太阳帆塔轨道和姿态耦合动力学建模及辛求解

在建立太阳帆塔太阳能电站简化模型的基础上,将系统的动力学方程从Lagrange体系导入到了Hamilton体系,给出了带约束的Hamilton正则方程;进而采用祖冲之类算法和辛Runge-Kutta方法分析了太阳帆塔轨道和姿态耦合系统的动力学特性,并讨论了算法的保能量、保约束特性;最后,数值模拟了系统的动力学特性,说明了所提方法的有效性.     

论约束的力学性质

研究约束的力学性质是一个非常重要而又实际的问题。本文在研究非定常的完整约束的力学性质的基础上，进一步研究了非完整约束的力学性质。内容复盖了Ｖａｃｃｏ动力学和Ｃｈｅｔａｅｖ动力学各类运动分方程中约束反力的性质。     

非线性非完整系统Vacco动力学方程的积分方法*

本文给出积分非线性非完整系统Vacco动力学方程的积分方法.首先,将Vacco动力学方程表示为正则形式和场方程形式;然后,分别用梯度法,单分量法和场方法积分相应完整系统的动力学方程,并加上非完整约束对初条件的限制而得到非线性非完整系统Vacco动力学方程的解.     

变质量非线性非完整系统相对运动动力学方程的积分方法

本文给出积分变质量非线性非完整系统相对于非惯性系动力学方程的梯度法,单分量法和场方法。首先,将这类问题的动力学方程表示为正则形式和场方程形式;然后,分别用梯度法,单分量法和场方法积分相应常质量完整系统相对于惯性系的动力学方程,并加上非完整约束对初始条件的限制而得到变质量非线性非完整系统相对于非惯性系动力学方程的解。     

基于虚拟完整约束的欠驱动起重机控制方法

欠驱动系统的控制是非线性控制的一个重要领域,欠驱动系统指系统控制输入个数小于自由度个数的非线性系统.目前,欠驱动非线性系统动力学和控制研究的主要方法包括线性二次型最优控制方法和部分反馈线性化方法等,如何使系统持续的稳定在平衡位置一直是研究的难点.虚拟约束方法是指通过选择一个周期循环变化的变量作为自变量来设计系统的周期运动.该文以典型的欠驱动模型起重机为例,采用虚拟约束方法,使系统能够在平衡位置稳定或周期振荡运动.首先,通过建立虚拟约束,减少系统自由度变量;然后,通过部分反馈线性化理论推导出系统的状态方程;最后,通过线性二次调节器设计反馈控制器.仿真结果表明,重物在反馈控制下可以在竖直位置的附近达到稳定状态,反映了虚拟约束方法对欠驱动系统的有效性.     

非完整非保守动力学系统的Noether定理及其逆定理

本文应用变换群G_r的无限小群变换的广义准对称性,给出了受一阶非线性非完整约束的非保守动力学系统的Noether定理及其逆定理.     

非线性非完整约束空间准坐标表示的系统的基本动力学方程

用与准坐标表示的一阶非线性非完整约束超曲面的基矢量共线的量和米歇尔斯基方程点来作为一阶非线性非完整约束变质量系统的基本动力学方程．由此可导出用准坐标表示的各种形式的运动微分方程．和约登（Jourdain）原理相容．举了例子．     

含有约束的两个状态变量系统的转迁集计算

周期解的分岔广泛存在于实际的非线性动力学系统中．该文对两个状态变量系统的约束分岔进行了讨论．在约束条件下系统将产生新的转迁集．此外,以一个二维系统为例,对含有约束条件和不含有约束条件的分岔特性进行了比较．所得的结果可以为系统的设计和参数选择提供理论依据．     

等式约束非线性控制系统的时程精细计算

针对等式约束非线性最优控制问题,通过一阶Taylor级数展开,得到线性化的动力学方程,进而在方程原变量的基础上,引入对偶向量(Lagrange乘子向量),将动力学方程从Lagrange体系引入到了Hamilton体系,在全状态下,从一个新的角度对等式约束非线性控制问题进行了描述,进一步基于时程精细积分理论,对其方程进行了有效的精细求解,并通过算例说明了文中方法的有效性。     

非线性非完整空间变质量体的一种运动方程*

引入非线性非完整空间的约束超曲面的基矢量和密歇尔斯基方程点乘,作为非线性非完整系统变质量体的基本动力学方程。它简明、运算简便,而且由它可导出,Nielsou,Appell,Mac-Millan等已有的方程,不必附加关于虚位移的Appell-定义或牛青萍定义。本方程与D'Alembert-Lagrange微分变分原理相容。     

具有动应力、位移和稳定性约束的离散变量桁架结构布局优化设计算法

给出了在动应力、动位移和动稳定约束下离散变量结构布局优化设计问题的数学模型,用“拟静力”算法,将具有动应力约束、动位移约束和动稳定约束的离散变量结构布局优化设计问题化为静应力、静位移和静稳定约束的优化问题,然后利用两级优化算法求解该模型．优化过程由两级组成,拓扑级优化和形状级优化．在每一级,都使用了综合算法,并且在搜索过程中都根据两类设计变量的相对差商值进行搜索．对包含稳定约束和不包含稳定约束的优化结果做了比较,结果显示稳定性约束对优化结果产生较大的影响．     

Constraint Programming Based Column Generation for Crew Assignment

Airline crew assignment problems are large-scale optimization problems which can be adequately solved by column generation. The subproblem is typically a so-called constrained shortest path problem and solved by dynamic programming. However, complex airline regulations arising frequently in European airlines cannot be expressed entirely in this framework and limit the use of pure column generation. In this paper, we formulate the subproblem as a constraint satisfaction problem, thus gaining high expressiveness. Each airline regulation is encoded by one or several constraints. An additional constraint which encapsulates a shortest path algorithm for generating columns with negative reduced costs is introduced. This constraint reduces the search space of the subproblem significantly. Resulting domain reductions are propagated to the other constraints which additionally reduces the search space. Numerical results based on data of a large European airline are presented and demonstrate the potential of our approach.     

A General Approach for Constraint Solving by Local Search

In this paper, we present a general approach for solving constraint problems by local search. The proposed approach is based on a set of high-level constraint primitives motivated by constraint programming systems. These constraints constitute the basic bricks to formulate a given combinatorial problem. A tabu search engine ensures the resolution of the problem so formulated. Experimental results are shown to validate the proposed approach. This revised version was published online in August 2006 with corrections to the Cover Date.     

Properties of Solutions to Second Order Evolution Control Systems. I

We consider a control system described by a nonlinear second order evolution equation defined on an evolution triple of Banach spaces (Gelfand triple) with a mixed multivalued control constraint whose values are nonconvex closed sets. Alongside the original system we consider a system with the following control constraints: a constraint whose values are the closed convex hull of the values of the original constraint and a constraint whose values are extreme points of the constraint which belong simultaneously to the original constraint. By a solution to the system we mean an admissible trajectory-control pair. In this part of the article we study existence questions for solutions to the control system with various constraints and density of the solution set with nonconvex constraints in the solution set with convexified constraints.     

具有动应力和动位移约束的离散变量结构拓扑优化设计方法

讨论了动应力、动位移约束下离散变量结构拓扑优化设计问题.首先给出问题的数学模型,然后用拟静力算法,将结构惯性力极值作为静载荷施加到结构上,求得结构的动位移和动内力,将考虑动应力约束和动位移约束的离散变量结构拓扑设计问题化为静应力和静位移约束的优化问题,然后利用两类变量统一考虑的离散变量结构拓扑优化设计的综合算法进行求解.     

Reflections on the Gauss Principle of Least Constraint

The Gauss principle of least constraint is derived from a new point of view. Then, an extended principle of least constraint is derived to cover the case of nonideal constraints. Finally, a version of the principle for general underdetermined systems is adumbrated. Throughout, the notion of generalized inverses of matices plays a prominent role.     

Sensitivity of solutions to systems of optimality conditions under the violation of constraint qualifications

A survey is given of old and new results on the sensitivity of solutions to systems of optimality conditions with respect to parametric perturbations. Results of this kind play a key role in subtle convergence analysis of various constrained optimization algorithms. General systems of optimality conditions for problems with abstract constraints, Karush-Kuhn-Tucker systems for mathematical programs, and Lagrange systems for problems with equality constraints are examined. Special attention is given to the cases where the traditional constraint qualifications are violated.     

Determination of the composition of the insurance and investment portfolios of a casualty insurance company

This paper presents a model in which expected return is maximized subject to two chance constraints. The first chance constraint requires that the total return is greater than some lower bound with a stipulated probability. The second chance constraint is used to maintain the firm's liquidity. An evaluation of the solution is given. The influence of a premium change on the data requirements of the model is discussed.     

Stabilization of the motions of mechanical systems in prescribed phase-space manifolds

A method for constructing a mathematical model of the dynamics of a mechanical system is proposed. An algorithm is constructed for determining the expressions for the control forces and the components of the constraint reactions. A modification is made to the dynamic equations which enables one to solve the problem of stabilizing the constraints and which ensures the required accuracy in the numerical solution of the corresponding system of differential-algebraic equations describing the constraints imposed on the system, its kinematics and dynamics. By virtue of well-known dynamic analogies, the proposed method can be used to investigate the dynamics of different physical systems. The problem of modelling the dynamics of an adaptive optical system with two degrees of freedom is considered.     

Continuous perturbations of infinite optimization problems

In this paper, continuity properties of the extremal value function and the solution function are studied for general optimization problems with perturbations in the objective function and the constraints. A classical stability condition is extended and compared with constraint qualification conditions.