采用内点约束的最优冲突解脱方法

在自由飞行中, 为了保证任何两架飞机之间的距离不能小于给定的安全间隔, 采用内点约束条件和最优控制中的庞特里亚金极小值原理, 研究了自由飞行中飞机的控制向量受约束时的平面冲突解脱问题, 考虑了只改变速度大小和只改变速度方向的解脱策略。不同的策略具有不同的控制变量, 各变量有不同的约束范围。采用极小值原理解得最优控制变量, 并由内点约束条件获得解脱开始时间、约束时间及控制变量转换时间。计算结果表明改变速度大小策略的协作解脱耗费是单机解脱的1/10, 而改变速度方向的策略在两机夹角过小时单机解脱耗费为协作解脱的1/3。

Optimal conflict resolution method based on inner-point restriction

In the condition of free flight, in order to ensure the distance of two aircrafts could not less than a given safety distance, the Pontryagin minimum principle(PMP) of optimal control theory and inner-point restriction condition were introduced to study the conflict resolution problem of free flight aircrafts, in which control vectors were restricted. Two different schemes were designed, one only changed flying velocity magnitude, the other only changed flying velocity angle. Different schemes had different control vectors, different control vectors had different restricted ranges. The optimal control variable was gained according to the PMP, the start time, end time and switch time of conflict resolution were obtained by inner-point restriction condition. An example shows that the method is feasible, the wasting cost of one aircraft resolution is tenfold of the wasting cast of two aircrafts resolution in changing velocity method, the wasting cost of one aircraft resolution is one third of the wasting cast of two aircrafts resolution in changing angle method when the intersectant angle of two aircrafts is smaller. 1 tab, 7 figs, 8 refs.