基于深度学习的弹道优化方法

doi:10.12305/j.issn.1001-506X.2025.12.29

Abstract

Abstract:

A deep learning based optimal control solution method is proposed for aircraft ballistic optimization. Unlike existing direct and indirect methods, this method uses neural networks to parameterize the control variables, making it possible to solve the multi-point boundary value problem of nonlinear Hamiltonian systems using back and forth integration, and avoiding the problem of guessing the initial values of covariates. Construct a loss function based on the Pontryagin maximum principle and optimize the control variables using stochastic gradient descent algorithm. Compared to the existing deep learning algorithms, this method does not require pre-generation of datasets or simplification of flight mechanics equations, making it suitable for spacecraft ballistic design. Taking Minuteman 3 missile as an example, this method achieves range extension while satisfying various constraints during flight by synergistically optimizing the first-level second consumption profile and active stage pitch angle program, demonstrating the effectiveness of the proposed method.

Key words: missile, ballistic optimization, optimal control, deep learning

CLC Number:

V 448

Zhe WANG, Zhiwen LI, Junzheng SUN, Zenghui ZHANG. Ballistic optimization method based on deep learning[J]. Systems Engineering and Electronics, 2025, 47(12): 4174-4185.

Figures/Tables 8

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参数	第1级	第2级	第3级
起飞质量/kg	34730	11930	4780
装药量/kg	20752	6246	3321
工作时间/s	61.6	65.2	59.6
真空比冲/（Ns/kg）	3030	2823	2793
横截面直径/m	1.67	1.32	1.32

参数	优化前	优化后
射程/km	9450.96	9715.88
关机点速度/（m/s）	6812.63	6868.95
关机点当地倾角/（$^\circ $）	21.03	21.05
关机点航程/km	448.14	461.51
关机点高度/km	225.29	212.88

参数	优化前	优化后
第一子级推力贡献	2515.44	2540.01
第一子级气动损失	−140.49	−127.07
第一子级重力损失	−461.00	−456.92
第二子级推力贡献	2089.90	2091.12
第二子级气动损失	−7.25	−6.68
第二子级重力损失	−307.59	−276.86
第三子级推力贡献	3309.31	3306.35
第三子级气动损失	0.00	0.00
第三子级重力损失	−212.47	−199.57

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Ballistic optimization method based on deep learning

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