针对含路径点和禁飞区约束的再入突防轨迹快速优化问题，提出了一种基于自适应hp 伪谱法的多阶段求解策略. 给出了含路径点、禁飞区、热流、过载、动压等约束条件的轨迹优化模型，利用Radau伪谱法将最优控制问题转化为非线性规划问题. 引入内点（连接点）概念，将路径点、禁飞区转化为内点约束，统一于一个优化框架内，结合自适应节点配置方式，在通用优化软件包内实施这一思想. 仿真结果表明，该方法能够更精确地捕捉状态变量、控制变量的不连续性、非平滑性及禁飞区的边界切点，适合求解含路径点和禁飞区的突防轨迹快速优化问题.
For penetration trajectory optimization of reentry vehicle with constraints of waypoints and no-fly zones, a multi-phase optimization strategy based on adaptive hp pseudospectral method is proposed. The trajectory optimization model considering waypoints, no-fly zones, heating rate, g-load and dynamic pressure
is given. The associated optimization is converted into a nonlinear programming problem by using the Radau pseudospectral method. The concept of linkage nodes is introduced to deal with constraints of waypoints and no-fly zones. Combined with adaptive distribution of nodes, the above idea is implemented with general pseudospectral optimization software. Simulation results show that the proposed method can capture any discontinuities and smoothness in states and control variables as well as the boundary of no-fly zones, and adapt to solve the optimization problem of penetration trajectory with waypoints and no-fly zones.
[1] 李瑜，杨志红，崔乃刚. 洲际助推-滑翔导弹全程突防
弹道优化 [J]. 固体火箭技术，2010, 33(2): 125-130.
LI Yu, YANG Zhihong, CUI Naigang. Optimization of overall penetration trajectory for intercontinental boost-glide missile [J]. Journal of Solid Rocket Technology, 2010, 33(2): 125-130. (in Chinese)
[2] 陈小庆，侯中喜，刘建霞. 高超声速滑翔式飞行器再入 轨迹多目标多约束优化 [J]. 国防科技大学学报，2009, 31(6): 76-83.
CHEN Xiaoqing, HOU Zhongxi, LIU Jianxia. Multi-objective optimization of reentry trajectory for hypersonic glide vehicle with multi-constraints [J]. Journal of national university of defense technology, 2009, 31(6): 76-83. (in Chinese)
[3] TIMOTHY R J. Common aero vehicle autonomous
reentry trajectory optimization satisfying waypoint and no-fly zone constraints [D]. The Faculty Graduate School of Engineering and Management Air Force Institute of Technology, 2007.
[4] WILLIAM J K. Optimal reentry trajectory terminal state
due to variations waypoint locations[D]. Department of Aeronautics and Astronautics Graduate School. 2008.
[5] RAO A V, BENSON D, HUNTINGTON G T, et al(补齐作者). Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using gauss pseudospectral methods [J]. ACM Transactions on Mathematical Software, 2010, 37(2): 22-39.
[6] 杨希祥，张为华. 基于Gauss伪谱法的固体运载火箭上升段轨迹快速优化研究 [J]. 宇航学报，2011, 32(1): 15-21.
YANG Xixiang, ZHANG Weihua. Rapid optimization of
ascent trajectory for solid launch vehicles based on gauss
pseudospectral method [J]. Journal of Astronautics, 2011,
32(1):15-21. (in Chinese)
[7] GUAN Chengqi, CHEN Cong. Multiphase path- constrained trajectory optimization for the boost-glide vehicle via the Gauss pseudospectral method [J]. Journal of Astronautics. 2010, 31(11): 2512-2518.
[8] GARG D. Advances in global pseudospectral method for optimal control [D]. America: University of Florida, 2011.
[9] DARBY C L, HAGER W W, ANIL V. R. An hp-adaptive pseudospectral method for solving optimal control problems [J]. Optimal control applications and methods. 2011, 32 (4): 476-502.
[10] ZHANG Kenna, CHEN Wanchun. Reentry vehicle constraints optimization [C]//17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. California, AIAA, 2011: 11-14.
