Terminal hypersonic trajectory modeling and optimization for maneuvering penetration and precision strike
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摘要:
针对高超声速飞行器再入末段机动突防、精确打击问题，从最优控制角度出发，提出了一种考虑拦截弹动力学特性的最优机动突防弹道优化方法，获得了高超声速飞行器的最大机动能力。该方法将拦截弹运动模型引入突防弹道优化的模型中，通过施加约束限制拦截弹按照比例导引律飞行。根据飞行任务和交战双方的弹道特点分段，结合各段的任务和特性，分别提出了突防性能指标和精确打击性能指标等，并通过加权函数将各个独立、矛盾的性能指标统一，建立了多对象、多段、多约束机动突防弹道优化模型，采用Radau多段伪谱法（MRPM）进行求解。针对该问题求解的初值敏感、可行域窄等问题，提出了一系列弹道优化策略，提高了收敛速度和求解精度，最终获得了最优机动弹道，并通过协态映射原理对其最优性进行了验证。结果表明，该方法能充分发挥高超声速飞行器的机动能力，获得满足落点精度要求的突防弹道，相对已有方法，将脱靶量提高了1~2个量级。灵敏度分析表明，该弹道对拦截弹的发射时间不敏感。
Abstract:Aimed at the maneuvering penetration and precision strike problem of hypersonic vehicle terminal trajectory, an optimal maneuvering trajectory optimization method considering the dynamic characteristics of intercepting was proposed from the viewpoint of optimal control, so as to obtain the maximum maneuverability of hypersonic vehicles. In this paper, the intercepting missile model was introduced into the model of penetration trajectory optimization, and a constraint was imposed to restrict the intercepting missile to fly according to the proportional guidance law. The trajectories were divided into phases according to the different missions and trajectory characteristics of the belligerents. The penetration performance index and the precision strike performance index are put forward according to the task and characteristics of each phase, and by the weighting function the independent and contradictory performance indicators are unified. Thus a multi-object, multi-phase and multi-constrained maneuvering penetration trajectory optimization model was established. And multiphase Radau pseudospectral method (MRPM) was used to solve the problem. Due to the initial sensitivity and narrow feasible region of the problem, a series of trajectory optimization strategies were proposed to improve the convergence rate and the precision of the solution. Finally, the optimal maneuvering trajectory was obtained, and the optimality of the solution was verified based on the principle of costate mapping. The results show that the method can give full play to the maneuverability of the hypersonic vehicle, and obtain the penetration trajectory which satisfies the terminal accuracy. Compared with the existing method, the miss distance is increased by 1-2 orders of magnitude. Sensitivity analysis shows that the trajectory is insensitive to the launch time of the interceptor.
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Key words:
- maneuvering /
- penetration /
- interception /
- optimization strategy /
- optimality condition /
- sensitivity analysis
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图 1 高超末段机动突防-对地打击示意图
Figure 1. Diagram of maneuvering penetration and ground attack in terminal phase of hypersonic trajectory
图 3 平滑性能指标对控制曲线的影响
Figure 3. Influence of smoothness performance index on control curves
图 12 突防弹攻角-时间曲线和倾侧角-时间曲线
Figure 12. Penetration missile attack angle-time curve and bank angle-time curves
图 13 不同机动形式突防弹攻角-时间曲线和倾侧角-时间曲线
Figure 13. Penetration missile attack angle-time curve and bank angle-time curves of different motivations
图 15 热流密度-时间，动压-时间，过载-时间曲线
Figure 15. Heat flux-time, dynamic pressure-time and overload-time curves
表 1 突防弹初始及终端状态约束
Table 1. Initial and terminal state constraints of penetration missile
时间 xA/m yA/m zA/m VA/(m·s-1) θA/(°) ψA/(°) αA/(°) σA/(°) t0 10 188.8 21 299.3 10 188.8 1 878.8 -18.9 135.0 10 -180 tf -9 346 0 -9 346 (800, 1 100) (-90, -75) (0, 7) 
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表 2 拦截弹初始状态约束
Table 2. Initial state constraints of interception missile
状态约束 xD0/
myD0/
mzD0/
mVD0/
(m·s-1)θD0/
(°)ψD0/
(°)mD0/
kg数值 -8 000 0 -8 000 1 000 38 -45 315
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表 3 突防弹常规路径约束
Table 3. Path constraints of penetration missile
路径约束 
q/(N·m-2) ny 数值 400 6×105 20
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表 4 优化结果终端状态
Table 4. Terminal states of optimal results
性能指标 xAf/m yAf/m zAf/m VAf/(m·s-1) θAf/(°) ψAf/(°) αAf/(°) σAf/(°) J1 -9 346.99 -1.00 -9 346.99 1 450.67 -84.37 132.49 6.00 -178.64 J2 -9 344.99 -1.00 -9 344.99 1 515.68 -75.01 135.00 6.00 -180.01 J3 -9 344.99 -1.00 -9 346.99 1 377.61 -75.01 180.01 6.00 -210.65 J4 -9 344.99 -1.00 -9 346.99 1 018.95 -90.01 180.01 6.00 -180.20 常值 -9 345.99 -1.81×10-12 -9 345.99 1 462.12 -84.62 135.01 10.00 -180.00
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表 5 突防脱靶量对比
Table 5. Comparison of penetration miss distance
性能指标 脱靶量/m J1 19.00 J2 5.18 J3 216.65 J4 234.59 常值 3.69
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表 6 不同机动形式突防脱靶量对比
Table 6. Comparison of penetration miss distance of different motivations
机动形式 最优机动 程序机动 脱靶量/m 234.6 119.7
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表 7 求解精度对比
Table 7. Comparison of solution accuracy
求解精度 GPOPS初值生成器 分段嵌套优化 节点数 41 105 节点误差 0.293 5 8.313 9×10-5 可行性 2.0×10-2 3.2×10-8 最优性 9.4×10-3 7.2×10-6
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