求解偏微分方程约束最优控制问题的径向基函数方法  

Radial Basis Function Method for Optimal Control Problems Constrained by Partial Differential Equation

作　　者：段献葆[1] 李熠晨 秦玲 DUAN Xian-bao;LI Yi-chen;QIN Ling(School of Sciences,Xi*an University of Technology,Xi'an 710048,China)

机构地区：[1]西安理工大学理学院,陕西西安710048

出　　处：《数学的实践与认识》2021年第22期180-187,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金资(11971379,61773016);陕西省自然科学基金(2017GY-090,2019JM-284)。

摘　　要：提出了一种求解非线性偏微方程约束最优控制问题的径向基函数方法.控制问题的状态约束是Navier-Stokes方程.最优控制问题的灵敏度分析结果采用的共轭方法.由于径向基函数方法是真正的无网格方法,比网格依赖方法有更好的适应性.Navier-Stokes方程是非常有代表性的非线性方程,所得算法可以适应于求解更广泛的最优控制问题.提供的数值算例说明了所提算法的稳定性和有效性.A radial basis function method for solving the optimal control problem constrained by the nonlinear partial differential equation is proposed.The state constraint of the control problem is the Navier-Stokes equation.The sensitivity analysis result of the optimal control problem was achieved by the adjoint method.Since the radial basis function method is a true meshfree method,it has better adaptability than the grid-dependent method.The Navier-Stokes equation is a very representative nonlinear equation,therefore,the obtained algorithm can be adapted to solve a wider range of optimal control problems.The numerical example was provided to illustrate the stability and effectiveness of the proposed algorithm.

关 键 词：最优控制问题 径向基函数 NAVIER-STOKES方程 微分求积方法 

分 类 号：O232[理学—运筹学与控制论]