多弹协同微分对策制导律研究
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摘要
针对多个拦截弹拦截单个大机动目标(如战术弹道导弹),提出了一种基于微分对策理论的多弹协同制导律。建立了多对一的平面追逃运动模型,分析了该模型下的弹目相对运动关系,设计了适用于所有对策参与者的线性二次型性能指标,避免了对非连续性能指标的处理。得出了理想条件下对策各方的闭环最优解,即拦截弹的最优协同拦截策略和目标的最优逃逸策略。仿真结果表明了所提方法的有效性。
To intercept a highly maneuvering target such as TBM cooperatively by multi-missile,a cooperative guidance law was proposed,based on differential games theory. A planar pursuit-evasion model which includes multi-pursuer and one evader was established,and the relative kinematic relation between the pursuers and the evader was analyzed,then a linear quadratic cost function that is suitable for all of the players was designed,so as to avoid dealing with non-continuous cost functions. Ideal dynamic cases were assumed,closed-form cooperative differential game guidance strategies,i. e. optimal pursuit strategies for the missiles and optimal evasion strategy for the target,were obtained under ideal dynamic case of the players. Two-dimensional simulation results were used to validate the guidance law proposed. It is shown that the requirement of maneuverability for the missiles is lowered obviously,compared with an existing method.
To intercept a highly maneuvering target such as TBM cooperatively by multi-missile,a cooperative guidance law was proposed,based on differential games theory. A planar pursuit-evasion model which includes multi-pursuer and one evader was established,and the relative kinematic relation between the pursuers and the evader was analyzed,then a linear quadratic cost function that is suitable for all of the players was designed,so as to avoid dealing with non-continuous cost functions. Ideal dynamic cases were assumed,closed-form cooperative differential game guidance strategies,i. e. optimal pursuit strategies for the missiles and optimal evasion strategy for the target,were obtained under ideal dynamic case of the players. Two-dimensional simulation results were used to validate the guidance law proposed. It is shown that the requirement of maneuverability for the missiles is lowered obviously,compared with an existing method.
引文
[1]花文华,孟庆龄,张金鹏,等.有界双重控制导弹微分对策制导律[J].北京航空航天大学学报,2016,42(9):1851-1856.
[2] SHAFERMAN V,SHIMA T. Cooperative optimal guidance laws for imposing a relative intercept angle[J]. Journal of Guidance,Control,and Dynamics,2015,38(8):1395-1408.
[3]常燕,陈韵,鲜勇,等.机动目标的空间交会微分对策制导方法[J].宇航学报,2016,37(7):795-801.
[4] BARDHAN R,GHOSE D. An SDRE based differential game approach for maneuvering target interception[C]//AIAA Guidance,Navigation,and Control Conference,Florida,2015.
[5] BARDHAN R,GHOSE D. Nonlinear differential gamesbased impact-angle-constrained guidance law[J]. Journal of Guidance,Control,and Dynamics,2015,38(3):384-402.
[6] TURETSKY V,SHIMA T. Pursuit-evasion guidance in a switched system[J]. SIAM J. CONTROL OPTIM. 2018,56(4):2613-2633.
[7] PERELMAN A,SHIMA T. Cooperative differential games strategies for active aircraft protection from a homing missile[J]. Journal of Guidance,Control,And Dynamics,2011,34(3):761-773.
[8] GARCIA E,CASBEER W E,PACHTER M. Cooperative strategies for optimal aircraft defense from an attacking missile[J]. Journal of Guidance,Control,and Dynamics,2015,38(8):1510-1520.
[9] LIU Yan-Fang,QI Nai-ming,TANG Zhi-wei. Linear quadratic differential game strategies with two-pursuit versus single-evader[J]. Chinese Journal of Aeronautics,2012,25(6):896-905.
[10] TURETSKY V,SHINAR J. Missile guidance laws based on pursuit-evasion game formulations[J]. Automatica,2003,39(4):607-618.
[2] SHAFERMAN V,SHIMA T. Cooperative optimal guidance laws for imposing a relative intercept angle[J]. Journal of Guidance,Control,and Dynamics,2015,38(8):1395-1408.
[3]常燕,陈韵,鲜勇,等.机动目标的空间交会微分对策制导方法[J].宇航学报,2016,37(7):795-801.
[4] BARDHAN R,GHOSE D. An SDRE based differential game approach for maneuvering target interception[C]//AIAA Guidance,Navigation,and Control Conference,Florida,2015.
[5] BARDHAN R,GHOSE D. Nonlinear differential gamesbased impact-angle-constrained guidance law[J]. Journal of Guidance,Control,and Dynamics,2015,38(3):384-402.
[6] TURETSKY V,SHIMA T. Pursuit-evasion guidance in a switched system[J]. SIAM J. CONTROL OPTIM. 2018,56(4):2613-2633.
[7] PERELMAN A,SHIMA T. Cooperative differential games strategies for active aircraft protection from a homing missile[J]. Journal of Guidance,Control,And Dynamics,2011,34(3):761-773.
[8] GARCIA E,CASBEER W E,PACHTER M. Cooperative strategies for optimal aircraft defense from an attacking missile[J]. Journal of Guidance,Control,and Dynamics,2015,38(8):1510-1520.
[9] LIU Yan-Fang,QI Nai-ming,TANG Zhi-wei. Linear quadratic differential game strategies with two-pursuit versus single-evader[J]. Chinese Journal of Aeronautics,2012,25(6):896-905.
[10] TURETSKY V,SHINAR J. Missile guidance laws based on pursuit-evasion game formulations[J]. Automatica,2003,39(4):607-618.