Abstract: 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.