Design of nonlinear optimal controller for multi-missile formation
-
摘要: 针对多导弹协同攻击编队控制问题,采用仿射非线性系统最优控制理论设计了基于领弹-从弹法的多导弹编队控制器.首先采用基于微分几何理论的非线性系统精确线性化方法,将导弹非线性运动模型线性化;然后根据从弹、领弹间的相对运动关系,给出了包含领弹运动信息和队形信息的从弹期望轨迹,建立了基于从弹跟踪误差向量的系统状态方程;最后采用基于稳态解的黎卡提矩阵微分方程求解方法解决最优控制问题,设计了从弹的三维非线性编队控制器;仿真结果表明所设计的控制器能够在领弹机动地情况下快速、稳定地实现编队队形的形成和保持.Abstract: To solve the formation control problem of multi-missile formation, the optimal control theory of affine nonlinear system was adopted to design the formation controller of missiles based on leader-follower approach. Firstly, precise linearization based on differential geometry theory was used to linearize the nonlinear motion model of the missile. Secondly, according to the relative motion model of leader and follower, the desired follower track including the states of leader and the desired formation relative distances was given, and system model with follower track errors was formulated. Finally, riccati matrix differential equation solution based on steady state solution was introduced to solve the optimal control problem and a three-dimensional nonlinear optimal formation controller was designed. Simulation results show that the controller is robust to leader maneuver, and is capable of forming and keeping formation figuration rapidly, stably and exactly.
-
Key words:
- cooperative engagement /
- formation control /
- precise linearization /
- leader-follower /
- optimal control
-
[1] 林涛,刘永才,关成启,等.飞航导弹协同作战使用方法探讨[J].战术导弹技术,2005(2):8-12 Lin Tao,Liu Yongcai,Guan Chengqi,et al.An investigation into the methods of cooperative engagement for aerodynamic missile [J].Tactical Missile Technology,2005(2):8-12(in Chinese) [2] Desai J P,Ostrowski J P,Kumar V.Modeling and control of formations of nonholonomic mobile robots[J].IEEE Transactions on Robotics and Automation,2001,17(6):905-908 [3] Liu Shicai,Tan Dalong,Liu Guangjun.Robust leader-follower formation control of mobile robots based on a second order kinematics model[J].Acta Automatica Sinica,2007,33(9):947-955 [4] Paul T,Krogstad T R,Gravdahl J T.Modelling of UAV formation flight using 3D potential field[J].Simulation Modelling Practice and Theory,2008,16(8):1453-1462 [5] Semsar E,Khorasani K.Adaptive formation control of UAVs in the presence of unknown vortex forces and leader commands[C]//Proceedings of the 2006 American Control Conference.Minneapolis,MN:IEEE,2006:3563-3568 [6] Ren W,Beard R W.Formation feedback control for multiple spacecraft via virtual structures[J].IEE Proc Control Theory Appl,2004,151(3):357-368 [7] 苏建敏,董云峰.利用人工势函数法的卫星电磁编队控制[J].北京航空航天大学学报,2012,38(2):213-217,238 Su Jianmin,Dong Yunfeng.Artificial potential function method for satellite electromagnetic formation control [J].Journal of Beijing University of Aeronautics and Astronautics,2012,38(2):213-217,238(in Chinese) [8] 张友安,马国欣,王兴平.多导弹时间协同制导:一种领弹-被领弹策略[J].航空学报,2009,30(6):1109-1118 Zhang Youan,Ma Guoxin,Wang Xingping.Time cooperative guidance for multi-missiles:a leader- follower strategy[J].Acta Aeronautica et Astronautica Sinica,2009,30(6):1109-1118(in Chinese) [9] 马培蓓,纪军.多导弹三维编队控制[J].航空学报,2010, 31(8):1660-1666 Ma Peibei,Ji Jun.Three-dimensional multi-missile formation control[J].Acta Aeronautica et Astronautica Sinica,2010, 31(8):1660-1666(in Chinese) [10] 韦常柱,郭继峰,崔乃刚.导弹协同作战编队队形最优保持控制器设计[J].宇航学报,2010,31(4):1043-1050 Wei Changzhu,Guo Jifeng,Cui Naigang.Research on the missile formation keeping optimal control for cooperative engagement[J].Journal of Astronautics,2010,31(4):1043-1050(in Chinese) [11] Marino R,Tomei P.非线性系统设计-微分几何、自适应及鲁棒控制[M].姚郁,贺风华,译.北京:电子工业出版社,2006:64-68 Marino R,Tomei P.Nonlinear control design geometric,adaptive and robust[M].Translated by Yao Yu,He Fenghua.Beijing:Publishing House of Electronics Industry,2006:64-68(in Chinese) [12] Anderson B D O,Moore J B.线性最优控制[M].尤云程,译.北京:科学出版社,1982:426-439 Anderson B D O,Moore J B.Linear optimal control[M].Translated by You Yuncheng.Beijing:Science Press,1982:426-439(in Chinese)
点击查看大图
计量
- 文章访问数: 1460
- HTML全文浏览量: 174
- PDF下载量: 634
- 被引次数: 0