董希旺 , 于江龙 , 化永朝 , 等 . 多飞行器攻击时间一致性协同制导进展综述与展望 [J ] . 北京航空航天大学学报 , 2022 , 48 ( 9 ): 1836 - 1844 .

DONG X W , YU J L , HUA Y Z , et al . Review and prospect of cooperative guidance with attack time consensus for multiple aerial vehicles [J ] . Journal of Beijing University of Aeronautics and Astronautics , 2022 , 48 ( 9 ): 1836 - 1844 . (in Chinese)

YOU H , CHANG X L , ZHAO J F , et al . Three-dimensional impact-angle-constrained cooperative guidance strategy against maneuvering target [J ] . ISA Transactions , 2023 , 138 : 262 - 280 . DOI: 10.1016/j.isatra.2023.02.030 http://doi.org/10.1016/j.isatra.2023.02.030 In order to improve the multiple-missile cooperative attack capability and penetration capability, this paper investigates two three-dimensional impact-angle-constrained cooperative guidance strategies against maneuvering target for controllable thrust missiles. First, a three-dimensional nonlinear guidance model is established that does not assume small missile lead angles in the guidance process. Second, in the line-of-sight (LOS) direction of the cluster cooperative guidance strategy, the proposed guidance algorithm transforms the simultaneous attack problem into a second-order multiagent consensus problem, which effectively solves the practical problem of low guidance precision provoked by the time-to-go estimation. Then, by combining second-order sliding mode control (SMC) and nonsingular terminal SMC theory, the guidance algorithms in the normal and lateral directions to the LOS are designed, respectively, so that the multi-missile can accurately attack a maneuvering target while satisfying the impact angle constraints. Finally, by utilizing the second-order multiagent consensus tracking control in the leader-following cooperative guidance strategy, a novel leader-following time consistency algorithm is investigated to ensure that the leader and followers can attack the maneuvering target simultaneously. Moreover, the stability of the investigated guidance algorithms is proved mathematically. The effectiveness and superiority of the proposed cooperative guidance strategies are verified by numerical simulations.Copyright © 2023 ISA. Published by Elsevier Ltd. All rights reserved.

CHEN Z Y , CHEN W C , LIU X M , et al . Three-dimensional fixed-time robust cooperative guidance algorithm for simultaneous attack with impact angle constraint [J ] . Aerospace Science and Technology , 2021 , 110 : 106523 . DOI: 10.1016/j.ast.2021.106523 http://doi.org/10.1016/j.ast.2021.106523 https://linkinghub.elsevier.com/retrieve/pii/S1270963821000353 https://linkinghub.elsevier.com/retrieve/pii/S1270963821000353

LI H X , LI H J , CAI Y L . Three-dimensional cooperative guidance law to control impact time and angle with fixed-time convergence [J ] . Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering , 2022 , 236 ( 8 ): 1647 - 1666 . DOI: 10.1177/09544100211043093 http://doi.org/10.1177/09544100211043093 http://journals.sagepub.com/doi/10.1177/09544100211043093 http://journals.sagepub.com/doi/10.1177/09544100211043093 This article proposes a new terminal cooperative guidance law to control both impact time and impact angle in three-dimensional engagement. The presented guidance law employs on and normal line-of-sight accelerations to control the impact time and angle together. Two parts are included in this guidance law, that is, the guidance laws with impact time constraint and impact angle constraint. The first is designed based on fixed-time consensus theory to fulfill the salvo attack of the target, and the second is developed based on fixed-time nonsingular fast terminal sliding mode control method to achieve the desired impact angles. The stability analysis of this guidance law based on Lyapunov theory is also presented in detail. Moreover, the maneuvering target can be intercepted successfully with the presented guidance law, and the fixed-time stability and less control energy are well ensured. Additionally, the effectiveness and applicability of the proposed guidance scheme are explicitly verified through simulation tests.

JEON I S , LEE J I , TAHK M J . Impact-time-control guidance law for anti-ship missiles [J ] . IEEE Transactions on Control Systems Technology , 2006 , 14 : 260 - 266 . DOI: 10.1109/TCST.2005.863655 http://doi.org/10.1109/TCST.2005.863655 https://ieeexplore.ieee.org/document/1597196/ https://ieeexplore.ieee.org/document/1597196/

LEE C H , RYU M Y . Practical generalized optimal guidance law with impact angle constraint [J ] . Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering , 2019 , 233 : 3790 - 3809 . DOI: 10.1177/0954410018807000 http://doi.org/10.1177/0954410018807000 http://journals.sagepub.com/doi/10.1177/0954410018807000 http://journals.sagepub.com/doi/10.1177/0954410018807000 In this paper, we provide a practical solution to the generalized optimal guidance problem with an impact angle constraint. The optimal guidance problem with arbitrary weighting functions is extended to explicitly consider a missile dynamic lag effect as well as a missile velocity variation. Therefore, compared to existing results, the proposed result can prevent performance degradation due to the dynamic lag effect and the velocity variation, which is an essential issue in practice. Besides, since the proposed guidance law is formulated from the generalized optimal control framework, it can directly inherit a vital feature of the framework: providing an additional degree of freedom in shaping a guidance command for achieving a specific guidance operational goal. An illustrative example is provided in order to validate this property. In this study, the proposed solution is also compared with the existing solutions. The comparison results indicate that the proposed result is a more general and practical solution. Finally, numerical simulations are also conducted to demonstrate the practical significance of the proposed method.

JEON I S , LEE J I , TAHK M J . Impact-time-control guidance with generalized proportional navigation based on nonlinear formulation [J ] . Journal of Guidance, Control, and Dynamics , 2016 , 39 : 1887 - 1892 .

DHANANJAY N , GHOSE D . Accurate time-to-go estimation for proportional navigation guidance [J ] . Journal of Guidance, Control, and Dynamics , 2015 , 37 ( 4 ): 1378 - 1383 . DOI: 10.2514/1.G000082 http://doi.org/10.2514/1.G000082 https://arc.aiaa.org/doi/10.2514/1.G000082 https://arc.aiaa.org/doi/10.2514/1.G000082

WANG C Y , YU H S , DONG W . Three-dimensional impact angle and time control guidance law based on two-stage strategy [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2023 , 58 ( 6 ): 5361 - 5372 . DOI: 10.1109/TAES.2022.3169124 http://doi.org/10.1109/TAES.2022.3169124 https://ieeexplore.ieee.org/document/9761742/ https://ieeexplore.ieee.org/document/9761742/

ERER K S , TEKIN R . Impact time and angle control based on constrained optimal solutions [J ] . Journal of Guidance, Control, and Dynamics , 2016 , 39 ( 10 ): 2445 - 2451 .

SINHA A , KUMAR S R . Super-twisting control-based cooperative salvo guidance using leader-follower approach [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2020 , 56 ( 5 ): 3556 - 3565 . DOI: 10.1109/TAES.7 http://doi.org/10.1109/TAES.7 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7

ZHANG S , GUO Y , LIU Z G , et al . Finite-time cooperative guidance strategy for impact angle and time control [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2021 , 57 ( 2 ): 806 - 819 . DOI: 10.1109/TAES.2020.3037958 http://doi.org/10.1109/TAES.2020.3037958 https://ieeexplore.ieee.org/document/9266104/ https://ieeexplore.ieee.org/document/9266104/

FANG F , CAI Y L . Optimal cooperative guidance with guaranteed miss distance in three-body engagement [J ] . Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering , 2018 , 232 ( 3 ): 492 - 504 . DOI: 10.1177/0954410016683416 http://doi.org/10.1177/0954410016683416 http://journals.sagepub.com/doi/10.1177/0954410016683416 http://journals.sagepub.com/doi/10.1177/0954410016683416 The three-body engagement where a target aircraft protects itself by using a cooperative defender missile to intercept an attacking missile is investigated. It is formulated as a constrained linear quadratic optimal problem. Two different optimal cooperative guidance laws for the target and defender are proposed in two cooperation schemes. Since any control effort to reduce the miss distance to smaller than missile’s lethal radius is wasted, the guidance laws are derived to achieve an upper bound on the missile–defender miss distance. In the two-way cooperation scheme, the target and the defender act as a team. How the target makes a trade-off between aiding the defender and evading the missile is investigated by considering both the missile–target zero-effort miss distance and the control effort into the cost function. Without the penalty weight on the missile–target zero-effort miss distance, the two-way minimum control effort guidance laws are available. In the one-way cooperation scheme, the target uses a known evasion strategy independently. The optimal cooperative guidance law is derived for minimizing the control effort of the defender. Simulation results show that these proposed guidance laws can provide a specified missile–defender miss distance and save the control effort compared with the zero-miss-distance guidance law. Two-way cooperation scheme outperforms one-way cooperation scheme.

SONG J H , SONG S M , XU S L . Three-dimensional cooperative guidance algorithm for multiple missiles with finite-time convergence [J ] . Aerospace Science and Technology , 2017 , 67 : 193 - 205 . DOI: 10.1016/j.ast.2017.04.007 http://doi.org/10.1016/j.ast.2017.04.007 https://linkinghub.elsevier.com/retrieve/pii/S1270963816308136 https://linkinghub.elsevier.com/retrieve/pii/S1270963816308136

LÜ T , LI C J , GUO Y . Three-dimensional finite-time cooperative guidance for multiple missiles without radial velocity measurements [J ] . Chinese Journal of Aeronautics , 2019 ( 5 ): 1294 - 1304 .

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 . DOI: 10.1016/j.ast.2022.107450 http://doi.org/10.1016/j.ast.2022.107450 https://linkinghub.elsevier.com/retrieve/pii/S1270963822001249 https://linkinghub.elsevier.com/retrieve/pii/S1270963822001249

ZHANG P , ZHANG X Y . Multiple missiles fixed-time cooperative guidance without measuring radial velocity for maneuvering targets interception [J ] . ISA Transactions , 2022 , 126 : 388 - 397 . DOI: 10.1016/j.isatra.2021.07.023 http://doi.org/10.1016/j.isatra.2021.07.023 https://linkinghub.elsevier.com/retrieve/pii/S0019057821003906 https://linkinghub.elsevier.com/retrieve/pii/S0019057821003906

WANG C Y , DONG W , WANG J N , et al . Impact-angle-constrained cooperative guidance for salvo attack [J ] . Journal of Guidance, Control, and Dynamics , 2022 , 45 ( 4 ): 684 - 703 . DOI: 10.2514/1.G006342 http://doi.org/10.2514/1.G006342 https://arc.aiaa.org/doi/10.2514/1.G006342 https://arc.aiaa.org/doi/10.2514/1.G006342

宋俊红 . 拦截机动目标的有限时间制导律及多弹协同制导律研究 [D ] . 哈尔滨 : 哈尔滨工业大学 , 2018 .

SONG J H . Research on finite-time guidance law and cooperative guidance law of multi-missiles for intercepting maneuvering target [D ] . Harbin : Harbin Institute of Technology , 2018 . (in Chinese)

ZHAO S Y , ZHOU R , WEI C , et al . Design of time constrained guidance laws via virtual leader approach [J ] . Chinese Journal of Aeronautics , 2010 , 23 ( 1 ): 103 - 108 . DOI: 10.1016/S1000-9361(09)60193-X http://doi.org/10.1016/S1000-9361(09)60193-X https://linkinghub.elsevier.com/retrieve/pii/S100093610960193X https://linkinghub.elsevier.com/retrieve/pii/S100093610960193X

马国欣 , 张友根 , 张友安 . 领弹控制下的多导弹时间协同三维制导律 [J ] . 海军航空工程学院学报 , 2013 , 28 ( 1 ): 11 - 16 .

MA G X , ZHANG Y G , ZHANG Y A . Three-dimensional guidance law for time-cooperative multi-missiles [J ] . Journal of Naval Aeronautical and Astronautical University , 2013 , 28 ( 1 ): 11 - 16 . (in Chinese)

王晓芳 , 张艺伟 , 田震 . 分布式通信模式下的多导弹协同制导与控制律 [J ] . 北京理工大学学报 , 2018 , 38 ( 6 ): 593 - 599 .

WANG X F , ZHANG Y W , TIAN Z . Cooperative guidance and control law based on decentralized communication topology [J ] . Transactions of Beijing Institute of Technology , 2018 , 38 ( 6 ): 593 - 599 . (in Chinese)

林德福 , 何绍溟 , 王江 , 等 . 基于虚拟领弹-从弹的集群分布式协同制导技术研究 [J ] . 中国科学:技术科学 , 2020 , 50 ( 5 ): 506 - 515 .

LIN D F , HE S M , WANG J , et al . On virtual leader-follower-based distributed cooperative swarm guidance strategy [J ] . Science China Technological Sciences , 2020 , 50 ( 5 ): 506 - 515 . (in Chinese)

LI G F , LIU 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 . DOI: 10.1016/j.jfranklin.2021.06.030 http://doi.org/10.1016/j.jfranklin.2021.06.030 https://linkinghub.elsevier.com/retrieve/pii/S0016003221003914 https://linkinghub.elsevier.com/retrieve/pii/S0016003221003914

LIN M , DING X J , WANG C Y , et al . Three-dimensional fixed-time cooperative guidance law with impact angle constraint and prespecified impact time [J ] . IEEE Access , 2021 , ( 9 ): 29755 - 29763 .

李国飞 , 李博皓 , 吴云洁 , 等 . 多群组飞行器攻击时间控制协同制导方法 [J ] . 宇航学报 , 2023 , 44 ( 1 ): 110 - 118 .

LI G F , LI B H , WU Y J , et al . Cooperative guidance law with impact time control for clusters of flight vehicles [J ] . Journal of Astronautics , 2023 , 44 ( 1 ): 110 - 118 . (in Chinese)

WANG X H , TAN C P . 3-D impact angle constrained distributed cooperative guidance for maneuvering targets without angular-rate measurements [J ] . Control Engineering Practice , 2018 , 78 : 142 - 159 . DOI: 10.1016/j.conengprac.2018.06.014 http://doi.org/10.1016/j.conengprac.2018.06.014 https://linkinghub.elsevier.com/retrieve/pii/S0967066118301904 https://linkinghub.elsevier.com/retrieve/pii/S0967066118301904

WANG X H , LU X . Three-dimensional impact angle constrained distributed guidance algorithm design for cooperative attacks [J ] . ISA Transactions , 2018 , 73 : 79 - 90 . DOI: 10.1016/j.isatra.2017.12.009 http://doi.org/10.1016/j.isatra.2017.12.009 https://linkinghub.elsevier.com/retrieve/pii/S0019057817306250 https://linkinghub.elsevier.com/retrieve/pii/S0019057817306250

KUMAR S R , RAO S , GHOST D . Nonsingular terminal sliding mode guidance with impact angle constraints [J ] . Journal of Guidance, Control, and Dynamics , 2014 , 37 ( 4 ): 1114 - 1130 . DOI: 10.2514/1.62737 http://doi.org/10.2514/1.62737 https://arc.aiaa.org/doi/10.2514/1.62737 https://arc.aiaa.org/doi/10.2514/1.62737

BISWAS B , MAITY A , KUMAR S R . Finite-time convergent three-dimensional nonlinear intercept angle guidance [J ] . Journal of Guidance, Control, and Dynamics , 2020 , 43 ( 1 ): 146 - 153 . DOI: 10.2514/1.G004454 http://doi.org/10.2514/1.G004454 https://arc.aiaa.org/doi/10.2514/1.G004454 https://arc.aiaa.org/doi/10.2514/1.G004454

YU S H , LONG X J . Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode [J ] . Automatica , 2015 , 54 : 158 - 165 . DOI: 10.1016/j.automatica.2015.02.001 http://doi.org/10.1016/j.automatica.2015.02.001 https://linkinghub.elsevier.com/retrieve/pii/S0005109815000540 https://linkinghub.elsevier.com/retrieve/pii/S0005109815000540