基于非线性模型预测控制的火星大气进入智能制导方法

doi:10.12305/j.issn.1001-506X.2021.07.26

摘要/Abstract

摘要：

针对火星大气进入精确制导问题, 提出了基于非线性模型预测控制(nonlinear model predictive control, NMPC)的智能进入制导方法。首先, 考虑了进入制导约束, 采用NMPC方法设计制导算法。通过引入衰减记忆滤波器, 提出了基于误差信息估计的预测模型修正方法, 增强系统对模型误差的鲁棒性, 并利用变预测时域策略提高系统性能。然后, 以NMPC制导系统为制导模板, 在实际条件下生成大量样本数据集, 进行深度神经网络(deep neural network, DNN)的离线训练。最后, 在进入制导过程中利用DNN代替求解复杂优化问题和积分预测的过程, 在线快速解算控制量, 并结合横向制导实现智能制导。仿真结果表明, 提出的制导方法能够快速计算指令, 实现了高精度制导。

关键词: 火星进入制导, 非线性模型预测控制, 衰减记忆滤波器, 深度神经网络, 智能制导

Abstract:

Aiming at the precision guidance problem of the Mars atmospheric entry guidance, an intelligent guidance method based on nonlinear model predictive control (NMPC) is proposed. First, considering guidance constraints, the guidance system is designed by using the NMPC method. By introducing the fading-memory filter, the prediction model correction method based on error information estimation is proposed to enhance the robustness of the system against model errors, and the system performance is improved by using the variable prediction time domain strategy. Then the NMPC guidance system is used as the guidance template to generate the sample data set under the actual entry conditions, which conduct the off-line training of the deep neural network. Finally, in the process of entry guidance, deep neural network is used to solve control variable online quickly instead of the process of solving complex optimization problem and integral prediction, and the intelligent guidance is realized by combining with lateral guidance. The simulation results show that the proposed guidance method can calculate command quickly and realize high-precision guidance.

Key words: mars entry guidance, nonlinear model predictive control, fading-memory filter, deep neural network, intelligent guidance

中图分类号:

V448.23

胥彪, 李翔, 李爽, 张金鹏. 基于非线性模型预测控制的火星大气进入智能制导方法[J]. 系统工程与电子技术, 2021, 43(7): 1943-1953.

Biao XU, Xiang LI, Shuang LI, Jinpeng ZHANG. Intelligent guidance method based on nonlinear model predictive control for Mars atmospheric entry[J]. Systems Engineering and Electronics, 2021, 43(7): 1943-1953.

图/表 16

图1

表1

图2

表2

表3

表4

表5

表6

图3

图4

图5

图6

图7

表7

表8

表9

参考文献 30

1	LI S , JIANG X Q . Review and prospect of guidance and control for mars atmospheric entry[J]. Progress in Aerospace Sciences, 2014, 69, 40- 57. doi: 10.1016/j.paerosci.2014.04.001
2	KLUEVER C A . Entry guidance performance for mars precision landing[J]. Journal of Guidance, Control, and Dynamics, 2008, 31 (6): 1537- 1544. doi: 10.2514/1.36950
3	JON C H , DONALD E G . Space shuttle entry guidance performance results[J]. Journal of Guidance, Control, and Dynamics, 1983, 6 (6): 442- 447. doi: 10.2514/3.8523
4	SANJAY B , ANIL V R , KENNETH D M . Entry trajectory tracking law via feedback linearization[J]. Journal of Guidance, Control, and Dynamics, 1998, 21 (5): 726- 732. doi: 10.2514/2.4318
5	TALOLE S E, JOEL B, KENNETH D M. Sliding mode observer for drag tracking in entry guidance[C]//Proc. of the AIAA Guidance, Navigation and Control Conference and Exhibit, 2007.
6	PENG Y M , LI S . Command generator tracker based direct model reference adaptive tracking guidance for Mars atmospheric entry[J]. Advances in Space Research, 2012, 49 (1): 49- 63. doi: 10.1016/j.asr.2011.08.016
7	XIA Y Q , CHEN R F , PU F , et al. Active disturbance rejection control for drag tracking in mars entry guidance[J]. Advances in Space Research, 2014, 53 (5): 853- 861. doi: 10.1016/j.asr.2013.12.008
8	吴超, 赵振华, 杨俊, 等. 基于约束预测控制的火星大气进入轨迹跟踪[J]. 深空探测学报, 2014, 1 (2): 128- 133.
	WU C , ZHAO Z H , YANG J , et al. Mars entry trajectory tracking using constrained predictive control[J]. Journal of Deep Space Exploration, 2014, 1 (2): 128- 133.
9	WU C, LI S H, YANG J, et al. Disturbance observer based constrained multi-model predictive control for Mars entry trajectory tracking[C]//Proc. of IEEE Chinese Guidance, Navigation and Control Conference, 2014.
10	LU P . Nonlinear predictive controllers for continuous systems[J]. Journal of Guidance, Control, and Dynamics, 1994, 17 (3): 553- 560. doi: 10.2514/3.21233
11	JOEL B, KENNETH D M. Nonlinear predictive controller for drag tracking in entry guidance[C]//Proc. of the AIAA Astrodynamics Specialist Conference and Exhibit, 2008.
12	赵振华, 杨俊, 李世华. 基于阻力跟踪的火星大气进入段非线性预测制导律设计[J]. 深空探测学报, 2015, 2 (2): 137- 143.
	ZHAO Z H , YANG J , LI S H . Drag-Based nonlinear predictive guidance law for Mars entry[J]. Journal of Deep Space Exploration, 2015, 2 (2): 137- 143.
13	YAN X D . Mars entry guidance based on nonlinear model predictive control with disturbance observer[J]. Journal of the Franklin Institute, 2019, 356 (17): 9824- 9843.
14	JARDON E R , BECERRO T A . Artificial neural networks to predict overall heat transfer coefficient and pressure drop on a simulated heat exchanger[J]. International Journal of Applied Engineering Research, 2019, 14 (13): 3097- 3103.
15	曾庆华, 董荣华, 皮术武. 基于最优制导模板的神经网络预测制导方法[J]. 国防科技大学学报, 2014, 36 (1): 137- 141.
	ZENG Q H , DONG R H , PI S W . Neural network predictive guidance method based on pattern of optimal guidance[J]. Journal of National University of Defense Technology, 2014, 36 (1): 137- 141.
16	LI Z , SUN X D , HU C , et al. Neural network based online predictive guidance for high lifting vehicles[J]. Aerospace Science and Technology, 2018, 82-83, 149- 160. doi: 10.1016/j.ast.2018.09.004
17	YANN L , YOSHUA B , GEOFFREY H . Deep learning[J]. Nature, 2015, 521 (7553): 436- 444. doi: 10.1038/nature14539
18	SCHMIDHUBER J . Deep learning in neural networks: an overview[J]. Neural Networks, 2015, 61, 85- 117. doi: 10.1016/j.neunet.2014.09.003
19	CHENG L , WANG Z B , SONG Y , et al. Real-time optimal control for irregular asteroid landings using deep neural networks[J]. Acta Astronautica, 2020, 170, 66- 79. doi: 10.1016/j.actaastro.2019.11.039
20	BIGGS JD , FOURNIER H . Neural-network-based optimal attitude control using four impulsive thrusters[J]. Journal of Guidance, Control, and Dynamics, 2020, 43 (2): 299- 309. doi: 10.2514/1.G004226
21	BERNIKER M , KORDING K P . Deep networks for motor control functions[J]. Frontiers in Computational Neuroscience, 2015, 9 (32): 1- 10.
22	CARLOS S , DARIO I . Real-time optimal control via deep neural networks: study on landing problems[J]. Journal of Guidance, Control, and Dynamics, 2018, 41 (5): 1122- 1135. doi: 10.2514/1.G002357
23	陈虹. 模型预测控制[M]. 北京: 科学出版社, 2013.
	CHEN H . Model predictive control[M]. Beijing: Science Press, 2013.
24	FARSHAD R , BEHROOZ R , ZAHRA R . A novel nonlinear model predictive control design based on a hybrid particle swarm optimization-sequential quadratic programming algorithm: application to an evaporator system[J]. Transactions of the Institute of Measurement and Control, 2016, 38 (1): 23- 32. doi: 10.1177/0142331214561917
25	赵汉元. 飞行器再入动力学和制导[M]. 长沙: 国防科技大学出版社, 1997.
	ZHAO H Y . Dynamics and guidance of aircraft reentry[M]. Changsha: National Defense Science and Technology University Press, 1997.
26	STEPHAN M , MATTHEW H , DAVID B . Stochastic gradient descent as approximate Bayesian inference[J]. Journal of Machine Learning Research, 2017, 18 (1): 4873- 4907.
27	LAARHOVEN T V. L2 regularization versus batch and weight normalization[C]//Proc. of 31st Conference on Neural Information Processing Systems, 2017.
28	KHAN S , HAYAT M , PORIKLI F . Regularization of deep neural networks with spectral dropout[J]. Neural Networks, 2019, 110 (1): 82- 90.
29	GLOROT X, BENGIO Y. Understanding the difficulty of training deep feedforward neural networks[C]//Proc. of the International Conference on Artificial Intelligence and Statistics, 2010, 9: 249-256.
30	JOEL B. Advances in spacecraft atmospheric entry guidance[D]. Irvine: University of California, 2010.

参数	数值
N_c	3
Q	[100, 0; 0, 500]
R	0.1
η	[1, 1]
[N₁, N₂]	[5, 10]
[λ₁, λ₂]	[0.05, 0.01]

初始状态量	取值
r₀/km	3 520.76
V₀/(m/s)	5 505
θ₀/(°)	-90.072
$ \varphi_0 $/(°)	-43.898
γ₀/(°)	4.99
$ \psi_0 $/(°)	-14.15

终端状态量	取值
θ_f/(°)	-74.865 9
$ \varphi _f$/(°)	-41.923 8
h_f/km	＞7
V_f/(m/s)	＜400

误差p_l	取值	类型
气动系数	±0.2[C_L, C_D]	高斯分布
大气密度/(kg/m³)	±0.3ρ	均匀分布
高度/km	±1	高斯分布
经度/(°)	±0.05	高斯分布
纬度/(°)	±0.05	高斯分布
速度/(m/s)	±2	高斯分布
航向角/(°)	±0.15	高斯分布
航迹角/(°)	±0.1	高斯分布

激活函数类型	E_train	E_test
tansig-purelin	7.81e-3	7.95e-3
Relu-purelin	6.68e-3	6.70e-3
tansig-tansig	7.94e-2	8.15e-3
Relu-tansig	6.93e-3	6.98e-3