是自 x 出发的 Brown 运动所产生的 Wiener 测度,E_x 表示关于 P_x 的积分.D 是R~d 中的一个区域,对 D 上的有界函数 c,令     

一类对称的平稳型随机控制问题

§1.前言 设W_t,t≥0为(Ω,(?),P)上的一个标准的Wiener过程,为由之生成的上升σ-域族,0=τ_0≤τ_1≤τ_2≤…≤τ_n≤…为一列非降停时且n→∞时τ_n↑∞,a.s.对每个τ_n确定一个可测的随机变量,我们称任一这样的对列为一脉冲控制。以后以V表脉冲控制的全体。 本文所研究的问题是求一个常数λ>0使对皆有     

Deterministic and Stochastic Control of Navier—Stokes Equation with Linear, Monotone, and Hyperviscosities

This paper deals with the optimal control of space—time statistical behavior of turbulent fields. We provide a unified treatment of optimal control problems for the deterministic and stochastic Navier—Stokes equation with linear and nonlinear constitutive relations. Tonelli type ordinary controls as well as Young type chattering controls are analyzed. For the deterministic case with monotone viscosity we use the Minty—Browder technique to prove the existence of optimal controls. For the stochastic case with monotone viscosity, we combine the Minty—Browder technique with the martingale problem formulation of Stroock and Varadhan to establish existence of optimal controls. The deterministic models given in this paper also cover some simple eddy viscosity type turbulence closure models. Accepted 7 June 1999     

网络流在清理三角债问题中的应用

本文把清理三角债中两种优化数学模型问题，化成求解相应网络上最小费用流的问题，从而得到（强）多项式算法，并把另外的一种优化数学模型问题。化成线性规划问题.于是解答了文[3]中提出的清理三角债的三个基本问题．     

Time optimal sampled-data controls for the heat equation

In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls.The study of such a time optimal sampled-data control problem is not easy, because it may have infinitely many optimal controls. We find connections among this problem, a minimal norm sampled-data control problem and a minimization problem, and obtain some properties on these problems. Based on these, we not only build up error estimates for optimal time and optimal controls between the time optimal sampled-data control problem and the time optimal distributed control problem, in terms of the sampling period, but we also prove that such estimates are optimal in some sense.     

成组加工中带可分配工期的误工任务数问题

本文研究了成组加工时带可分配工期的误工任务数问题的排序与工期分配.对于成组加工中带可分配工期的误工任务数问题的不同模型,或给出其最优序,或证明了其是NP-难问题.     

Nonconvex and relaxed infinite-horizon optimal control problems

In this paper, we consider the Lagrange problem of optimal control defined on an unbounded time interval in which the traditional convexity hypotheses are not met. Models of this form have been introduced into the economics literature to investigate the exploitation of a renewable resource and to treat various aspects of continuous-time investment. An additional distinguishing feature in the models considered is that we do not assume a priori that the objective functional (described by an improper integral) is finite, and so we are led to consider the weaker notions of overtaking and weakly overtaking optimality. To treat these models, we introduce a relaxed optimal control problem through the introduction of chattering controls. This leads us naturally to consider the relationship between the original problem and the convexified relaxed problem. In particular, we show that the relaxed problem may be viewed as a limiting case for the original problem. We also present several examples demonstrating the applicability of our results.     

Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer Chemotherapy

A class of mathematical models for cancer chemotherapy which have been described in the literature take the form of an optimal control problem over a finite horizon with control constraints and dynamics given by a bilinear system. In this paper, we analyze a two-dimensional model in which the cell cycle is broken into two compartments. The cytostatic agent used as control to kill the cancer cells is active only in the second compartment where cell division occurs and the cumulative effect of the drug is used to model the negative effect of the treatment on healthy cells. It is shown that singular controls are not optimal for this model and the optimality properties of bang-bang controls are established. Specifically, transversality conditions at the switching surfaces are derived. In a nondegenerate setting, these conditions guarantee the local optimality of the flow if satisfied, while trajectories will be no longer optimal if they are violated.     

Proper orthogonal decomposition in sparse optimal control of some reaction diffusion equations using model predictive control

We investigate optimal sparse control problems for reaction diffusion equations with non-monotonous cubic non-linearities. In particular, we consider the Schlöl equation as well as the FitzHugh-Nagumo system. In these models, the solutions form pattern of traveling wave fronts or spiral waves. To control them turns out to be very challenging and computational difficult. The needed computational times are enormous. The use of sparse optimal control techniques was surprisingly very helpful. On the one hand the optimal control becomes sparse and on the other hand we achieve our control goals with satisfying accuracy for much less computational time then before. Trying to decrease it even more by POD model reduction does not work sufficiently well since too many POD modes are needed to approximate the solutions satisfactorily. Our second approach is the application of model predictive controls. This technique performs very well for the control aim of following a desired trajectory. An additional use of POD model reduction for each - now very small - time horizon yields even better results in computational time with a marginal loss of precession. This result holds for optimal controls as well as for optimal sparse controls. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

非负权重最优组合预测方法的基本理论研究

本文从三个方面研究了非负权重最优组合预测方法的基本理论，给出了一种解决三阶非负权重最优组合预测问题的简捷方法。     

Some stochastic inventory models with deterministic variable lead time

In this paper we determine optimal reduction in the procurement lead time duration for some stochastic inventory models, jointly with the optimal ordering decisions. The models are developed with complete and partial information about the lead time demand distribution. The stochastic models analyzed in this paper are the classical continuous and periodic review models with a mixture of backorders and lost sales and the base stock model. For each of these models, we provide sufficient conditions for the uniqueness of the optimal operating policy. We also develop algorithms for solving these models and provide illustrative numerical examples.     

Optimal financing and dividend control in the dual model

In this paper, we study the optimal financing and dividend control in the dual model. Under some constraints, we firstly construct two categories of suboptimal models and identify the value functions and the optimal policies corresponding to these two categories of suboptimal models. Finally we identify the value function and present an optimal policy corresponding to the general optimal model.