A novel cooperative mid-course guidance scheme for multiple intercepting missiles

In the interception engagement,if the target movement information is not accurate enough for the mid-course guidance of intercepting missiles,the interception mission may fail as a result of large handover errors.This paper proposes a novel cooperative mid-course guidance scheme for multiple missiles to intercept a target under the condition of large detection errors.Under this scheme,the launch and interception moments are staggered for different missiles.The earlier launched missiles can obtain a relatively accurate detection to the target during their terminal guidance,based on which the latter missiles are permitted to eliminate the handover error in the mid-course guidance.A significant merit of this scheme is that the available resources are fully exploited and less missiles are needed to achieve the interception mission.To this end,first,the design of cooperative handover parameters is formulated as an optimization problem.Then,an algorithm based on Monte Carlo sampling and stochastic approximation is proposed to solve this optimization problem,and the convergence of the algorithm is proved as well.Finally,simulation experiments are carried out to validate the effectiveness of the proposed cooperative scheme and algorithm.     

空-空导弹全向攻击最优制导规律研究

 将发射瞬时所确定的平行接近弹道作为基准弹道,由于各种干拢所引起的相对于基准弹道的偏离作为偏差来处理;用最优控制理论导出空-空导弹进行全向攻击的最优制导律,此制导律包含目标加速度反馈。当目标作非机动飞行时,最优制导律是一种变比例系数的比例制导。数字仿真结果表明:在相同条件下,最优制导弹道需用过载、终端脱靶量均小于比例制导,特别是从目标前方攻击时,其制导精度大大优于比例制导。     

Three-dimensional cooperative guidance strategy and guidance law for intercepting highly maneuvering target

Cooperative interception of the target with strong maneuverability by multiple missiles with weak maneuverability in the three-dimensional nonlinear model is studied. Firstly, the three-dimensional nonlinear model of cooperative guidance is established. The three-dimensional reachable region is represented composed of lateral acceleration and longitudinal acceleration in the two-dimensional coordinate system. Secondly, the problem of the multiple missile's reachable coverage area is transformed into the problem of cooperative coverage. A cooperative coverage strategy is proposed and an algorithm for quickly calculating the number of required missiles is designed. Then, the guidance law based on the cooperative coverage strategy is proposed, and it is proved that cooperative interception of the target can be achieved under the acceleration limit. Moreover, the relations among the number of missiles, the initial array position of terminal guidance and the coverage area of the target’s large maneuver are analyzed. The dynamic adjustment strategy of guidance parameters is proposed to reduce the guidance error. Finally, simulation results show that multiple missiles with low maneuverability can achieve effective interception of target with strong maneuverability through the proposed cooperative strategy and cooperative guidance method.     

过载约束下的大机动目标协同拦截

研究了非线性拦截几何下具有过载约束的多枚弱机动能力的导弹拦截强机动能力的目标的协同拦截问题。首先，在建立导弹的可达域、导弹的可行域以及目标的逃逸域这3个概念的基础上提出了非线性拦截几何下的基于逃逸域覆盖的协同拦截策略，并提出了基于标准弹道的设计方法。然后，给出了协同拦截制导律的形式，研究了导弹的末制导初始阵位、制导律参数以及导弹对目标机动的覆盖区域这三者间的关系，并设计了数值求解算法来实现对多弹的覆盖区域的分配、协同制导律的设计以及多弹初始拦截阵位的配置。最后，对理论结果进行仿真。结果显示，多枚机动性较小的导弹，通过初始拦截阵位的合理配置和协同拦截制导律的合理设计，可以实现对机动性能较强的目标的协同拦截。     

Distributed cooperative guidance for multiple missiles with fixed and switching communication topologies

This study investigates cooperative guidance problems for multiple missiles with fixed and switching directed communication topologies.A two-step guidance strategy is proposed to realize the simultaneous attack.In the first step,a distributed cooperative guidance law is designed using local neighboring information for multiple missiles to achieve consensus on range-to-go and leading angle.The second step begins when the consensus of multiple missiles is realized.During the second step,multiple missiles disconnect from each other and hit the target using the proportional navigation guidance law.First,based on the local neighboring communications,a sufficient condition for multiple missiles to realize simultaneous attack with a fixed communication topology is presented,where the topology is only required to have a directed spanning tree.Then,the results are extended to the case of switching communication topologies.Finally,numerical simulations are provided to validate the theoretical results.     

三维自适应终端滑模协同制导律

针对多枚导弹协同作战的问题,且多枚导弹之间保持有向拓扑通信的条件下,基于终端滑模法设计了视线方向及视线法向的双层协同制导律。其中,视线方向的制导指令能够保证导弹同时完成拦截任务;视线法向上的三维制导律能够保证每枚导弹以期望的视线角攻击目标,从而发挥各枚导弹的最大杀伤力,并且视线角的约束相当于规划了末制导段导弹的弹道问题,在一定程度上避免攻击目标前导弹间发生碰撞。同时,针对所设计的滑模制导律设计了新的自适应律,从而加快了滑模面的收敛速度并且削弱了由符号函数引起的系统抖振现象。基于李雅普诺夫稳定性理论,证明了所设计制导律的正确性,并在最后给出了数学仿真实验,验证了所设计制导律的有效性及优越性。     

考虑目标安全性的最优协同拦截制导律研究

针对目标和其发射的拦截弹对来袭攻击弹进行协同拦截问题,设计了一种最优协同拦截制导律。建立描述目标、攻击弹和拦截弹三者相对运动关系的模型,引入零控脱靶量对模型进行降阶处理。考虑拦截弹对攻击弹的拦截精度、拦截末端时目标的安全性以及目标、拦截弹的控制能量问题,基于攻击弹-拦截弹零控脱靶量、攻击弹-拦截弹终端横向相对运动速度零控脱靶量、目标-攻击弹零控脱靶量以及目标和拦截弹的加速度,建立了性能指标函数,同时考虑目标和拦截弹加速度的有限性,基于极小值原理设计了最优协同拦截制导律。仿真结果表明,相比目标和拦截弹独立飞行的情况,采用协同拦截制导律,在考虑了目标安全性的前提下,机动性较弱的拦截弹能够以较平直的弹道成功拦截攻击弹。     

Three-dimensional cooperative guidance laws against stationary and maneuvering targets

This paper presents the cooperative strategies for salvo attack of multiple missiles based on the classical proportional navigation(PN) algorithm.The three-dimensional(3-D) guidance laws are developed in a quite simple formulation that consists of a PN component for target capture and a coordination component for simultaneous arrival.The centralized algorithms come into effect when the global information of time-to-go estimation is obtained, whereas the decentralized algorithms have better performance when each missile can only collect information from neighbors.Numerical simulations demonstrate that the proposed coordination algorithms are feasible to perform the cooperative engagement of multiple missiles against both stationary and maneuvering targets.The effectiveness of the 3-D guidance laws is also discussed.     

多导弹系统协同攻击机动目标分布式制导律

基于增强型比例导引律和分布式网络同步理论,设计了一类攻击机动目标的多导弹系统分布式协同制导律。该制导律由各导弹本地制导律和分布式协同导引策略两部分组成:本地制导律为增强型比例导引律,进一步利用代数图论和非线性系统一致性理论,得到基于邻接个体信息交互的分布式协同制导律,实现多导弹对目标的同时协同攻击;该分布式协同制导律仅需视距内各相邻导弹间互相传输各自的状态信息,算法具有较低的通信代价和较好的可扩展性。最后给出了相关数值仿真算例,仿真结果验证了算法的有效性。     

带空间协同的多导弹时间协同制导律

针对多导弹在平面内从期望的弹目视线（LOS）相对方向同时击中固定目标问题,提出了一种带空间协同的多导弹时间协同制导律。基于平面内的导弹-目标相对运动方程,建立了带空间协同的多导弹时间协同制导模型;基于多智能体协同控制理论,在视线方向设计了分布式时间协同制导律,可保证所有导弹的打击时刻在有限时间内达到一致,在视线法向方向设计了分布式空间协同制导律,可保证所有导弹的相对视线角在有限时间内收敛到期望值;最后,通过仿真验证了所设计的协同制导律可使多导弹从期望的弹目视线相对方向同时击中目标。