分布控制偏微分方程约束下微分代数方程组多目标优化

发布时间：2018-05-29 05:12

本文选题：物理系统 + 偏微分方程约束　；参考：《科技通报》2017年04期

【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。
[Abstract]:The use of differential algebraic equations to express the physical behavior of time domain involving algebraic constraints is an important way to express the behavior laws of physical systems. In this paper, the analytic method of differential algebraic equations in complex physical systems is presented. The differential algebraic equations constrained by distributed control partial differential equations are chosen as the object of study. The local parameterized differential transformation method is used to realize the multiobjective optimization of the equations. First of all, the partial differential constrained optimization problem should be transformed into a sparse linear equation system with saddle point form. For this reason, it is necessary to discretize the distributed control differential equation constrained problem by Galerkin finite element method. The finite dimensional discrete simulation form of constrained optimization problem is obtained by using the method of discretization first and then optimized. Secondly, according to the characteristics of one-dimensional differential transformation method applied to nonlinear differential algebraic equations, A local parameterization algorithm based on differential transformation method is established for constrained systems. At the same time, the constrained system is used as a set of differential equations on the manifold to complete the local parameterization. This operation can effectively reduce the difficulty of solving constrained manifolds and equations. The simulation results show that the local parameterized differential transformation method proposed in this paper can effectively solve the multi-objective optimization problem of differential algebraic equations.
【作者单位】：荆楚理工学院数理学院;
【分类号】：O175

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