A PRIORI ERROR ESTIMATE AND SUPERCONVERGENCE ANALYSIS FOR AN OPTIMAL CONTROL PROBLEM OF BILINEAR TYPE

In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.     

一个最优控制问题解的存在性

剩用松弛化方法,讨论了一个特定的最优控制存在性问题.在系统初始状态固定的前提下,分别给出了在系统终端状态固定或自由的两种情形下,最优控制存在的判别条件.所涉及的控制问题中,状态方程及性能指标都较为简单,但控制区域及性能指标不具对称性且性能指标中状态变量和控制变量不分离.这与一般文献中基于对称性给出的最优控制不存在的证明以及状态变量和控制变量分离时的存在性结果有非常大的区别.     

AN EFFICIENT METHOD FOR MULTIOBJECTIVE OPTIMAL CONTROL AND OPTIMAL CONTROL SUBJECT TO INTEGRAL CONSTRAINTS

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a ＂budget＂ remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian ＂marching＂ method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced ＂weighted sum＂ based algorithm for the same problem [25]. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.     

OPTIMAL CONTROL THEORY APPLIED TO JOINT PRODUCTION OF TIMBER AND FORAGE

Renewable natural resource systems often represent examples of joint production. Optimal control theory is employed using the linear variational method to derive the general solution to the timber-forage joint production problem, with the objective of maximizing present value of revenue. The results indicate that optimal control theory can successfully solve such problems. The functional forms of the solution provide insight into how changes in parameters will influence the optimal joint production system.     

淡水湖泊藻类模型分析

利用非经典生物操纵法建立了鱼直接捕食藻类的模型.气候变化导致的温室效应越来越突出,鱼及藻类的生长对磷的消耗率等因素都与湖水温度有关,模型中考虑了温度的影响.分析了边界平衡点、正平衡点的存在性以及稳定性.得到了藻类和鱼灭绝的阈值,讨论了生态学意义.     

AN OPTIMAL MODEL AND ITS IDENTIFICATION FOR THE THERMODYNAMICS OF KEROGEN EV

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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.     

生长曲线模型中二次估计的非负最优性

考虑生长曲线模型Ｙ＝Ｘ１ＢＸ２＇＋ε，Ｅε＝０。设ε＝（εβ．．．εｎ）＇，ε＝（ε＇．．．εｎ＇）＇．Ｅεε＇＝Ｉ为未知协差阵，本文讨论了ｔｒ（ＣΣ）（Ｃ＜０）的一致最小方差非负二次无偏估计（简称为最优非负估计）问题，给出了一般二次估计是ｔｒ的最优非负估计的充要条件，从而得到ｔｒ的最优非负估计存在的充要条件，以及ｔｒ是ｔｒ的最优非负估计的充要条件。     

一类拟变分不等式的优化问题

本文用构造的方法证明了一类受拟变分不等式支配的优化问题的解的存在性。它提供在此基础上构造近似解的方法。     

SUPERCONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR OPTIMAL CONTROL PROBLEMS OF THE STATIONARY BENARD TYPE

In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in L^∞-norm and optimal error estimates in L^2-norm.     

土地资源的可拓性及优化配置系统结构模型

本文应用可拓学的理论和方法，对土地资源的特征及优化配置原理进行分析，设计了优化配置系统结构模型，为土地资源的优化配置和合理利用提供了一种新的科学方法。     

对偶理论在国民经济按比例最优增长分析中的应用

本文根据宏观经济行为和微观经济行为的辩证关系，设计了一类数学模型，并利用该模型研究了国民经济按比例最优增长及其实现问题．基于模型的分析表明．只要政府调控合适，国民经济就能够按比例最优增长．     

基于非单一类型的组合模型在回归分析中的应用

本文研究的是非单一类型的组合模型应用于回归预测的问题.利用不同类型的子模型来构建组合模型,最大程度上减小了子模型间的相关性,得到了具有更好泛化能力的组合模型这一结果,在预测分析中具有重要的指导意义.     

蛙卵有丝分裂模型的定性分析

本文对M.T.Borisuk和J.J.Tyson在[1]中所提出的一个有关蛙卵有丝分裂的平面三次系统模型证明了大范围周期解的存在性，给出了周期解所在的空间区域和所对应的参数区域及周期解不存在的空间区域和参数区域，所得结果严格地证明了[1]中给出的数值结果，最后我们证明在[1]的数值结果所用的参数下极限环的唯一性。     

OPTIMAL INVESTMENT IN THE PROTECTION OF A VULNERABLE BIOLOGICAL RESOURCE

It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.     

Logistic模型阈值控制悖论及复杂性分析

研究了Logistic模型稳态均值在阈值控制下产生反直觉变化现象与复杂响应的机理.结果表明,阈值控制能引起映射区间改变和映射分布变化,二者之间的竞争导致了受控Logistic模型稳态均值的反直觉变化现象与复杂响应.在阈值下限接近0或阈值上限接近1时,映射分布变化是影响稳态均值复杂响应的主导因素.阈值下限大于其临界值或阈值上限小于其临界值时,稳态均值变化主要由映射区间改变决定,此时,受控Logistic模型稳态均值会出现反直觉变化现象.理论分析结果通过数值仿真得到进一步证实.     

一类最优控制问题的最大值原理

本文研究具有终端约束的最优控制问题.利用构造罚函数的方法将其转化为无约束的近似问题,从而证明最优控制的存在性及其所满足的最大值原理.     

离散双线性系统二次型最优控制的迭代算法

1引言众所周知,某些复杂的工业过程用线性近似动态模型是不适宜的,而且许多对象如工业生产,生态,生物和社会经济等过程可以用双线性模型自然描述,能够在稳态工作点的一个较大领域内描述一大类严重非线性系统的动态特性,描述精度优于传统的线性模型     

QUALITATIVE ANALYSIS OF AN EPIDEMIC MODEL WITH VACCINATION

An SIRS epidemic modei with vaccination, temporary immunity and vary-ing total population size is considered. The threshold of existence of endemic equilibrium is found. The disease-free equilibrium is globally asymptotically stable below the threshold, the endemic equilibrium is globally asymptotically stable above the threshold.