VARIATIONAL DISCRETIZATION FOR OPTIMAL CONTROL GOVERNED BY CONVECTION DOMINATED DIFFUSION EQUATIONS

In this paper, we study variational discretization for the constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization Galerkin method. A priori error estimates are derived for the state, the adjoint state and the control. Moreover, residual type a posteriori error estimates in the L^2-norm are obtained. Finally, two numerical experiments are presented to illustrate the theoretical results.     

分数阶抛物方程控制系统最优控制的稳定性

本文研究了一类分数阶抛物方程的最优控制问题,主要讨论了其最优控制与最优值的稳定性.利用了凸方法获得了获得了这类问题最优控制的稳定性结果,并且推广了在参考文献[3]中的最优控制稳定性结论.     

多值非线性系统最优控制的一阶必要条件

由 E,(?)的最大单调性,及 int(D(?))∩D(E)≠φ得,E+(?)为 Y→2~(Y′) 的最大单调算子.再由(H_(?))知 E+(?)为强制的,故由多值最大单调算子的满射性得,(1.3)存在唯一解 y∈D(E),即 y 满足(1.1).证毕.记θ为(1.1)从控制到状态 y 的解映射.现考虑其最优控制问题.设允许控制集(?)_(ad)为(?)=L~∞(0,T;U)中的有界弱~*     

一类向量极值问题的最优性条件

本文利用序线性空间中关于次似凸集值映射的择一性定理,得出了具有广义等式和不等式约束的向量极值问题的最优性条件.     

SINGULAR PERTURBATION OF OPTIMAL CONTROL FOR SEMILINEAR INTEGRO-DIFFERENTIAL EQUATIONS

1 IlltroductionWe shall solve a problem Of optimal control consisting of the systemon the interval 0 5 t 5 1, with initial conditionsand the quadratic cost functionalwhich is to be minimized. Here the "T" denotes transposition; I = jot K(t, asx) fi are m-vectors; is gi are n-vectors, u is an r--vector, and the matrix R.is symmetric and positive definite, while the matrices Q and T are symmetricand positive semidefinite throughout 0 5 t S 1 for E > 0 small. fi, g2, 51 and6z are matrix functi…     

A POSTERIORI ERROR ESTIMATE FOR BOUNDARY CONTROL PROBLEMS GOVERNED BY THE PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state, the boundary state and the final state. It is proven that these estimators are reliable bounds of the finite element approximation errors, which can be used as the indicators of the mesh refinement in adaptive finite element methods.     

TIME OPTIMAL IMPLUSE CONTROL PROBLEMS

ＴＩＭＥ　ＯＰＴＩＭＡＬ　ＩＭＰＬＵＳＥ　ＣＯＮＴＲＯＬ　ＰＲＯＢＬＥＭＳＴＩＭＥＯＰＴＩＭＡＬＩＭＰＬＵＳＥＣＯＮＴＲＯＬＰＲＯＢＬＥＭＳ￥ＸｕＺｏｎｇｙｕｎ（ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ａｃｌａｓｓ...     

二阶不连续微分方程周期边值问题解的存在性

本文研究Lienard方程x"+f(t,x,x')x'+g(t,x)=h(t,x,x')的周期边值问题,其中f,g,h均为Caratbeodory函数.利用Leray-Schauder度理论,在适当的条件下证明了该问题解的存在性.     

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.     

Semiconcavity of the value function for the Bolza control problem

In this paper we investigate the regularity of the value function of the Bolza control problem. We propose sufficient conditions for the value function to be semiconcave or locally Lipschitz when the controls are unbounded.     

Generalized Bellman-Hamilton-Jacobi optimality conditions for a control problem with a boundary condition

In this paper we study conditions for optimality of a deterministic control problem where the state of the system is required to stop at the boundary. Using the Clarke generalized gradient, we refine the classical verification theorem and show that it is not only sufficient but also necessary for optimality. It is also shown that the solution to the generalized Bellman-Jacobi-Hamilton equation involving the Clarke generalized gradient is unique among the class of regular functions.     

FINITE ELEMENT ANALYSIS OF OPTIMAL CONTROL PROBLEM GOVERNED BY STOKES EQUATIONS WITH L^2-NORM STATE-CONSTRAINTS

An optimal control problem governed by the Stokes equations with L2-norm state constraints is studied.Finite element approximation is constructed.The optimality...     

SUPERCONVERGENCE AND A POSTERIORI ERROR ESTIMATES FOR BOUNDARY CONTROL GOVERNED BY STOKES EQUATIONS

In this paper, the superconvergence results are derived for a class of boundary con-trol problems governed by Stokes equations. We derive superconvergence results for boththe control and the state approximation. Base on superconvergence results, we obtainasymptotically exact a posteriori error estimates.     

带障碍的广义插值样条与带状态约束的最优控制

本文由样条的极值性质出发给同分算子插值样条（即广义插值样条）新的推导方法。用这种方法可推导出带障碍（即带不等式约束）的微分算子插值样条的解析性质,为简便计,本文以非负广义插值样条为例。最后,揭示了状态带不等式的最优控制解的必要性准则与带障碍的广义插值样条的联系。     

Banach空间二阶非线性混合型脉冲微分-积分方程边值问题的解

在较弱的条件下,利用MSnch不动点定理,研究了Banach空间中二阶非线性混合型脉冲微分-积分方程边值问题解的存在性,推广和改进了某些已有的结果.     

Sufficient Optimality Conditions for Optimal Control Problems with State Constraints

It is well-known in optimal control theory that the maximum principle, in general, furnishes only necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum principle turns to be likewise a sufficient condition. Here an invexity type condition for state constrained optimal control problems is defined and shown to be a sufficient optimality condition. Further, it is demonstrated that all optimal control problems where all extremal processes are optimal necessarily obey this invexity condition. Thus optimal control problems which satisfy such a condition constitute the most general class of problems where the maximum principle becomes automatically a set of sufficient optimality conditions.     

OPTIMAL CONTROL PROBLEM FOR A PERIODIC PREDATOR-PREY MODEL WITH AGE-DEPENDENCE

In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur's theorem and optimality condition is derived by means of normal cone.     

原子核反应系统的最优控制问题

本文讨论基于单能静态稆向同性迁移方程的原子核反应堆系统的最优控制问题。本文把散射裂变截面函数当作控制变量，在一定条件下，证得最优控制的存在唯一性。本文最后给出最优散射裂变截控制存在的一个必要条件。     

关于一类连续最优控制问题的一种可实现的离散方法

本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法，此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象，文中给出这种做法的理论证明和实现方案。