基于神经网络的高超声速飞行器时间协同再入制导

doi:10.12305/j.issn.1001-506X.2026.10.30

摘要/Abstract

摘要：

为实现高超声速飞行器滑翔段时间协同再入，提出一种结合双参数插值侧倾角剖面和神经网络预测器的时间协同再入制导方法。首先，将高度-速度平面内的过程约束和终端约束转换为侧倾角走廊，并在其中构建基于双参数插值的侧倾角剖面以进行约束管理。其次，采用双层前馈神经网络实现航程与飞行时长的高精度实时预测，并通过求解双变量求根问题对剖面参数进行校正更新。在此基础上，结合航向角走廊横向制导与协同飞行时间确定方法，构建时间协同再入制导框架，实现制导指令的在线快速生成。最后，数值仿真结果表明，该算法能满足时间协同再入的各项约束，且制导精度高、适应性强；相比数值积分方法，神经网络仅需约10%的计算时间即可达到相近的预测精度；蒙特卡罗仿真表明，算法在初始状态与气动参数存在不确定性时，仍具备良好的鲁棒性。

关键词: 高超声速飞行器, 预测校正制导, 神经网络, 时间协同制导

Abstract:

To achieve time-coordinated reentry for hypersonic glide vehicles, a time-cooperative reentry guidance method based on dual-parameter interpolated bank angle profiles and neural network predictors is proposed. Firstly, the path constraints and terminal constraints in the height-velocity plane are transformed into bank angle corridors, and a bank angle profile based on dual-parameter interpolation is constructed within these corridors for constraint management. Secondly, a two-layer feedforward neural network is employed to achieve high-precision real-time predictions of the flight range-to-go and time-to-go, and the profile parameters are corrected and updated by solving the bivariate root-finding problem. Building upon this, a time-coordinated reentry guidance framework is established by integrating heading angle corridor-based lateral guidance with a cooperative flight time determination method, enabling rapid online generation of guidance commands. Finally, numerical simulation results demonstrate that the proposed algorithm satisfies all the constraints for time-coordinated reentry, with high guidance precision and strong adaptability. Compared to numerical integration methods, the neural network achieves comparable prediction accuracy with only 10% of the computational time. Monte Carlo simulations further confirm that the algorithm maintains excellent robustness under uncertainties in initial states and aerodynamic parameters.

Key words: hypersonic vehicle, predictor-corrector guidance, neural network, time-coordination guidance

中图分类号:

V 448.235

孙世昌, 于国川, 南英, 张绍良. 基于神经网络的高超声速飞行器时间协同再入制导[J]. 系统工程与电子技术, 2026, 48(10): 3596-3610.

Shichang Sun, Guochuan Yu, Ying Nan, Shaoliang Zhang. Time-coordination reentry guidance for hypersonic vehicle using neural network[J]. Systems Engineering and Electronics, 2026, 48(10): 3596-3610.

图/表 23

图1

图2

图3

图4

表1

表2

图5

表3

图6

图7

表4

表5

图8

图9

图10

图11

表6

图12

图13

表7

表8

图14

表9

参考文献 30

1	郭杰, 郑金库, 王浩凝, 等. 高超声速滑翔飞行器再入制导方法及热点问题研究综述[J]. 空天技术, 2022,, (1): 54. doi: 10.16338/j.issn.2097-0714.20220607
2	闫循良, 王培臣, 郭杨. 再入滑翔机动突防轨迹规划与制导方法研究综述[J]. 航空学报, 2025, 46 (17): 331810.
3	吕金虎, 于江龙, 董希旺. 飞行器集群协同制导新进展[J]. 自动化学报, 2025, 51 (4): 727. doi: 10.16383/j.aas.c240499
4	南英, 龙吉松, 杨毅, 等. 自然控制理论与飞行控制[M]. 北京: 科学出版社, 2025.
5	He S M, Luo H W, Lee C H, et al. Review of data-driven computational guidance for unmanned aerospace vehicles[J]. Progress in Aerospace Sciences, 2025, 157, 101129. doi: 10.1016/j.paerosci.2025.101129
6	黄国强, 陆宇平, 南英. 飞行器轨迹优化数值算法综述[J]. 中国科学: 技术科学, 2012, 42 (9): 1016.
7	Liu X F, Shen Z J, Lu P. Entry trajectory optimization by second-order cone programming[J]. Journal of Guidance, Control, and Dynamics, 2016, 39 (2): 227.
8	Lu P. Entry guidance: a unified method[J]. Journal of Guidance, Control, and Dynamics, 2014, 37 (3): 713.
9	Wang T, Zhang H B, Zeng L, et al. A robust predictor-corrector entry guidance[J]. Aerospace Science and Technology, 2017, 66, 103. doi: 10.1016/j.ast.2017.03.010
10	Lee Y, Lee D D, Wie B. Autonomous numerical predictor-corrector guidance for human Mars landing missions[J]. Aerospace Science and Technology, 2025, 156, 109755. doi: 10.1016/j.ast.2024.109755
11	张旭辉, 汪韧, 马超越. 考虑禁飞区约束的飞行器协同轨迹规划[J]. 宇航学报, 2025, 46 (4): 641. doi: 10.3873/j.issn.1000-1328.2025.04.001
12	Liu X, Li X, Zhang H J, et al. Entry guidance with terminal time constraint based on reduced-order dynamics[J]. IEEE Trans. on Aerospace and Electronic Systems, 2025, 61 (3): 5949. doi: 10.1109/TAES.2024.3524200
13	Li Z H, He B, Wang M H, et al. Time-coordination entry guidance for multi-hypersonic vehicles[J]. Aerospace Science and Technology, 2019, 89, 123. doi: 10.1016/j.ast.2019.03.056
14	韩宛汝, 刘俊辉, 单家元, 等. 终端航向角与时间约束的迭代再入制导方法[J]. 系统工程与电子技术, 2026, 48(2): 638.
15	Yang H D, Liang H Z, Liu J Q, et al. Analytical time-coordinated entry guidance for multi-hypersonic vehicles within three-dimensional corridor[J]. Aerospace Science and Technology, 2024, 155, 109639. doi: 10.1016/j.ast.2024.109639
16	Wang P C, Yan X L, Nan W J, et al. Adaptive entry guidance with time and full state constraints using analytical drag-vs-energy profile[J]. Advances in Space Research, 2025, 75 (12): 8860. doi: 10.1016/j.asr.2025.04.017
17	Liu Z Z, Zheng G D, Zhang B, et al. Predictor-corrector reentry guidance for hypersonic glide vehicles based on high-precision analytical solutions[J]. Aerospace Science and Technology, 2024, 155, 109545. doi: 10.1016/j.ast.2024.109545
18	Zhang T F, Zhang L C, Gong C L, et al. Weight-adaptive parameter estimation assisted event-triggered model predictive guidance for reentry[J]. Aerospace Science and Technology, 2025, 158, 109938. doi: 10.1016/j.ast.2025.109938
19	方科, 张庆振, 倪昆, 等. 高超声速飞行器时间协同再入制导[J]. 航空学报, 2018, 39 (5): 321958. doi: 10.7527/S1000-6893.2018.21958
20	Li Z, Guo J, Tang S, et al. A deep learning-based approach to time-coordination entry guidance for multiple hypersonic vehicles[J]. The Aeronautical Journal, 2023, 127 (1310): 604. doi: 10.1017/aer.2022.82
21	Cheng L, Jiang F H, Wang Z B, et al. Multiconstrained real-time entry guidance using deep neural networks[J]. IEEE Trans. on Aerospace and Electronic Systems, 2020, 57 (1): 325.
22	Li Q, Yu J L, Hua Y Z, et al. Cooperative time-guidance strategy for multihypersonic vehicles with irregular no-fly zones: a Transformer-based real-time planning method[J]. IEEE Trans. on Aerospace and Electronic Systems, 2024, 61 (2): 1283.
23	闫循良, 王宽, 张子剑, 等. 基于LSTM-DDPG的再入制导方法[J]. 系统工程与电子技术, 2025, 47 (1): 268. doi: 10.12305/j.issn.1001-506X.2025.01.27
24	Tong X D, Song J, Li W L, et al. Penetration game strategy of high dynamic vehicles with constraints of no-fly zones and interceptors[J]. Engineering Applications of Artificial Intelligence, 2024, 136, 109018. doi: 10.1016/j.engappai.2024.109018
25	Wu T C, Wang H L, Liu Y H, et al. Learning-based interfered fluid avoidance guidance for hypersonic reentry vehicles with multiple constraints[J]. ISA Transactions, 2023, 139, 291. doi: 10.1016/j.isatra.2023.04.004
26	南英, 吕学富, 陈士楷. 航天器的再入走廊及其计算方法[J]. 飞行力学, 1993, 11 (2): 34. doi: 10.13645/j.cnki.f.d.1993.02.005
27	南英, 陈士楷, 王志刚. 航天器最优再入轨迹的选择分析[J]. 宇航学报, 1996, 17 (4): 105.
28	Cheng L, Wang Z B, Cheng Y, et al. Multi-constrained predictor-corrector reentry guidance for hypersonic vehicles[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2018, 232 (16): 3049. doi: 10.1177/0954410017724185
29	王肖, 郭杰, 唐胜景, 等. 基于解析剖面的时间协同再入制导[J]. 航空学报, 2019, 40 (3): 322565.
30	Phillips T H. A common aero vehicle (CAV) model, description, and employment guide[R]. New York: Schafer Corporation for Air Force Research Laboratory and Air Force Space Command, 2003.

状态	偏差范围	分布
$h({t_0})$/km	60$ \pm $10	均匀分布
$V({t_0})$/（m/s）	7200$ \pm $200	均匀分布
$\gamma ({t_0})$/（°）	0$ \pm 1 $	均匀分布
${w_1}$	$ \left[\mathrm{0,1}\right] $	均匀分布
${w_2}$	$ \left[\mathrm{0,1}\right] $	均匀分布
${C_L}$/%	$ \pm $10	均匀分布
${C_D}$/%	$ \pm $10	均匀分布
$\rho $/%	$ \pm $10	均匀分布

设置	参数
网络输入	$r,v,\gamma ,{w_1},{w_2}$
网络输出	${s_{{\text{pre}}}},{\tau _{{\text{pre}}}}$
节点数	32
激活函数	隐藏层：Sigmoid；输出层：Purelin
训练算法	Adam

参数	${s_{{\mathrm{pre}}}}$	${t_{{\mathrm{pre}}}}$
MSE	2.7795E−7	4.4565E−6
RMSE	5.2721E−4	0.0021
MAE	3.9130E−4	0.0016
R²	0.99999499	0.99998329

再入任务	高度/km	经度/（°）	纬度/（°）	速度/（m·s⁻¹）	航迹角/（°）	航向角/（°）	时间约束/s
任务1	60	0	0	5500	0	90	1530
任务2	60	0	0	5500	0	90	1450
任务3	60	10	10	5500	0	90	1230
任务4	60	−2	−5	5500	0	90	1600
终端条件	23.5	49	2	1330	—	—	—

再入任务	速度/（m·s⁻¹）	高度/m	航程/m	时间/s
任务1	−3.4579	475.5216	2854.4683	0.3
任务2	3.5671	−475.5875	4374.6438	−1.5
任务3	6.1777	−794.6082	2750.9104	−0.4
任务4	2.5495	−338.8542	2756.9456	1.2