正定矩阵流形上的系统控制算法

非线性问题出现在多个领域，如何处理非线性问题是科学工作者们关注的热点.本文针对控制系统的结构和控制问题，利用正定矩阵流形上的几何结构，设计出一个以正定矩阵为输出的控制系统.为使得系统输出尽可能接近相应的指标，根据不同的度量结构设计出相应的自然梯度算法，实验结果验证了算法的有效性. 

Control Algorithms for Positive Definite Matrix Manifolds

Nonlinear problems appear in many fields. How to deal with nonlinear problems is a hot topic in scientist attention. On the structure and control problems of control systems,in this paper,making use of the geometric structure of positive definite matrix manifold,a control system was designed with positive definite matrix as its output. In order to make the system output as close to the corresponding index as possible,a corresponding natural gradient algorithm was designed according to different measured structures,and some experiments were carried out to verify the effectiveness of the algorithm.