基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

Theory of chemical bonds in metalloenzymes XXII: a concerted bond-switching mechanism for the oxygen–oxygen bond formation coupled with one electron transfer for water oxidation in the oxygen-evolving complex of photosystem II

ABSTRACT

QM(UB3LYP)/MM(AMBER) calculations were performed for the locations of the transition structure (TS) of the oxygen–oxygen (O–O) bond formation in the S₄ state of the oxygen-evolving complex (OEC) of photosystem II (PSII). The natural orbital (NO) analysis of the broken-symmetry (BS) solutions was also performed to elucidate the nature of the chemical bonds at TS on the basis of several chemical indices defined by the occupation numbers of NO. The computational results revealed a concerted bond switching (CBS) mechanism for the oxygen–oxygen bond formation coupled with the one-electron transfer (OET) for water oxidation in OEC of PSII. The orbital interaction between the σ-HOMO of the Mn(IV)₄–O₍₅₎ bond and the π*-LUMO of the Mn(V)₁=O₍₆₎ bond plays an important role for the concerted O–O bond formation for water oxidation in the CaMn₄O₆ cluster of OEC of PSII. One electron transfer (OET) from the π-HOMO of the Mn(V)₁=O₍₆₎ bond to the σ*-LUMO of the Mn(IV)₄–O₍₅₎ bond occurs for the formation of electron transfer diradical, where the generated anion radical [Mn(IV)₄–O₍₅₎]^-? part is relaxed to the ?Mn(III)₄?…?O₍₅₎^- structure and the cation radical [O₍₆₎=Mn(V)₁]⁺ ? part is relaxed to the ⁺O₍₆₎–Mn(IV)₁? structure because of the charge-spin separation for the electron-and hole-doped Mn–oxo bonds. Therefore, the local spins are responsible for the one-electron reductions of Mn(IV)₄->Mn(III)₄ and Mn(V)₁->Mn(IV)₁. On the other hand, the O₍₅₎^- and O₍₆₎⁺ sites generated undergo the O–O bond formation in the CaMn₄O₆ cluster. The Ca(II) ion in the cubane- skeleton of the CaMn₄O₆ cluster assists the above orbital interactions by the lowering of the orbital energy levels of π*-LUMO of Mn(V)₁=O₍₆₎ and σ*-LUMO of Mn(IV)₄–O₍₅₎, indicating an important role of its Lewis acidity. Present CBS mechanism for the O–O bond formation coupled with one electron reductions of the high-valent Mn ions is different from the conventional radical coupling (RC) and acid-base (AB) mechanisms for water oxidation in artificial and native photosynthesis systems. The proton-coupled electron transfer (PC-OET) mechanism for the O–O bond formation is also touched in relation to the CBS-OET mechanism.     

Optimal Harvesting in an Age-Structured Predator–Prey Model

We investigate optimal harvesting control in a predator–prey model in which the prey population is represented by a first-order partial differential equation with age-structure and the predator population is represented by an ordinary differential equation in time. The controls are the proportions of the populations to be harvested, and the objective functional represents the profit from harvesting. The existence and uniqueness of the optimal control pair are established.     

光突发交换网络中最长队列优先调度组装机制

提出了光突发交换网络中的最长队列优先调度（LQF-SA）机制，将边缘节点的突发组装和突发调度两种技术紧密结合在一起.在现实网络中，业务通常是非均匀分布的，即在某些源宿对之间存在更大的业务流量.仿真结果表明，LQF-SA机制可以很好地完成非均匀分布业务流的组装.即使在均匀分布业务流输入下，LQF-SA机制在突发大小分布、组装效率和突发丢失率等方面也优于已提出的轮询调度组装（RR-SA）机制.     

Optimal Control of Non-well-posed Heat Equations

This work is concerned with Pontryagin＇s maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given.     

光突发交换的交换控制策略和光缓存配置

光突发交换是面向下一代互联网的光交换模式.讨论了异步光突发交换系统的交换控制策略以及相应光缓存的优化配置策略.除了传统预约模式的交换策略,还研究了非预约和改进型预约模式,它们的性能评估由计算机仿真给出.结果表明:在条件相当情况下,改进型预约模式具有最低的丢包率.同时光缓存的配置对上述几类交换控制策略的性能都有很大影响,仿真结果指出:光缓存的粒度对系统性能具有重要影响,所讨论的几类交换模式都存在最佳时延粒度,研究结果对光交换矩阵的设计有指导意义.     

强流束晕-混沌的外部磁场开关控制

研究了强流离子束在周期聚焦磁场通道中束晕-混沌的外部磁场开关参数控制方法. 将该方法应用在多粒子模型中，实现了对5种不同初始分布质子束的束晕-混沌的有效控制，得到了消除束晕及其再生现象的理想结果.在强流加速器系统中，由于外部磁场是可测和可调 的物理量，因此该控制方法有利于实验研究，可为强流质子加速器中周期聚焦磁场的设计和实验提供参考. 关键词： 强流离子束 周期聚焦磁场通道 束晕_混沌 混沌控制 开 关控制     

Differentiability of the Value Function of Nonclassical Optimal Growth Models

We consider an optimal growth (multi-sector) model with nonconvex technology. Using the Clarke results on generalized gradients, we prove that the value function has left and right derivatives with respect to the initial capital stock, without requiring supermodularity assumptions.     

Efficient Sequential Quadratic Programming Implementations for Equality-Constrained Discrete-Time Optimal Control

Efficient sequential quadratic programming (SQP) implementations are presented for equality-constrained, discrete-time, optimal control problems. The algorithm developed calculates the search direction for the equality-based variant of SQP and is applicable to problems with either fixed or free final time. Problem solutions are obtained by solving iteratively a series of constrained quadratic programs. The number of mathematical operations required for each iteration is proportional to the number of discrete times N. This is contrasted by conventional methods in which this number is proportional to N ³. The algorithm results in quadratic convergence of the iterates under the same conditions as those for SQP and simplifies to an existing dynamic programming approach when there are no constraints and the final time is fixed. A simple test problem and two application problems are presented. The application examples include a satellite dynamics problem and a set of brachistochrone problems involving viscous friction.     

一类经典”秘书问题”的推广

”秘书问题”在最优停时理论的发展中曾起过重要作用 ,实际中的一类问题与”秘书问题”有类似之处 ,但比”秘书问题”更复杂 .本文将经典”秘书问题”进行推广 ,建立了一类比经典”秘书问题”更有实际意义的模型 ,并给出了该类模型的解 .