多段分支弹道的两级全局优化方法

摘要

针对多段分支弹道设计存在的弹道交班点选取困难、交班控制变量突变等问题,提出一种两级全局优化方法.对各弹道段分别建立子级优化问题,采用系统级优化实现各段交班点耦合变量协调,以及最佳交班点求解;将交班点耦合变量中质量参数转为局部优化变量,其他状态参数转为系统级优化变量,实现了同层优化问题解耦;在子级优化问题中引入控制变量一阶导数作为优化变量,并作为系统级协调变量,保证各段控制变量光滑过渡.某两级重复使用运载器全程弹道优化算例表明,本文提出的方法能将高度耦合的全程弹道优化转化为简单有效的两级优化问题,可推广应用于其它各类多段分支弹道设计.%To solve the problems of the staging point selection and control variables jumping faced during design of the multi-branching trajectory,a bi-level global optimization method is proposed.In the given method,the sub-level optimization problem is set up for each trajectory section,and the system level optimization problem is set up to coordinate the coupling variables of the staging point.For these coupling variables,the mass variable is transformed to the local variable of the sub-level optimization problem,and other state variables are transformed as the global variables of the system level optimization problem.By this strategy,the couplings between the sub-level optimizations are decoupled hierarchically,and the optimal staging point can be obtained.Meanwhile,the first-order derivatives of control is introduced as the system-level coordinating variables to ensure the smooth transition of the control variables between the trajectory sections.The global trajectory optimization problem of a two-stage-to-orbit reusable launch vehicle is tested.The results show that the provided method is able to transform the highly coupled trajectory optimization problem into the simple and efficient bi-level optimization formulation,therefore can support the design of the multi-branching trajectory.