Abstract: In this paper, the control system of the positive-definite matrix whose output only relied on its input was considered, where the optimal control was described as the output matrix which is as close as possible to the target matrix. The geodesic distance was adopted as the measure of the initial input and the target, and then the trajectory of the control input turning from the initial output matrix to the final output matrix was achieved based on the extended Hamiltonian algorithm. Finally, some numerical simulations were given to illustrate our outcome for optimizing the control system of the positive-definite matrix.