临近空间飞行器再入轨迹优化设计

摘要

This research introduces the application of genetic algorithms method on the optimization design of the near space vehicles' re-entry trajectory. The performance index is chosed to minimize the square of the difference between the actual terminal velocity and the ideal velocity. Using the penalty function method and the bound operator method, the constrained optimal control problem is transformed into the unconstrained optimal control problem. By imposing the pangteliya the principle of the minimum and optimal control theory on the performance index, a group of the canonical equation, control equation and boundary condition are ultimately got. In the last, the reentry trajectory optimization problem is solved using conjugate gradient method in C++ environment. It is shown that the optimal re-entry trajectory by above methods could meet various restrictive conditions. Therefore, the conjugate gradient method is a viable approach to the optimization of the near space vehicles' re-entry trajectory.%针对临近空间飞行器再入轨迹的优化设计问题,给出了临近空间飞行器再入轨迹运动学模型和再入轨迹优化模型.选取飞行器末端飞行速度实际值与理想值之差的平方最小为性能指标,控制变量为迎角和滚转角.过程约束为过载、动压、热流,终端约束为高度、轨道偏角、轨道倾角. 应用罚函数法和约束算子法将有约束最优控制问题转化为无约束最优控制问题.应用庞特里亚金极小值原理及最优控制理论对性能指标进行处理,得到最优控制问题的正则方程、控制方程及横截条件.在C + +环境下应用共轭梯度法对无约束优化问题进行数值解算.仿真结果表明应用共轭梯度法能够得到满足各种约束的再入轨迹.因此,共轭梯度法对于临近空间飞行器再入轨迹优化问题的求解是可行的.