The explicit synthesis of stabilizing (time optimal) feedback controls for the attitude control of a rotating satelite

The attitude stabilization problem for a spinning satellite controlled by two small jets may be modelled as a four-dimensional, nonlinear control system, linear in the controls. The recent feedback linearization theorem of Hunt and Su may be applied to transform this system, via state feedback and a local coordinate change, to a pair of uncoupled, two-dimensional, linear systems. Feedback controls for the problem of time optimal transfer to the origin for these linear systems are explicitly calculated and then transformed to give explicit feedback controls for time optimal stabilization in the original nonlinear problem. The theory is illustrated by sample calculations.     

带停时的奇异型随机控制问题研究

利用随机分析的知识及最优控制理论,推广了一类带停时的随机控制问题,针对不同参数,证明了最佳控制的存在性,分两种情况给出了最佳控制的存在区域,并给出了不同初始状态下,最佳控制的结构和最佳费用函数.由于将原模型中费用结构中的R-S积分的被积函数由1推广为满足某些条件的一般函数,所以推广后的模型更具一般性.     

Optimal multilevel matrix algebra operators

We study the optimal Frobenius operator in a general matrix vector space and in particular in the multilevel trigonometric matrix vector spaces, by emphasizing both the algebraic and geometric properties. These general results are used to extend the Korovkin matrix theory for the approximation of block Toeplitz matrices via trigonometric vector spaces. The abstract theory is then applied to the analysis of the approximation properties of several sine and cosine based vector spaces. Few numerical experiments are performed to give evidence of the theoretical results.     

Numerical solution of minimax optimal control problems by multiple shooting technique

This paper presents the application of the multiple shooting technique to minimax optimal control problems (optimal control problems with Chebyshev performance index). A standard transformation is used to convert the minimax problem into an equivalent optimal control problem with state variable inequality constraints. Using this technique, the highly developed theory on the necessary conditions for state-restricted optimal control problems can be applied advantageously. It is shown that, in general, these necessary conditions lead to a boundary-value problem with switching conditions, which can be treated numerically by a special version of the multiple shooting algorithm. The method is tested on the problem of the optimal heating and cooling of a house. This application shows some typical difficulties arising with minimax optimal control problems, i.e., the estimation of the switching structure which is dependent on the parameters of the problem. This difficulty can be overcome by a careful application of a continuity method. Numerical solutions for the example are presented which demonstrate the efficiency of the method proposed.     

双指数跳扩散过程的最优停止问题

美式期权定价问题是金融数学的热点问题,一般要用最优停止理论。本文给出了双指数跳扩散过程的最优停止问题的解析解。     

Generalized gradients of Lipschitz functionals

The purpose of this article is threefold: (i) to present in a unified fashion the theory of generalized gradients, whose elements are at present scattered in various sources; (ii) to give an account of the ways in which the theory has been applied; (iii) to prove new results concerning generalized gradients of summation functionals, pointwise maxima, and integral functionals on subspaces of L^∞. These last-mentioned formulas are obtained with an eye to future applications in the calculus of variations and optimal control. Their proofs can be regarded as applications of the existing theory of subgradients of convex functionals as developed by Rockafellar, Ioffe and Levin, Valadier, and others.     

NSGA-II算法在农业水保措施配置优化中的应用

农业水保措施的配置要考虑其生态效益和经济效益.不同水保措施组合方案有其相应的生态和经济效益,如何配置使综合效益最佳是一个最优化问题.分析了农业水保措施配置最优化需要考虑的两个目标,并将其公式化,建立了水保措施配置优化模型,并应用NSGA-II多目标遗传算法求解该模型.最后,以甘肃天水市罗玉沟流域的水保措施配置为例,进行了初步应用.结果表明,采用NSGA-II算法在水保措施配置优化模型求解时,计算效率较高,优化结果稳定,具有一定的应用价值.     

Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients

We demonstrate the construction of generalized Rough Polyharmonic Splines (GRPS) within the Bayesian framework, in particular, for multiscale PDEs with rough coefficients. The optimal coarse basis can be derived automatically by the randomization of the original PDEs with a proper prior distribution and the conditional expectation given partial information on, for example, edge or first order derivative measurements as shown in this paper. We prove the (quasi)-optimal localization and approximation properties of the obtained bases. The basis with respect to edge measurements has first order convergence rate, while the basis with respect to first order derivative measurements has second order convergence rate. Numerical experiments justify those theoretical results, and in addition, show that edge measurements provide a stabilization effect numerically.     

带利率和随机观测时间的布朗运动模型中最优分红策略

本文研究了带利率和随机观测时间的布朗运动模型中的最优分红问题.利用随机控制理论,获得了最优值函数相应的HJB方程,表明最优分红策略是障碍策略,并给出了最优值函数的显式表达式,推广了文献[19]的结果.     

Duality for Set-Valued Multiobjective Optimization Problems,Part 1: Mathematical Programming

The duality of multiobjective problems is studied with the help of the apparatus of conjugate set-valued mappings introduced by the author. In this paper (Part 1), a duality theory is developed for set-valued mappings, which is then used to derive dual relations for some general multiobjective optimization problems which include convex programming and optimal control problems. Using this result, in the companion paper (Part 2), duality theorems are proved for multiobjective quasilinear and linear optimal control problems. The theory is applied to get dual relations for some multiobjective optimal control problem.     

混沌优化算法在不可分稳态大系统优化中的应用

讨论了整体目标函数关于各子系统不具有可加形式的大规模稳态系统的优化问题,将混沌优化算法应用于其最优值的求解,利用混沌运动的遍历性来得到优化问题的全局最优值.仿真结果表明,该算法简单易行,求解精度和可靠性较高,是解决不可分稳态大系统优化问题的一种有效方法.     

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.     

求解弱线性双层规划问题的一种全局优化方法

双层规划在经济、交通、生态、工程等领域有着广泛而重要的应用.目前对双层规划的研究主要是基于强双层规划和弱双层规划.然而,针对弱双层规划的求解方法却鲜有研究.研究求解弱线性双层规划问题的一种全局优化方法,首先给出弱线性双层规划问题与其松弛问题在最优解上的关系,然后利用线性规划的对偶理论和罚函数方法,讨论该松弛问题和它的罚问题之间的关系.进一步设计了一种求解弱线性双层规划问题的全局优化方法,该方法的优势在于它仅仅需要求解若干个线性规划问题就可以获得原问题的全局最优解.最后,用一个简单算例说明了所提出的方法是可行的.     

Equations of attainable set dynamics,part 1: Integral funnel equations

In control theory, there is growing interest in the evolution of sets, especially attainable sets at timet. This is caused due to their applications to control under uncertainty, optimal control, and differential games. Recently, a new mathematical theory for attainable set evolution was developed. It is based on the concept of approximate localization, instead of differentiation. Here, we give a generalization of this theory.     

Sufficient conditions for duality in homogeneous programming

A symmetric duality theory for programming problems with homogeneous objective functions was published in 1961 by Eisenberg and has been used by a number of authors since in establishing duality theorems for specific problems. In this paper, we study a generalization of Eisenberg's problem from the viewpoint of Rockafellar's very general perturbation theory of duality. The extension of Eisenberg's sufficient conditions appears as a special case of a much more general criterion for the existence of optimal vectors and lack of a duality gap. We give examples where Eisenberg's sufficient condition is not satisfied, yet optimal vectors exist, and primal and dual problems have the same value.     

Thermally driven acoustic oscillations, part IV: Tubes with variable cross-section

The problem of thermally driven acoustic oscillations is treated for tubes with variable cross-section, with particular emphasis on the possible reduction of the necessary temperature ratio for excitation. Tubes with optimal conditions in the vicinity of the temperature jump, and with big cross-sections in parts with constant temperature are found to give the best performance in this respect. Included in the family of devices which were treated is the classical Sondhauss-tube. Experiments which give a striking confirmation of the theory are reported.     

进化博弈决策机制设计综述

进化博弈论是一门交叉性强的综合性理论,在国内外已得到广泛研究和应用.本文系统论述了进化博弈的决策机制及其特点,指出了进化博弈研究的趋势,进化博弈论可作为中国科技工作者学习、研究和应用的有力工具.     

财政收支平衡控制模型及其应用

本文运用现代控制论的原理与方法研究了地区（或县、市）一级财政收支平衡的控制问题。把财政收支平衡的控制问题置于国民经济系统之中，运用最优控制论建立了最优积累率控制模型；进而，从所求得的最优积累率为出发点，讨论了财政收支的平衡控制，并建立了相应的控制模型。