Optimal control on special Euclidean group via natural gradient algorithm

Considering the optimal control problem about the control system of the special Euclidean group whose output only depends on its input is meaningful in practical applications. The optimal control considered here is described as the output matrix is as close as possible to the target matrix by adjusting the system input. The geodesic distance is adopted as the measure of the difference between the output matrix and the target matrix, and the trajectory of the control input obtained in the process is achieved. Furthermore, some numerical simulations are shown to illustrate our outcomes based on the natural gradient descent algorithm for optimizing the control system of the special Euclidean group.创新点本文借助于自然梯度算法研究特殊欧几里德群的最优控制问题。这一控制系统的输出仅仅与控制输入有关。具体来说, 文中考虑的特殊欧几里德群上的最优控制问题为: 通过调节系统的输入, 使得系统的输出矩阵尽可能的接近目标矩阵, 输出矩阵与目标矩阵的差异用相应矩阵流形的测地距离来描述, 同时, 在控制过程中, 可以得到系统输入的控制轨线。在文章的最后, 利用数值模拟进一步说明文中利用自然梯度算法来解决特殊欧几里德群的最优控制问题的可行性和有效性。