弹群分布式一致误差约束自适应最优协同拦截方法

doi:10.12382/bgxb.2022.1160

摘要/Abstract

摘要：

为解决机动目标干扰下协同制导系统模型部分未知以及一致误差约束限制导致协同一致性差的问题,建立前馈补偿+反馈优化的复合协同制导架构,提出分布式自适应最优协同拦截制导方法。在前馈补偿部分,设计障碍Lyapunov函数非线性映射机制,补偿误差约束影响。设计权值自适应的神经网络观测器,实现对目标未知机动干扰的在线估计;在反馈优化部分,采用自适应动态规划技术设计虚拟控制量和实际控制量,将每一步中控制量设计转化为非线性耦合哈密顿-雅可比-贝尔曼(HJB)方程的求解问题。构建分布式自适应评价网络,设计残余误差驱动的评价网络权值自适应更新律,实现对HJB方程中最优代价函数的在线迭代求解。基于Lyapunov稳定性理论证明了非线性协同制导闭环系统的稳定性,确保了协同一致性误差的收敛性。数值仿真结果表明:新方法能够在保证拦截制导精度的同时将协同一致性误差降低至0.01s。

关键词: 协同拦截, 目标机动, 自适应动态规划, 误差约束, 自适应评价网络

Abstract:

To deal with the problem of poor synchronization for partial unknown nonlinear cooperative guidance system subject to synchronization error constraints caused by unknown maneuvering targets, a feedforward compensation+feedback optimization cooperative guidance framework is constructed. Then, a distributed adaptive optimal cooperative interception guidance method is proposed. In the feedforward compensation part, a nonlinear mapping mechanism is provided by designing a novel barrier Lyapunov function (BLF) for compensating the system effects of synchronization error constraints. To estimate the unknown nonlinear term caused by the maneuvering target, a neural network (NN) observer is built, in which the weight values are updated adaptively for estimating the target's unknown maneuvering disturbance. In the feedback optimization part, the virtual and actual control inputs are designed recursively by using the ADP technique, in which the control input in every backstepping process is transformed into the issue of solving the nonlinear coupled HJB equation. An adaptive critic network is built to solve the optimal cost function of the HJB equation online, in which a residual error based adaptive updating law of critic weight is derived. The stability of the nonlinear cooperative guidance closed-loop system is analyzed and the convergence of cooperative synchronization error is guaranteed theoretically based on the Lyapunov theory. The simulation results show that the synchronization error can be reduced to 0.01s while ensuring the interception precision with the proposed method.

Key words: cooperative interception, target maneuvering, ADP, error constraints, adaptive critic network

中图分类号:

V448

刘大卫, 孙景亮, 龙腾, 何镜, 王晓悦. 弹群分布式一致误差约束自适应最优协同拦截方法[J]. 兵工学报, 2023, 44(9): 2580-2590.

LIU Dawei, SUN Jingliang, LONG Teng, HE Jing, WANG Xiaoyue. Distributed Adaptive Optimal Cooperative Interception Method for Missile Swarm with Synchronization Error Constraints[J]. Acta Armamentarii, 2023, 44(9): 2580-2590.

图/表 9

图1 多弹协同制导几何关系

Fig.1 Multi-missile cooperative guidance geometry

图2 弹间信息交互拓扑图

Fig.2 Information exchange topology between missiles

表1 弹-目初始参数

Table 1 Initial parameters of missile and target

对象	初始位置/m	初始航迹角/(°)
领弹	(0,0)	45
从弹1	(200,0)	60
从弹2	(100,0)	60
目标	(1000,500)	60

图3 多弹协同拦截轨迹

Fig.3 Trajectories of multi-missile cooperative interception

图4 弹-目相对距离

Fig.4 Relative distance between missile and target

图5 弹-目相对速率

Fig.5 Relative velocity between missile and target

图6 视线角速率曲线

Fig.6 Trajectories oflight-of-sight rate

表2 协同制导性能

Table 2 Cooperative guidance performance

导弹	脱靶量/m	拦截时间/s
领弹	0.8	4.72
从弹1	1.1	4.72
从弹2	0.7	4.73

图7 一致邻域误差曲线

Fig.7 Trajectories of synchronization neighbor error

参考文献 28

[1]	魏明英, 崔正达, 李运迁. 多弹协同拦截综述与展望[J]. 航空学报, 2020, 41(增刊1): 723804.
	WEI M Y, CUI Z D, LI Y Q. Review and future development of multi-missile coordinated interception[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(S1): 723804. (in Chinese) doi: 10.7527/S1000-6893.2019.23804
[2]	赵建博, 杨树兴. 多导弹协同制导研究综述[J]. 航空学报, 2017, 38(1): 020256.
	ZHAO J B, YANG S X. Review of multi-missile cooperative guidance[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(1): 020256. (in Chinese)
[3]	ZHOU J L, YANG J Y. Distributed guidance law design for cooperative simultaneous attacks with multiple missiles[J]. Journal of Guidance, Control, and Dynamics, 2016, 39(10): 2439-2447. doi: 10.2514/1.G001609 URL
[4]	姜尚, 陈锋, 高伟鹏, 等. 弹群在复杂作战空间下的自适应分布式协同制导策略[J]. 兵工学报, 2022, 43(增刊2): 97-106.
	JIANG S, CHEN F, GAO W P, et al. An adaptive distributed cooperative guidance strategy for projectile clusters in complex combat environment[J]. Acta Armamentarii, 2022, 43(S2): 97-106. (in Chinese) doi: 10.12382/bgxb.2022.B023
[5]	MA M C, SONG S M. Three-dimensional prescribed performance cooperative guidance law with spatial constraint for intercepting manoeuvring targets[J]. International Journal of Control, 2023, 96(3):1424-1435. doi: 10.1080/00207179.2022.2051075 URL
[6]	赵启伦, 陈建, 董希旺, 等. 拦截高超声速目标的异类导弹协同制导律[J]. 航空学报, 2016, 37(3): 936-948. doi: 10.7527/S1000-6893.2015.0235
	ZHAO Q L, CHEN J, DONG X W, et al. Cooperative guidance law for heterogeneous missiles intercepting hypersonic weapon[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(3): 936-948. (in Chinese) doi: 10.7527/S1000-6893.2015.0235
[7]	于江龙, 董希旺, 李清东. 拦截机动目标的分布式协同围捕制导方法[J]. 航空学报, 2022, 43(9): 521-541.
	YU J L, DONG X W, LI Q D. Distributed cooperative encirclement hunting guidance method for intercepting maneuvering target[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(9): 521-541. (in Chinese)
[8]	李国飞, 朱国梁, 吕金虎, 等. 主-从多飞行器三维分布式协同制导方法[J]. 航空学报, 2021, 42(11): 524926. doi: 10.7527/S1000-6893.2020.24926
	LI G F, ZHU G L, LÜ J H, et al. Three dimensional distributed cooperative guidance law for multiple leader-follower flight vehicles[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(11): 524926. (in Chinese)
[9]	LIU F, DONG X W, LI Q D, et al. Robust multi-agent differential games with application to cooperative guidance[J]. Aerospace Science and Technology, 2021, 111: 106568. doi: 10.1016/j.ast.2021.106568 URL
[10]	KANG S, WANF J N, LI G, et al. Optimal cooperative guidance law for salvo attack: an MPC-based consensus perspective[J]. IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(5): 2397-2410. doi: 10.1109/TAES.2018.2816880 URL
[11]	GARCIA E, CASBEER D W, PACHTER M. Cooperative strategies for optimal aircraft defense from an attacking missile[J]. Journal of Guidance, Control, and Dynamics, 2015, 38(8): 1510-1520. doi: 10.2514/1.G001083 URL
[12]	TAN L N. Distributed optimal integrated tracking control for separate kinematic and dynamic uncertain non-holonomic mobile mechanical multi-agent systems[J]. IET Control Theory & Applications, 2017, 11(18): 3249-3260. doi: 10.1049/cth2.v11.18 URL
[13]	TAN L N. Distributed cooperative H_∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming[J]. International Journal of Control, 2017, 91(4): 952-968. doi: 10.1080/00207179.2017.1300685 URL
[14]	TAN L N. Omnidirectional-vision-based distributed optimal tracking control for mobile multirobot systems with kinematic and dynamic disturbance rejection[J]. IEEE Transactions on Industrial Electronics, 2018, 65(7): 5693-5703. doi: 10.1109/TIE.2017.2782245 URL
[15]	SUN J L, LIU C S. Auxiliary-system-based composite adaptive optimal backstepping control for uncertain nonlinear guidance systems with input constraints[J]. ISA Transactions, 2020, 107: 294-306. doi: 10.1016/j.isatra.2020.07.042 pmid: 32798045
[16]	DUAN D D, LIU C S, SUN J L. Adaptive periodic event-triggered control for missile-target interception system with finite-horizon convergence[J]. Transactions of the Institute of Measurement and Control, 2020, 42(10): 1808-1822. doi: 10.1177/0142331219897186 URL
[17]	ZHANG W G, YI W J. Composite adaptive dynamic programming for missile interception systems with multiple constraints and less sensor requirement[J]. ISA Transactions, 2021, 117: 40-53. doi: 10.1016/j.isatra.2021.01.040 pmid: 33546863
[18]	SUN J L, LIU C S. Distributed fuzzy adaptive backstepping optimal control for nonlinear multimissile guidance systems with input saturation[J]. IEEE Transactions on Fuzzy Systems, 2019, 27(3): 447-461.
[19]	ZHANG Y X, LIANG X L, LI D Y, et al. Barrier Lyapunov function-based safe reinforcement learning for autonomous vehicles with optimized backstepping[J]. IEEE Transactions on Neural Networks and Learning Systems, 2022(2022-07-12). https://doi.org/10.1109/TNNLS.2022.3186528.
[20]	LI Y M, FAN Y L, LI K W, et al. Adaptive optimized backstepping control-based RL algorithm for stochastic nonlinear systems with state constraints and its application[J]. IEEE Transactions on Cybernetics, 2022, 52(10): 10542-10555. doi: 10.1109/TCYB.2021.3069587 URL
[21]	ZHANG J X, LI K W, LI Y M. Output-feedback based simplified optimized backstepping control for strict-feedback systems with input and state constraints[J]. IEEE/CAA Journal of Automatica Sinica, 2021, 8(6): 1119-1132. doi: 10.1109/JAS.2021.1004018 URL
[22]	ZHANG W G, YI W J. Composite adaptive dynamic programming for missile interception systems with multiple constraints and less sensor requirement[J]. ISA Transactions, 2021, 117: 40-53. doi: 10.1016/j.isatra.2021.01.040 pmid: 33546863
[23]	DONG C Y, LIU Y, WANG Q. Barrier Lyapunov function based adaptive finite-time control for hypersonic flight vehicles with state constraints[J]. ISA Transactions, 2020, 96: 163-176. doi: S0019-0578(19)30272-1 pmid: 31280884
[24]	DOU L Q, CAI S Y, ZHANG X Y, et al. Event-triggered-based adaptive dynamic programming for distributed formation control of multi-UAV[J]. Journal of the Franklin Institute, 2022, 359(8): 3671-3691. doi: 10.1016/j.jfranklin.2022.02.034 URL
[25]	LONG T, CAO Y, SUN J L, et al. Adaptive event-triggered distributed optimal guidance design via adaptive dynamic programming[J]. Chinese Journal of Aeronautics, 2022, 35(7): 113-127.
[26]	VAMVOUDAKIS K G, MIRANDA M F, HESPANHA J P. Asymptotically stable adaptive-optimal control algorithm with saturating actuators and relaxed persistence of excitation[J]. IEEE Transactions on Neural Networks and Learning Systems, 2016, 27(11): 2386-2398. pmid: 26513810
[27]	LI Y M, SUN K K, TONG S C. Observer-based adaptive fuzzy fault-tolerant optimal control for SISO nonlinear systems[J]. IEEE Transactions on Cybernetics, 2019, 49(2): 649-661. doi: 10.1109/TCYB.2017.2785801 pmid: 29993971
[28]	张帅, 郭杨, 王仕成, 等. 考虑探测效能的有限时间协同制导方法[J]. 兵工学报, 2019, 40(9): 1849-1859. doi: 10.3969/j.issn.1000-1093.2019.09.010
	ZHANG S, GUO Y, WANG S C, et al. A finite-time cooperative guidance method considering cooperative detection efficiency[J]. Acta Armamentarii, 2019, 40(9): 1849-1859. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.09.010