Gaussian Discretization-based Non-uniform Control Vector Parameterization for Terminal Constrained Hypersonic Unmanned System trajectory Optimization

Since the hypersonic vehicle has a strong sensitivity to the initial parameter values during the trajectory optimization process, a control vector parameterization method based on Gaussian distribution time nodes is proposed, and related solutions are given. By solving the zero point of the Legendre polynomial, the time nodes with Gaussian distribution in the entire control time domain are obtained. Then the control vector is parameterized by using the obtained new time grid, and a high-quality control parameterization strategy is achieved. The numerical results show that the proposed method can increase the performance index of downrange and flight time of hypersonic unmanned system.