分布控制偏微分方程约束下微分代数方程组多目标优化  

Differential Algebraic Equations With Multiple Objective Optimization by Constrained Distribution Control Partial Differential Equations

作　　者：刘旖[1] Liu Yi(School of Mathematics and Physics,Jingchu University of Technology,Jingmen 448000,China)

机构地区：[1]荆楚理工学院数理学院,湖北荆门448000

出　　处：《科技通报》2017年第4期11-14,共4页Bulletin of Science and Technology

摘　　要：运用微分代数方程表示涉及代数约束的系统时间域的物理行为是一种表述物理系统行为规律的重要方式。文中复杂物理系统中微分代数方程组的解析方法,选择了分布控制偏微分方程约束下微分代数方程组作为研究对象,利用以局部参数化微分变换法实现方程组多目标优化。首先要将偏微分约束优化问题转变成具有鞍点形式的稀疏线性方程组,为此需要将分布控制微分方程约束化问题进行Galerkin有限元离散,利用先离散后优化的方法获取具备约束优化问题的有限维离散模拟形式;第二,根据一维微分变换法应用在非线性微分代数方程的特性,针对约束系统建立以微分变换法为基础的局部参数化算法,同时将约束系统作为流形上的微分方程组对其完成局部参数化,此操作可有效降低约束流形和方程组的求解难度。仿真实验证明,本文中提出的基于局部参数化微分变换法可以有效地解决微分代数方程组多目标优化问题。Using of differential algebraic equations involving the algebraic constraint system for timedomain of physical behavior is a kind of important way to the law of the physical system.In this paper,analytical method of differential algebraic equations in complex physical system,select the distributioncontrol partial differential equation constraints under differential algebraic equations as the researchobject,using local parameterized differential transformation method to realize equations multi-objectiveoptimization.First we will partial differential constrained optimization problem into a sparse linearequations of a saddle point form,therefore we need to distribution control Galerkin finite elementdiscrete differential equations with constraint problem,after the first discrete optimization method isused to collect with constrained optimization problems of discrete finite dimensional simulation;Second,according to one dimensional differential transformation method is applied in the characteristics ofnonlinear differential algebraic equation for the constraint system is built based on the differentialtransform method of local parameterized algorithm,at the same time the constraint system as a system ofdifferential equations are considered on the complete local parameterized,this operation can effectively reduce the difficulty of solving the constraint manifold and equations.Simulation experiments show thatthis article is put forward based on local parameterized differential transformation method can effectivelysolve the problem of multi-objective optimization differential algebraic equations.

关 键 词：物理系统 偏微分方程约束 微分变换法 微分代数方程组 

分 类 号：O175.2[理学—数学]