基于广义Hamilton算法的正定矩阵系统上的控制

Control for Positive-Definite Matrix System Based on Extended Hamiltonian Algorithm

考虑控制输出仅依赖控制输入的正定矩阵系统,控制的最优性被描述为输出矩阵尽可能接近目标矩阵.控制输入和目标矩阵之间的度量采用测地距离,则基于广义Hamilton算法可得到从控制输入到最终控制输出的最优控制轨迹.最后,给出了正定矩阵系统上控制问题的数值模拟结果.

In this paper, the control system of the positive-definite matrix whose output onlyrelied on its input was considered, where the optimal control was described as the output matrixwhich is as close as possible to the target matrix. The geodesic distance was adopted as themeasure of the initial input and the target, and then the trajectory of the control input turningfrom the initial output matrix to the final output matrix was achieved based on the extendedHamiltonian algorithm. Finally, some numerical simulations were given to illustrate our outcomefor optimizing the control system of the positive-definite matrix.