BP Neural Network-Based Adaptive Biased Proportional Navigation Guidance Law

doi:10.12382/bgxb.2021.0594

Abstract

Abstract: To address the drawback of traditional analytical biased proportional guidance with poor guidance accuracy when maneuvering in a wide range，an adaptive biased proportional guidance law based on BP(Back propagation) neural network is proposed. The bias term is accurately solved online through the BP neural network. Firstly，the error of solving bias term in analytic form is investigated. Specifically，the influence of different parameters on the solution error of bias term is demonstrated. Secondly，the mapping relationship between parameter and constant term is proved. BP neural network is used to fit the mapping accurately. Thirdly，sensitivity analysis was performed for multidimensional input parameters，on this basis，equilibrium samples for BP neural network in parameter space batch are generated. Finally，the bias term solution model based on BP neural network is established and Adam learning method is used to train the network. In addition，the stability of the guidance law is proved in theory. The effectiveness of the training is tested and verified by mathematical simulation. The simulation results show that the proposed method can be implemented with limited computational cost and effectively improve guidance accuracy，and the average impact angle error is 0.024°. This paper provides a reference for engineering application.

Key words: biasedproportionalnavigationguidancelaw, mapping, sensitivityanalysis, backpropagationneuralnetwork

CLC Number:

TJ765.3

LIU Chang, WANG Jiang, FAN Shipeng, LI Ling, LIN Defu. BP Neural Network-Based Adaptive Biased Proportional Navigation Guidance Law[J]. Acta Armamentarii, 2022, 43(11): 2798-2809.

References

［1］姚郁，郑天宇，贺风华，等.飞行器末制导中的几个热点问题与挑战［J］.航空学报，2015，36(8): 2696-2716.
YAO Y, ZHENG T Y, HE F H, et al. Several hot issues and challenges in terminal guidance of flight vehicles［J］. Acta Aeronautica et Astronautica Sinica, 2015, 36(8): 2696-2716. (in Chinese)
［2］ ZHANG Y A, MA G X, LIU A L. Guidance law with impact time and impact angle constraints［J］. Chinese Journal of Aeronautics, 2013, 26(4): 960-966.
［3］ LIU D, QI Z K. Impact angle and final position constrained optimal guidance law［J］. Transactions of Beijing Institute of Technology, 2001, 21(3): 278-281.
［4］ YUAN P J, CHERN J S. Ideal proportional navigation［J］. Journal of Guidance, Control, and Dynamics, 1992, 15(5): 1161-1165.
［5］ ERER K S，KERMAL OZGOREN M. Control of impact angle using biased proportional navigation［C］∥Proceedings of AIAA Guidance, Navigation, and Control (GNC) Conference. Boston, US: AIAA, 2013: AIAA2013-5113.
［6］ KIM B S，LEE J G，HAN H S. Biased PNG law for impact with angular constraint［J］. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(1): 277-288.
［7］ LEE C H，KIM T H，TAHK M J. Interception angle control guidance using proportional navigation with error feedback［J］.Journal of Guidance，Control，and Dynamics， 2013, 36(5): 1556-1561.
［8］ GAO F, TANG S, SHI J, et al. A bias proportional navigation guidance law based on terminal impact angle constraint［J］. Transactions of Beijing Institute of Technology, 2014, 34(3): 277-282.
［9］马帅，王旭刚，王中原，等.带初始前置角和末端攻击角约束的偏置比例导引律设计以及剩余飞行时间估计［J］.兵工学报，2019，40(1):68-78.
MA S，WANG X G，WANG Z Y，et al. BPNG law with arbitrary initial lead angel and terminal impact angle constraint and time-to-go estimation［J］. Acta Armamentarii, 201 9, 40(1): 68-78. (in Chinese)
［10］王广帅，林德福，范世鹏，等.一种适用于红外制导弹药的偏置比例导引律［J］.系统工程与电子技术，2016，38(10): 2346-2352.
WANG G S，LIN D F，FAN S P，et al. Biased proportional navigation applicable for infrared guidance munitions［J］. Systems Engineering and Electronics, 2016, 38(10): 2346-2352.(in Chinese)
［11］ LEE C H，KIM T H，TAHK M J. Biased PNG for target observability enhancement against nonmaneuvering targets［J］. IEEE Transactions on Aerospace & Electronic Systems, 2015, 51(1): 2-17.
［12］ ERER K S，MERTTOPCUOGLU O. Indirect control of impact angle against stationary targets using biased PPN［C］∥Proceedings of AIAA Guidance，Navigation，and Control Conference. Toronto: AIAA，2010: AIAA 2010-8184.
［13］ HONG D，KIM M，PARK S. Study on Reinforcement Learning-Based Missile Guidance Law［J］.Applied Sciences，2020，10(18): 6567.
［14］田春军.基于BP神经网络的潜地导弹落点参数计算方法［J］.兵器装备工程学报，2021，42(4): 145-149.
TIAN C J. Calculation method of impact point parameter based on BP neural network for submarine launched ballistic missile［J］. Journal of Ordnance Equipment Engineering，2021，42(4): 145-149. (in Chinese)
［15］ SHAO G H J，XU Z，WANG X M，et al. Adaptive three-dimensional guidance law based on neural dynamic surface control［C］∥Proceedings of 2016 IEEE International Conference on Aircraft Utility Systems (AUS). Beijing，China: IEEE，2016: 92-97.
［16］王因翰，范世鹏，吴广，等.基于GRU的敌方拦截弹制导律快速辨识方法［J］. 航空学报, 2022, 43(2): 398-409.
WANG Y H，FAN S P，WU G，et al. Fast guidance law identification approach for incoming missile based on GRU network［J］. Acta Aeronautica et Astronautica Sinica, 2022, 43(2): 398-409. (in Chinese)
［17］ FILICI C，SNCHEZ PEA R S. Online guidance updates using neural networks［J］.Acta Astronautica，2010，66(3/4): 477-485.
［18］余跃，王宏伦.基于深度学习的高超声速飞行器再入预测校正容错制导［J］.兵工学报，2020，41(4): 656-669.
YU Y，WANG H L. Deep learning-based reentry predictor-corrector fault-tolerant guidance for Hypersonic vehicles［J］. Acta Armamentarii，2020，41(4): 656-669. (in Chinese)
［19］张宏鹏，黄长强，轩永波，等.基于深度神经网络的无人作战飞机自主空战机动决策［J］.兵工学报，2020，41(8): 1613-162.
ZHANG H P，HUANG C Q，XUAN Y B，et al. Maneuver decision of autonomous air combat of unmanned combat aerial vehicle based on deep neural network［J］. Acta Armamentarii，2020，41(8): 1613-162. (in Chinese)
［20］ GUO Y H，LI X，ZHANG H J，et al. Data-driven method for impact time control based on proportional navigation guidance［J］.Journal of Guidance，Control，and Dynamics，2020，43(5): 955-966.
［21］ COTTRELL R G，VINCENT T L，SADATI S H. Minimizing interceptor size using neural networks for terminal guidance law synthesis［J］. Journal of Guidance，Control，and Dynamics，1996，19(3):557-562.
［22］ NARENDRA K S, PARTHASARATHY K. Identification and control of dynamical systems using neural networks［J］. IEEE Transactions on Neural Net Works，1990，1(1): 4-27.
［23］ FUNAHASHI K I. On the approximate realization of continuous mappings by neural networks［J］.Neural networks，1989，2(3): 183-192.
［24］ HECHT-NIELSEN R. Theory of the backpropagation neural network[C]∥Proceedings of the International 1989 Joint Conference on Neural Networks. Washington, DC, US: IEEE, 1989(1): 593-605.
［25］ WANG Y H，FAN S P，WANG J，et al. Quick identification of guidance law for an incoming missile using multiple-model mechanism［J］. Chinese Journal of Aeronautics，2022, 35(9): 282-292.
［26］ RAFAEL Y. Modern missile guidance［M］. Boca Raton: CRC Press，2007: 102-112.

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