基于改进hp自适应伪谱法的高超声速飞行器上升段轨迹规划

摘要

An improved hp⁃adaptive pseudospectral method is developed in the present paper for solving hypersonic vehicle trajectory optimization in ascent phase. The method adopts double⁃layer optimization strategy to adjust both the mesh spacing and the degree of the polynomial on each interval. First, a relative error estimate is derived based on the residual of the differential⁃algebraic constraints at sample points. The derived relative error estimate is then used to predict the polynomial degree within a mesh interval. If the polynomial degree estimate remains below a maximum allowable degree, the degree of polynomial is increased to degree estimate. Otherwise, the mesh interval is divided into subinterval. Simulation results show the proposed method is more efficient than either h method or p method.%针对高超声速飞行器的上升段轨迹优化问题，提出了一种改进的hp自适应Radau伪谱法。该算法将轨迹划分为多个子区间，采用双层优化策略迭代调整子区间个数和区间内的配点数。首先，以微分－代数约束在采样点处的相对误差作为解的误差评估准则；在需要提高精度的区间，将相对误差作为迭代判据，若通过相对误差求得的多项式阶数小于允许的最大阶数，增加区间内的配点数（p法）；否则，细化时间区间（h法）来提高求解精度。仿真结果表明，相较于h方法和p方法，文中的算法在求解最优问题时配点总数更少，求解效率更高。