张振林 , 张科 , 郭正玉 , 等 . 一种新型领从式多弹协同制导律设计 [J ] . 航空兵器 , 2020 , 27 ( 5 ): 33 - 38 .

ZHANG Z L , ZHANG K , GUO Z Y , et al. Design of a new guidance law for guided multiple missiles [J ] . Aero Weaponry , 2020 , 27 ( 5 ): 33 - 38 . (in Chinese)

LI G F , LÜ J H , ZHU G L , et al. Distributed observer-based cooperative guidance with appointed impact time and collision avoidance [J ] . Journal of the Franklin Institute , 2021 , 358 ( 14 ): 6976 - 6993 .

李文 , 尚腾 , 姚寅伟 , 等 . 速度时变情况下多飞行器时间协同制导方法研究 [J ] . 兵工学报 , 2020 , 41 ( 6 ): 1096 - 1110 . DOI: 10.3969/j.issn.1000-1093.2020.06.006 http://doi.org/10.3969/j.issn.1000-1093.2020.06.006 针对无动力飞行器在速度时变情况下的同时攻击问题，提出基于非线性扩张状态观测器的分布式时间协同三维制导方法。定义飞行器的总前置角以推导简化的相对运动方程，并选取飞行器与目标的相对距离和接近速度为协调变量。考虑实际中飞行器速度时变的情况，把速度变化率建模误差及外界干扰作为扰动，弥补了已有方法对速度严格限制为常速的不足。为了估计系统扰动，设计非线性扩张状态观测器，并证明了带扰动估计的一致性控制协议可以保证多飞行器系统攻击时间的有界一致性。基于该控制协议的时间协同制导律由于在飞行器速度方向与视线方向之间始终存有夹角，当时间协同基本达成时切换成前置角有限时间收敛制导律，以保证最终的制导精度和攻击效果，两种制导律采用模糊逻辑规则平滑连接。通过仿真实验验证了所提制导方法的有效性以及优势。

LI W , SHANG T , YAO Y W , et al. Research on time-cooperative guidance of multiple flight vehicles with time-varying velocity [J ] . Acta Armamentarii , 2020 , 41 ( 6 ): 1096 - 1110 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.06.006 http://doi.org/10.3969/j.issn.1000-1093.2020.06.006 A distributed time-cooperative three-dimensional guidance method based on nonlinear extended state observer is proposed for the simultaneous attack of powerless flight vehicles with time-varying velocity. The complex leading angle of flight vehicle is defined to deduce the simplified relative motion equation，and the relative distances between flight vehicle and target and the approaching velocity are selected as the coordination variables. Considering the time-varying velocity of flight vehicle in practical situation, the modeling error of velocity change rate and the external interference are taken as the disturbance, which make up for the shortcomings of the existing methods that restrict the velocity strictly to a constant velocity. The nonlinear extended state observer is designed to estimate system disturbances, and the consensus control protocol with disturbance estimation is demonstrated to guarantee the bounded consensus of all flight vehicles' attack times. For an angle between the velocity direction and the line of sight direction always existing in the time-cooperative guidance law based on the control protocol, the time-cooperative guidance law is switched to the finite-time convergent guidance law to ensure the final guidance accuracy and attack effect when simultaneous attack is basically realized, and the fuzzy logic rules are used to achieve the smooth connection of the two guidance laws. The effectiveness and advantages of the proposed distributed time-cooperative guidance method are verified by using the simulated results. Key

于航 , 李清玉 , 戴可人 , 等 . 三维自适应固定时间多导弹协同制导律 [J ] . 兵工学报 , 2024 , 45 ( 8 ): 2646 - 2657 . DOI: 10.12382/bgxb.2023.0640 http://doi.org/10.12382/bgxb.2023.0640 针对三维空间内多导弹对机动目标同时攻击的问题,提出一种具有自适应律的三维多导弹固定时间协同制导律。建立三维空间导弹-目标动力学模型,以弹目视线方向和其垂直方向设计制导律,可保证剩余飞行时间和法向速度在固定时间内完成一致性收敛。采用自适应律来跟踪机动目标运动参数策略,提高多导弹系统的稳定性与对机动目标的打击精度。改进多导弹系统收敛条件,所设计的制导律具备了对攻击时间的约束能力。向制导律中加入饱和函数,避免因符号函数带来的系统抖振。通过仿真实验验证所提固定时间协同制导律的有效性及对抗通信拓扑切换的鲁棒性。实验结果表明:相较于对比文献所设计的制导律具有系统快速收敛以及高精度。

YU H , LI Q Y , DAI K R , et al. Three-dimensional adaptive fixed-time multi-missile cooperative guidance law [J ] . Acta Armamentarii , 2024 , 45 ( 8 ): 2646 - 2657 . (in Chinese) DOI: 10.12382/bgxb.2023.0640 http://doi.org/10.12382/bgxb.2023.0640 An adaptive fixed-time cooperative guidance law is proposed for multiple missiles simultaneously attacking a maneuvering target in three-dimensional space. A 3-D missile-target dynamics model is established, and the adaptive guidance law are designed based on the line of sight (LOS) direction and its vertical direction. This ensures that the remaining flight time and normal velocity converge consistently within a fixed time. The adaptive guidance law are employed to track the motion parameters of maneuvering targets, thus enhancing the stability of multiple missile system and its strike accuracy against the maneuvering targets. The convergence conditions of the multiple missile system are improved, and the designed guidance law possess the capability to constrain the attack time. Saturated functions are introduced into the guidance law to avoid system oscillations caused by the sign function. The effectiveness of the proposed fixed-time cooperative guidance law and its robustness against communication topology switches are validated through simulation experiment. The experimental results indicate that, compared to the guidance law designed in the reference literatures, the proposed guidance law exhibit rapid system convergence and high accuracy.

李军 , 廖宇新 , 李珺 , 等 . 三维多变量超螺旋固定时间滑模制导律 [J ] . 电光与控制 , 2020 , 27 ( 10 ): 47 - 52 ,61.

LI J , LIAO Y X , LI J , et al. Three-dimensional multivariable super-twisting fixed-time sliding mode guidance law [J ] . Electronics Optics & Control , 2020 , 27 ( 10 ): 47 - 52 ,61. (in Chinese)

李贵栋 , 陆海英 , 李志维 , 等 . 一种改进的带角度约束最优制导律 [J ] . 现代防御技术 , 2022 , 50 ( 5 ): 52 - 58 . DOI: 10.3969/j.issn.1009-086x.2022.05.008 http://doi.org/10.3969/j.issn.1009-086x.2022.05.008 为了实现拦截任务需求,考虑拦截弹的角度约束以及能量过早损失而不能满足后续拦截需求，推导了一种改进的最优制导律。基于能量最小目标函数结构，提出一种使初始段需用过载尽量小且终端视线角能收敛到期望值的控制权函数；基于小角度假设，采用最优控制理论，推导了带视线角约束的最优制导律；基于制导律能使终端视线角收敛的特点，将带终端视线角问题转换为终端交会角问题，得到带终端交会角约束的最优制导律。仿真结果表明，所设计的制导律能实现终端交会角控制，同时能保证制导初始段能量消耗较小，且命中精度较高。所设计的方法对拦截弹的最优制导律研究具有一定参考和应用价值。

LI G D , LU H Y , LI Z W , et al. An improved optimal guidance law with angle constraint [J ] . Modern Defence Technology , 2022 , 50 ( 5 ): 52 - 58 . (in Chinese)

LI X J , MA J W , GAO J W , et al. Adaptive super-twisting cooperative guidance law with fixed-time convergence [J ] . International Journal of Aerospace Engineering , 2022 , 2022 : 8650592 .

YU H , DAI K R , LI H J , et al. Three-dimensional adaptive fixed-time cooperative guidance law with impact time and angle constraints [J ] . Aerospace Science and Technology , 2022 , 123 : 107450 .

ZHANG M J , MA J J , CHE R , et al. Fixed-time convergence cooperative guidance law against maneuvering target [C ] //YAN L,DUAN H B,YU X.Advances in Guidance,Navigation and Control. Singapore:Springer , 2022 : 3975 - 3986 .

王伟 , 于之晨 , 林时尧 , 等 . 针对机动目标的三维领从协同制导律 [J ] . 兵工学报 , 2024 , 45 ( 10 ): 3538 - 3554 . DOI: 10.12382/bgxb.2023.0777 http://doi.org/10.12382/bgxb.2023.0777 针对多飞行器协同拦截机动目标的实际需求,提出一种三维领从时空协同制导律。在视线方向上,基于齐次度理论和固定时间稳定理论设计一种领从协同制导律,确保从飞行器与领飞行器的相对距离和相对速度在固定时间内趋于一致,并且给出一致性误差收敛时间的上界,实现多飞行器的同时刻拦截。在视线法向上为实现以特定的碰撞角度拦截目标,设计一种固定时间收敛的非奇异终端滑模制导律,实现攻击角度的固定时间收敛,并避免了制导指令奇异引起的控制饱和问题。考虑到目标的机动对制导系统产生的不利影响,引入固定时间扰动观测器对目标加速度进行前馈补偿。运用李雅普诺夫稳定性理论来证明系统的固定时间稳定特性。通过仿真实验验证所设计制导律可以有效控制多飞行器在领从框架下同时打击机动目标,并以期望的终端角度攻击目标。

WANG W , YU Z C , LIN S Y , et al. Three-dimensional leader-follower cooperative guidance law with maneuvering target [J ] . Acta Armamentarii , 2024 , 45 ( 10 ): 3538 - 3554 . (in Chinese) DOI: 10.12382/bgxb.2023.0777 http://doi.org/10.12382/bgxb.2023.0777 In response to the actual need for coordinated interception of multiple flight vehicle targets, this paper presents a three-dimensional spatio-temporal coordinative guidance law. Firstly, a leader-follower cooperative guidance law is developed based on the homogeneity theory and the fixed-time stability theory. This law ensures that the relative distance and relative velocity between the follower and the leader converge to a consistent value within a fixed time, respoectively. Furthermore, an upper bound for the convergence time of consistency error is provided to enable the simultaneous interception of multiple flight vehicles. Secondly, a non-singular terminal sliding mode guidance law with fixed time convergence is proposed to intercept the target with a specific collision angle in the normal direction of the line of sight. This law achieves the fixed time convergence of attack angle and mitigates the control saturation problem caused by the singularity of guidance command. Additionally, a fixed-time disturbance observer is introduced to compensate for the effects of the target's maneuvering on the guidance system. This observer performs feedforward compensation for the target acceleration. Finally, the Lyapunov stability theory is employed to prove the fixed-time stability properties of the system. The simulated results show that the proposed guidance law can be used to effectively control multiple aircrafts to attack the maneuvering targets at the same time under the leader-follower framework, and attack the targets at the desired terminal angle.

于江龙 , 董希旺 , 李清东 , 等 . 拦截机动目标的分布式协同围捕制导方法 [J ] . 航空学报 , 2022 , 43 ( 9 ): 325817 . DOI: 10.7527/S1000-6893.2021.25817 http://doi.org/10.7527/S1000-6893.2021.25817 研究了多领导者-多跟随者模式下多飞行器协同拦截机动目标的分布式协同围捕制导问题。借鉴狼群协同围捕大机动猎物的行为学机理,在数学层面抽象出领-从模式协同制导架构、分布式通信与状态估计以及多路多方向协同围捕制导律3种映射策略。首先,针对领-从模式协同制导架构,提出了多领导者-多跟随者协同围捕方案。其次,针对多领导者飞行器,设计带有目标不确定机动补偿的协同逆轨拦截制导律,为跟随者飞行器提供有利的围捕拦截参考轨迹。再次,针对多跟随者,利用分布式状态观测器对多领导者状态轨迹凸组合进行估计,进而设计了时变围捕视线角编队跟踪制导律,引入动态增益补偿系统来解决最大可用过载受限问题。然后,证明了闭环系统稳定性,并给出了协同制导可行性分析结论。最后,对理论结果进行仿真验证,结果显示,多飞行器在目标逃逸方向两侧形成一定散布的围捕构型,即存在若干飞行器的末制导拦截阵位是合适的,提高了对机动目标的拦截效能。

YU J L , DONG X W , LI Q D , et al. Distributed cooperative encirclement hunting guidance method for intercepting maneuvering target [J ] . Acta Aeronauticaet et Astronautica Sinica , 2022 , 43 ( 9 ): 325817 (in Chinese)

王翰 , 姜吉祥 , 程林 , 等 . 基于覆盖控制的多机动目标合围拦截制导方法 [J ] . 飞行力学 , 2024 , 42 ( 5 ): 64 - 71 .

WANG H , JIANG J X , CHENG L , et al. Cooperative encirclement guidance strategy for intercepting multiple maneuverable targets [J ] . Flight Dynamics , 2024 , 42 ( 5 ): 64 - 71 . (in Chinese)

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SHI H , ZHU J H . Optimal cooperative prediction guidance law for active defense [J ] . Aerospace Control and Application , 2019 , 45 ( 4 ): 64 - 70 . (in Chinese)

WANG C Y , DING X J , WANG J N , et al. A robust three-dimensional cooperative guidance law against maneuvering target [J ] . Journal of the Franklin Institute , 2020 , 357 ( 10 ): 5735 - 5752 .

尤浩 , 常新龙 , 赵久奋 , 等 . 带攻击角度约束的三维领弹-从弹时间协同制导律 [J ] . 兵工学报 , 2023 , 44 ( 11 ): 3369 - 3381 . DOI: 10.12382/bgxb.2023.0174 http://doi.org/10.12382/bgxb.2023.0174 针对多导弹在三维空间以期望角度协同攻击机动目标的问题,提出一种三维领弹-从弹时间协同制导律。根据弹目相对运动关系建立领弹-从弹三维非线性协同制导模型,无需小角度假设;在视线法向和侧向上,基于2阶滑模控制理论和设计的有限时间收敛滑模面,分别设计领弹-从弹三维角度控制制导律,在提高系统收敛速度的同时抑制了抖振现象;在从弹视线方向上提出时间协同制导律,创新性地将领弹-从弹协同制导问题转化为2阶多智能体一致性跟踪控制问题,充分利用导弹间的信息交互,在实现从弹和领弹时间协同的同时避免传统的剩余时间估计造成的误差问题;同时对新算法分别进行严格的Lyapunov稳定性证明。仿真结果表明:新的三维领弹-从弹时间协同制导律可以有效控制领弹和从弹在三维空间以期望角度高精度协同攻击机动目标。

YOU H , CHANG X L , ZHAO J F , et al. Three-dimensional leader-follower cooperative guidance law with impact angle constraints [J ] . Acta Armamentarii , 2023 , 44 ( 11 ): 3369 - 3381 . (in Chinese) DOI: 10.12382/bgxb.2023.0174 http://doi.org/10.12382/bgxb.2023.0174 A three-dimensional leader-follower cooperative guidance law is proposed for the salvo attack of multiple missiles against a maneuvering target with the desired angles of impact. A three-dimensional nonlinear guidance model for the multiple missiles is established based on the relative motion relationship of missile and target, in which it is not necessary to assum a small lead angle. The three-dimensional guidance laws of leader and followers in the normal and lateral directions to the LOS are designed, respectively, based on the second-order sliding mode control (SMC) theory and designed finite-time convergence SMC surface, which can improve the system convergence speed while suppressing chattering phenomenon. The proposed guidance law innovatively transforms the time consistency problem of the leader-following missiles into a second-order multiagent consensus tracking in the LOS direction of the followers, which achieves the time consistency of leader and followers and, effectively solves the practical problem of low guidance precision caused by the time-to-go estimation. Moreover, the proposed guidance algorithms are proved by strict Lyapunov stability, respectively. The simulated results show that the proposed three-dimensional leader-follower cooperative guidance law can effectively control the leader and followers to attack a maneuvering target with high precision at the desired angles of attack.

WANG S B , GUO Y , WANG S C , et al. Cooperative interception with fast multiple model adaptive estimation [J ] . Defence Technology , 2021 , 17 ( 6 ): 1905 - 1917 . DOI: 10.1016/j.dt.2020.11.001 http://doi.org/10.1016/j.dt.2020.11.001 For the case that two pursuers intercept an evasive target, the cooperative strategies and state estimation methods taken by pursuers can seriously affect the guidance accuracy for the target, which performs a bang For the case that two pursuers intercept an evasive target, the cooperative strategies and state estimation methods taken by pursuers can seriously affect the guidance accuracy for the target, which performs a bang-bang evasive maneuver with a random switching time. Combined Fast multiple model adaptive estimation (Fast MMAE) algorithm, the cooperative guidance law takes detection configuration affecting the accuracy of interception into consideration. Introduced the detection error model related to the line-of-sight (LOS) separation angle of two interceptors, an optimal cooperative guidance law solving the optimization problem is designed to modulate the LOS separation angle to reduce the estimation error and improve the interception performance. Due to the uncertainty of the target bang-bang maneuver switching time and the effective fitting of its multi-modal motion, Fast MMAE is introduced to identify its maneuver switching time and estimate the acceleration of the target to track and intercept the target accurately. The designed cooperative optimal guidance law with Fast MMAE has better estimation ability and interception performance than the traditional guidance law and estimation method via Monte Carlo simulation. © 2021 China Ordnance Society

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张友安 , 马培蓓 . 带有攻击角度和攻击时间控制的三维制导 [J ] . 航空学报 , 2008 , 29 ( 4 ): 1020 - 1026 . 在三维空间导引动力学与运动学模型的基础上，假设目标静止，而导弹本身以恒速运动，根据实际的攻击角度与设定的攻击角度误差，分析和设计了期望的视线（LOS）角运动学，基于李雅普诺夫稳定性理论设计了带有攻击角度控制的三维导弹导引律。为了对攻击时间进行预测与控制，假设导弹本身以恒速或者匀加/减速运动，先将导弹导引到预定的攻击角度上，根据待飞直线距离对待飞时间进行估算，再根据预测时间误差，确定导弹按照特定的圆弧轨迹机动飞行的指令和机动飞行的时间，通过机动飞行来对时间误差进行补偿，最后，再利用所设计的导引律攻击目标。给出了仿真结果。

ZHANG Y A , MA P B . Three-dimensional Guidance Law with Impact Angle and Impact Time Constraints [J ] . Acta Aeronauticaet Astronautica Sinica , 2008 , 29 ( 4 ): 1020 - 1026 . (in Chinese)

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王晓芳 , 洪鑫 , 林海 . 一种控制多弹协同攻击时间和攻击角度的方法 [J ] . 弹道学报 , 2012 , 24 ( 2 ): 1 - 5 ,24. 为了提高导弹的突防及精确打击能力,提出一种对协同作战的导弹进行攻击角度和攻击时间控制的方法.选取一枚导弹作为领弹,以目标为球心,以领弹距目标的距离为半径构造虚拟球体,根据从弹的理想攻击角在虚拟球体上确定从弹所对应的虚拟点.建立从弹与虚拟点的相对运动模型,然后基于最优控制理论设计了状态调节器,控制从弹逼近且跟踪虚拟点,最后实现几枚导弹攻击时间和攻击角度的协同.为了降低对从弹需用过载的要求,对虚拟点的轨迹进行了改进设计.仿真结果表明,所提出的控制方法及对虚拟点轨迹的改进设计是有效的.

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XIAO W , YU J L , DONG X W , et al. Cooperative interception against highly maneuvering target with acceleration constraints [J ] . Acta Aeronautica et Astronautica Sinica , 2020 , 41 ( S1 ): 723777 (in Chinese) DOI: 10.7527/S1000-6893.2019.23777 http://doi.org/10.7527/S1000-6893.2019.23777 In this paper, the cooperative interception of multiple inferior missiles with acceleration constraints to intercept a highly maneuvering target is studied using the nonlinear interception geometry. Firstly, based on the establishment of the reachable region of the missile, the feasible region of the missile, and the escape region of the target, a cooperative interception strategy based on the coverage of escape region using nonlinear interception geometry and a design method based on the standard trajectory are proposed. Secondly, after giving the form of co-operative guidance law, the relationship between the initial position of the terminal guidance phase, the parameters of the guidance law, and the coverage area of the maneuvering range of the target is studied. A numerical algorithm is designed to realize the allocation of the coverage area, the design of the cooperative guidance law, and the configuration of the initial interception position. Finally, the theoretical results are simulated. The results show that multiple missiles with weak maneuverability can intercept highly maneuvering target through a reasonable configuration of the initial interception position and a reasonable design of parameters in the cooperative guidance law.

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