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KUMAR S R , MUKHERJEE D . Deviated pursuit-based nonlinear cooperative salvo guidance using finite-time consensus [J ] . Nonlinear Dynamics , 2021 , 106 ( 1 ): 605 - 630 . DOI: 10.1007/s11071-021-06874-6 http://doi.org/10.1007/s11071-021-06874-6

LI G F , LI Q , WU Y J , et al . Leader-following cooperative guidance law with specified impact time [J ] . Science China-Technological Sciences , 2020 , 63 ( 11 ): 2349 - 2356 . DOI: 10.1007/s11431-020-1669-3 http://doi.org/10.1007/s11431-020-1669-3

YANG X Y , ZHANG Y C , SONG S M . Two-stage cooperative guidance strategy with impact-angle and field-of-view constraints [J ] . Journal of Guidance Control and Dynamics , 2022 , 46 ( 3 ): 590 - 599 . DOI: 10.2514/1.G007040 http://doi.org/10.2514/1.G007040 https://arc.aiaa.org/doi/10.2514/1.G007040 https://arc.aiaa.org/doi/10.2514/1.G007040

SINHA A , KUMAR S R , MUKHERJEE D . Cooperative salvo based active aircraft defense using impact time guidance [J ] . IEEE Control Systems Letters , 2021 , 5 ( 5 ): 1573 - 1578 . DOI: 10.1109/LCSYS.7782633 http://doi.org/10.1109/LCSYS.7782633 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7782633 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7782633

陈中原 , 韦文书 , 陈万春 . 基于强化学习的多发导弹协同攻击智能制导律 [J ] . 兵工学报 , 2021 , 42 ( 8 ): 1638 - 1647 .

CHEN Z Y , WEI W S , CHEN W C . Reinforcement learning-based intelligent guidance law for cooperative attack of multiple missiles [J ] . Acta Armamentarii , 2021 , 42 ( 8 ): 1638 - 1647 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.08.008 http://doi.org/10.3969/j.issn.1000-1093.2021.08.008 A reinforcement learning-based cooperative guidance law utlitizing a deep deterministic policy gradient descent neural network is proposed to achieve the cooperative attack of multiple missiles against a target and improve the attack effectiveness. The estimation equation of time-to-go based on the linear engagement dynamics is revised to improve the estimation accuracy of time-to-go, which is no longer restricted by the assumption of small angle. The time-to-go error of each missile is regarded as the coordination variable. The time-to-go error and range-to-go of each missile are used as the observables of the reinforcement learning algorithm. The reward function is constructed by using miss distance and time-to-go error, and then a reinforcement learning agent is generated by offline training. In the process of closed-loop guidance, the reinforcement learning agent generates guidance commands in real time, by that simultaneous attack can be achieved. Simulated results verify that the proposed reinforcement learning guidance law can achieve simultaneous attack on the target. Compared with the traditional cooperative guidance law, the reinforcement learning cooperative guidance law can be used to obtain smaller miss distances and smaller attack time errors.

CEVHER F Y , LEBLEBICIOĞLU M K . Cooperative guidance law for high-speed and high-maneuverability air targets [J ] . Aerospace , 2023 , 10 ( 2 ): 155 . DOI: 10.3390/aerospace10020155 http://doi.org/10.3390/aerospace10020155 https://www.mdpi.com/2226-4310/10/2/155 https://www.mdpi.com/2226-4310/10/2/155 In this paper, a novel cooperative and predictive guidance law is proposed to intercept high-speed and high-maneuverability targets with inferior interceptors. The purpose of guidance is cooperatively covering the most-probable locations where the target may be in the future. To fulfill this purpose, predicted target states in the form of a probability density function were obtained using limited target information, i.e., noisy position data for one case and maneuverability limits for the second case, at first. Next, the likelihood of the reachable set of interceptors was computed over the predicted target state. Then, to increase the probability of interception in a finite time, the interceptors’ trajectories were adjusted collaboratively depending on the likelihood values. An extensive Monte Carlo study, with practically applicable simulation parameters, was used to demonstrate the effectiveness of the proposed methods against targets in challenging maneuvering modes.

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LI G F , ZUO Z . Robust leader-follower cooperative guidance under false-data injection attacks [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2023 , 59 ( 4 ): 4511 - 4524 . DOI: 10.1109/TAES.2023.3242637 http://doi.org/10.1109/TAES.2023.3242637 https://ieeexplore.ieee.org/document/10038503/ https://ieeexplore.ieee.org/document/10038503/

张友安 , 王星亮 , 吴华丽 , 等 . 带攻击时间约束的导引律综述 [J ] . 海军航空工程学院学报 , 2015 , 30 ( 4 ): 301 - 309 .

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张春妍 , 宋建梅 , 侯博 , 等 . 带落角和时间约束的网络化导弹协同制导律 [J ] . 兵工学报 , 2016 , 37 ( 3 ): 431 - 438 . DOI: 10.3969/j.issn.1000-1093.2016.03.007 http://doi.org/10.3969/j.issn.1000-1093.2016.03.007 对网络化导弹的协同攻击问题进行了带命中落角约束和攻击时间约束的协同偏置比例导引律研究。对单枚导弹给出了带命中落角约束的偏置比例导引律，并推导出了对应的导弹剩余攻击时间的估算表达式。针对网络化导弹系统,根据各导弹的剩余攻击时间之差对偏置比例导引律中的比例系数进行调节，设计得到了同时满足命中落角和攻击时间约束的协同偏置比例导引律，进一步从理论上证明了该导引律能够使多枚导弹的攻击时间趋于一致。网络化导弹制导系统数学仿真实验结果表明，协同偏置比例导引律及剩余攻击时间估算方法是有效和正确的。

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尹依伊 , 王晓芳 , 周健 . 基于Q学习的多无人机协同航迹规划方法 [J ] . 兵工学报 , 2023 , 44 ( 2 ): 484 - 495 . DOI: 10.12382/bgxb.2021.0606 http://doi.org/10.12382/bgxb.2021.0606 针对多无人机同时到达目标的航迹规划问题,建立战场环境模型和单无人机航迹规划的马尔可夫决策模型,基于Q学习算法解算航程最短的最优航迹,应用基于Q学习算法得到的经验矩阵快速解算各无人机的最短航迹并计算协同航程,通过调整绕行无人机的动作选择策略,得到各无人机满足时间协同的航迹组。考虑多无人机的避碰问题,通过设计后退参数确定局部重规划区域,基于深度Q学习理论,采用神经网络替代Q_table对局部多无人机航迹进行重规划,避免维度爆炸问题。对于先前未探明的障碍物,参考人工势场法思想设计障碍物Q矩阵,将其叠加至原Q矩阵,实现无人机的避碰。仿真结果表明:所提基于Q学习的多无人机协同航迹规划算法能够得到时间协同与碰撞避免的协同航迹,并对环境建模时所未探明的障碍物进行躲避;与A^*算法相比,针对在线应用问题,新算法具有更高的求解效率。

YIN Y Y , WANG X F , ZHOU J . Q-learning-based multi-UAV cooperative path planning method [J ] . Acta Armamentarii , 2023 , 44 ( 2 ): 484 - 495 . (in Chinese) DOI: 10.12382/bgxb.2021.0606 http://doi.org/10.12382/bgxb.2021.0606 To solve the path planning problem of multiple UAVs' synchronous arrival at the target, the battlefield environment model and the Markov decision process model of the path planning for a single UAV is established, and the optimal path is calculated based on the Q-learning algorithm. With this algorithm, the Q-table is obtained and used to calculate the shortest path of each UAV and the cooperative range. Then the tim e-coordinated paths is obtained by adjusting the action selection strategy of the circumventing UAVs. Considering the collision avoidance problem of multiple UAVs, the partical replanning area is determined by designing retreat parameters, and based on the deep reinforcement learning theory, the neural network is used to replace Q-table to re-plan the partical path for UAVs, which can avoid the problem of dimensional explosion. As for the previously unexplored obstacles, the obstacle matrix is designed based on the idea of the artificial potential field theory, which is then superimposed on the original Q-table to realize collision avoidance for the unexplored obstacle. The simulation results verify that with the proposed reinforcement learning path planning method, the coordinated paths with time coordination and collision avoidance can be obtained, and the previously unexplored obstacles in the simulation can be avoided as well. Compared with A * algorithm, the proposed method can achieve higher efficiency for online application problems.

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黄伟 , 徐建城 , 吴华兴 , 等 . 基于非数据通信的导弹编队制导律算法 [J ] . 兵工学报 , 2018 , 39 ( 5 ): 910 - 918 . DOI: 10.3969/j.issn.1000-1093.2018.05.010 http://doi.org/10.3969/j.issn.1000-1093.2018.05.010 针对无数据链支持的作战条件下，仅利用导弹主动雷达导引头量测的弹间相对位置和相对速度等参数，基于多智能体一致性理论，提出一种适用于解决领从结构导弹编队队形控制问题的制导律算法。该算法在实现过程中无需各弹之间进行数据通信，即无需弹间数据链传递编队成员的绝对位置信息，就可实现既定队形的收敛和速度一致。应用代数图论证明了闭环制导控制系统的渐进稳定性，并基于坐标变换和导弹运动学方程，建立了编队控制过程中所需的导弹控制力模型。仿真结果表明该算法有效，适用于导弹编队系统的总体设计。

HUANG W , XU J C , WU H X , et al . Missile formation guidance algorithm independent of data communication [J ] . Acta Armamentarii , 2018 , 39 ( 5 ): 910 - 918 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2018.05.010 http://doi.org/10.3969/j.issn.1000-1093.2018.05.010 To solve the control problem of missile formation without support of weapon data-link, a new guidance algorithm for systems grouped by the leader-follower structure based on multi-agent consensus theory is proposed, which only requires the motion parameters, such as relative distance and relative speed among missiles, which can be measured by the followers’ active radar seeker. The proposed algorithm needs no data communication among missiles and absolute positions of formation members, but can make all members approach to ideal positions and consistent velocity simultaneously. Algebraic graph theory is employed to prove the asymptotic stability of closed loop control system, and a model of required force for missile formation control is built based on coordinate conversion and missile motion equation. Simulated results are used to verify the validity of the proposed algorithm and its application prospect for general design of missile formation system. Key

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