Aiming at the problem of multi-missile cooperative operation and the directed topological communication between multi-missiles, a dual-layer cooperative guidance law based on the terminal sliding mode method is designed. The guidance command of line-of-sight direction can guarantee multiple-missile attacking the target at the same time. The three-dimensional guidance law normal to line-of-sight can ensure that each missile attacks the target at the desired line-of-sight angles, so as to exert the maximum lethality of each missile. Moreover, the constraint of line-of-sight angles is equivalent to the trajectory planning for the ballistic problem of the missile, which can avoid the collision between the missiles before attacking the target to some extent. At the same time, new adaptive laws are designed for the designed sliding mode guidance laws, accelerating the convergence speed of the sliding mode surface and attenuating the chattering phenomenon caused by the symbolic function. Based on the Lyapunov stability theory, the correctness of the guidance law is proved. Finally, a mathematical simulation experiment is conducted to verify the effectiveness and the superiority of the proposed guidance law.
[1] JEON I S, LEE J I, TAHK M J. Impact-time-control guidance law for anti-ship missiles[J]. IEEE Transactions on Control Systems Technology, 2006, 14(2):260-266.
[2] JEON I S, LEE J I, TAHK M J. Homing guidance law for cooperative attack of multiple missiles[J]. Journal of Guidance, Control, and Dynamics, 2010, 33(1):275-280.
[3] 邹丽,孔繁峨,周锐,等. 多导弹分布式自适应协同制导方法[J]. 北京航空航天大学学报, 2012,38(1):128-132. ZOU L, KONG F E, ZHOU R, et al. Distributed adaptive cooperative guidance for multi-missile salvo attack[J]. Journal of Beijing University of Aeronautics & Astronautics, 2012, 38(1):128-132(in Chinese).
[4] JEON I S, LEE J I, TAHK M J. Guidance law to control impact time and angle[C]//International Conference on Control & Automation, 2007.
[5] SHIM S W, HONG S M, MOON G H, et al. Impact angle and time control guidance under field-of-view constraints and maneuver limits[J]. International Journal of Aeronautical & Space Sciences, 2018, 19(1):217-226.
[6] ZHANG Y, WANG X, WU H. Impact time control guidance law with field of view constraint[J]. Aerospace Science and Technology, 2014, 39:361-369.
[7] 高晔, 周军, 郭建国, 等. 红外成像制导导弹分布式协同制导律研究[J]. 红外与激光工程, 2019, 48(9):0904007. GAO Y, ZHOU J, GUO J G, et al. Study on distributed cooperative guidance law for infrared imaging guided missiles[J]. Infrared and Laser Engineering, 2019, 48(9):0904007(in Chinese).
[8] SUN X, XIA Y. Optimal guidance law for cooperative attack of multiple missiles based on optimal control theory[J]. International Journal of Control, 2012, 85(8):1063-1070.
[9] 王利国, 马国欣, 矫永康. 带角度约束的多飞行器编队协同拦截制导律设计[J]. 海军航空工程学院学报, 2018, 33(3):289-296 WANG L G, MA G X, JIAO Y K. Cooperative interception guidance law design for multi-aircrafts formation with angular constraints[J]. Journal of Naval Aeronautical and Astronautical University, 2018, 33(3):289-296(in Chinese).
[10] 赵世钰, 周锐. 基于协调变量的多导弹协同制导[J]. 航空学报, 2008, 29(6):1605-1611. ZHAO S Y, ZHOU R. Multi-missile cooperative guidance using coordination variables[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(6):1605-1611(in Chinese).
[11] ZHAO S Y, ZHOU R. Cooperative guidance for multimissile salvo attack[J]. Chinese Journal of Aeronautics, 2008, 21(6):533-539.
[12] ZHAO Y, DUAN Z S, WEN G H, et al. Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration[J]. Systems & Control Letters, 2015, 81:8-13.
[13] LIU Q, LIANG Z. Finite-time consensus of time-varying nonlinear multi-agent systems[M]. 2016.
[14] CHEN M, WU Q X, CUI R X. Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems[J]. ISA Transactions, 2013, 52(2):198-206.
[15] PHAN V D, HUYNH V V, TSAI Y W. Adaptive output feedback sliding mode control for time-delay systems with extended disturbance[J]. Journal of the Chinese Institute of Engineers, 2015, 39(3):1-9.
[16] SHIMA T. Intercept-angle guidance[J]. Journal of Guidance, Control, and Dynamics, 2011, 34(2):484-492.
[17] TEKIN R, ERER K S. Switched-gain guidance for impact angle control under physical constraints[J]. Journal of Guidance, Control, and Dynamics, 2015, 38(2):205-216.
[18] FENG L, FAN Z E, ZHANG Y G. Design of guidance law with impact angle and impact time constraints[J]. Advanced Materials Research, 2014, 945-949:1493-1499.
[19] 谭诗利, 雷虎民, 王斌. 高超声速目标拦截含攻击角约束的协同制导律[J]. 北京理工大学学报, 2019,39(6):597-602. TAN S L, LEI H M, WANG B. Cooperative guidance law for hypersonic targets with constrained impact angle[J]. Transactions of Beijing Institute of Technology, 2019, 39(6):597-602(in Chinese).
[20] 赵久奋, 史绍琨, 崇阳, 等. 带落角约束的多导弹分布式协同制导律[J]. 中国惯性技术学报, 2018, 26(4):132-139. ZHAO J F, SHI S K, CHONG Y, et al. Distributed cooperative guidance law for multiple missiles with impact angle constraint[J]. Journal of Chinese Inertial Technology, 2018, 26(4):132-139(in Chinese).
[21] 宋俊红, 宋申民, 徐胜利. 拦截机动目标的多导弹协同制导律[J]. 宇航学报, 2016, 37(12):1307-1314. SONG J H, SONG S M, XU S L. A cooperative guidance law for multiple missiles to intercept maneuvering target[J]. Journal of Astronautics, 2016, 37(12):1307-1314(in Chinese).
[22] ZHEN S, HE C D, WANG S S. Cooperative guidance law based on second-order sliding mode control[C]//2018 Chinese Control And Decision Conference (CCDC), 2018.
[23] TENG L, LI C, GUO Y, et al. Three-dimensional finite-time cooperative guidance for multiple missiles without radial velocity measurements[J]. Chinese Journal of Aeronautics, 2019, 32(5):1294-1304.
[24] YU S H, YU X H, MAN Z H. Continuous finite-time control for robotic manipulators with terminal sliding mode[J]. Automatica, 2005, 41(11):1957-1964.
[25] FENG X, LONG W. Reaching agreement in finite time via continuous local state feedback[C]//2007 Chinese Control Conference, 2007:711-715.
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