拟线性椭圆变分不等式的障碍最优控制问题

对拟线性椭圆变分不等式的障碍最优控制问题(即以障碍为控制变量)进行了研究.指标泛函为Lagrange型,其中含有控制变量二阶导数的p次幂,这使得最优性条件的推导颇为不易.对所考虑的问题给出了最优控制的存在性定理以及必要条件.     

半线性抛物方程支配系统的最优性条件

本文讨论了控制变量含于高阶导数项系数中的抛物型偏微分方程支配系统的最优控制问题,给出了最优控制的必要条件．     

一类区域优化问题

本文讨论了一类区域优化问题．通过引入控制变量，将原来的区域优化问题转化为一个等价的最优控制问题，并证明了最优区域的存在性     

具有年龄结构和迁移的非线性种群的最优生育控制

对一类非线性种群模型，以生育率为控制变量，研究最小代价一规模问题和最小代价一偏差问题．证明了最优控制的存在唯一性，给出了一阶最优性条件，讨论了最优反馈的合成．所得结论推广了文献中的一个结果．     

部分信息的完全耦合正倒向系统的随机最大值原理

本文研究了系统为Brown运动驱动的完全耦合的非线性正倒向随机微分方程的随机最优控制问题．系统要求可允许控制过程适应于标的Brown运动生成的盯域流的一个子盯域流．对于这种部分信息的随机最优控制问题,在控制区域为凸集和控制变量可以进入控制系统正向扩散系数的情形下,证明了最优性的一个充分条件（验证定理）和一个必要条件．     

一类状态受限的随机延迟最优控制问题的最大值原理

本文考虑一类状态受限的随机延迟最优控制问题,其中控制域为凸集且扩散项系数中含有控制变量.控制域可以是无界集合.用最大值原理方法建立了最优控制满足的必要条件.也给出了充分最优性条件,从而有助于找到最优控制.     

有两种可修复方法的复杂可修复系统的最优控制

研究了具有两种可修复方法的复杂可修复系统的最优控制问题,首先将此类系统方程转化为对应的Volterra积分方程的形式,然后利用算子半群理论证明了系统解的存在唯一性,再利用范数指标函数作为衡量控制变量的标准,研究有此类系统的最优控制问题,证明了对应的最优控制问题的解的存在唯一性.     

刮板沉降箱式除尘可修复系统的最优控制

研究了刮板沉降箱式除尘可修复系统稳态解的最优控制问题.通过利用范数指标泛函作为控制变量的标准,并采用极小化序列的方法,得到了系统最优控制元.     

具人为错误的两同型部件并联可修复系统的最优控制

利用Banach空间相关理论,以范数指标函数作为衡量控制变量的标准,研究了在人为错误下两同型部件并联可修复系统的最优控制问题,并证明了对应的最优控制问题解的存在唯一性.     

一类机器人系统的最优控制

本文通过把结构阻尼系数当作控制变量来讨论一类弹性机器人系统的最优控制问题 ,并利用Banach空间几何性质证明了最优控制元的存在唯一性     

Generalized Derivatives for the Solution Operator of the Obstacle Problem

We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed Dirichlet problems. The generalized derivatives can be used to obtain a novel necessary optimality condition for the optimal control of the obstacle problem with control constraints. A comparison shows that this system is stronger than the known system of C-stationarity.

     

Optimal control of unilateral obstacle problem with a source term

We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function which is the control function is assumed in H². We use an approximate technique to introduce a family of problems governed by variational equations. We prove optimal solutions existence and give necessary optimality conditions. The author is grateful to Prof. M. Bergounioux for her instructive suggestions.     

Indirect Obstacle Minimax Control for Elliptic Variational Inequalities

A minimax control problem for a coupled system of a semilinear elliptic equation and an obstacle variational inequality is considered. The major novelty of such problem lies in the simultaneous presence of a nonsmooth state equation (variational inequality) and a nonsmooth cost function (sup norm). In this paper, the existence of optimal controls and the optimality conditions are established.     

Optimal Control of the Obstacle Problem in a Perforated Domain

We study the problem of optimally controlling the solution of the obstacle problem in a domain perforated by small periodically distributed holes. The solution is controlled by the choice of a perforated obstacle which is to be chosen in such a fashion that the solution is close to a given profile and the obstacle is not too irregular. We prove existence, uniqueness and stability of an optimal obstacle and derive necessary and sufficient conditions for optimality. When the number of holes increase indefinitely we determine the limit of the sequence of optimal obstacles and solutions. This limit depends strongly on the rate at which the size of the holes shrink.     

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．     

Bilevel programming problems with simple convex lower level

This article is dedicated to the study of bilevel optimal control problems equipped with a fully convex lower level of special structure. In order to construct necessary optimality conditions, we consider a general bilevel programming problem in Banach spaces possessing operator constraints, which is a generalization of the original bilevel optimal control problem. We derive necessary optimality conditions for the latter problem using the lower level optimal value function, ideas from DC-programming and partial penalization. Afterwards, we apply our results to the original optimal control problem to obtain necessary optimality conditions of Pontryagin-type. Along the way, we derive a handy formula, which might be used to compute the subdifferential of the optimal value function which corresponds to the lower level parametric optimal control problem.     

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.     

Control Localized on Thin Structures for the Linearized Boussinesq System

We study optimal control problems for the linearized Boussinesq system when the control is supported on a submanifold of the boundary of the domain. This type of problem belongs to the class of optimal control problems with measures as controls, which has been studied recently by several authors. We are mainly interested in the optimality conditions for such problems. It is known that the differentiability properties needed to obtain the optimality conditions are more demanding, in terms of regularity of the data, than what is needed to prove the existence of optimal controls. Here we are able to derive the optimality conditions by taking advantage of the particular structure of the controls.     

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.