磁约束热核聚变中的电流密度位形动力学可以描述为抛物型偏微分方程控制问题。利用正交分解方法生成典型子空间，将原系统利用嘎辽金方法投影到子空间获取低维双线性系统，其最优控制问题可以描述为非线性两端边界值问题。已有的求解该问题的数值方法很多，本文中提出了序列二次最优控制综合，并讨论其收敛性。

 

The current density profile dynamics can be modeled by a parabolic partial differential equation (PDE) which could be controlled via the boundary and interior actuators. By using the proper orthogonal decomposition (POD) method and Galerkin method, we can obtain a low dimensional bilinear system capturing the dominant dynamics. The optimal control is governed by a two boundary value problem and we propose a novel numerical method, the sequential linear quadratic controller synthesis to obtain numerical solutions, and give a detailed theoretical convergence analysis.