魏明英 , 崔正达 , 李运迁 . 多弹协同拦截综述与展望 [J ] . 航空学报 , 2020 , 41 ( 增刊1 ): 723804 .

WEI M Y , CUI Z D , LI Y Q . Review and future development of multi-missile coordinated interception [J ] . Acta Aeronautica et Astronautica Sinica , 2020 , 41 ( S1 ): 723804 . (in Chinese) DOI: 10.7527/S1000-6893.2019.23804 http://doi.org/10.7527/S1000-6893.2019.23804 Multi-missile coordination is an important direction of missile development in the future. According to the coordination effect, multi-missile coordination includes coordinated attack, coordinated interception, and coordinated detection. The development of cooperative attack started early, and cooperative interception has gradually developed from information collaboration to autonomous collaboration. Cooperative detection is the basic condition. With the progress of technology, these three categories are also converging and developing. In this paper, firstly, the development course of multi-missile cooperative guidance technology is briefly described, and the confrontation, fusion, and development of cooperative attack and cooperative interception are summarized. The key point is the autonomous combat technology of multi-missile cooperative long-range interception, and the difficulties of its technical implementation are analyzed, and the future development direction is presented.

赵建博 , 杨树兴 . 多导弹协同制导研究综述 [J ] . 航空学报 , 2017 , 38 ( 1 ): 020256 .

ZHAO J B , YANG S X . Review of multi-missile cooperative guidance [J ] . Acta Aeronautica et Astronautica Sinica , 2017 , 38 ( 1 ): 020256 . (in Chinese)

ZHOU J L , YANG J Y . Distributed guidance law design for cooperative simultaneous attacks with multiple missiles [J ] . Journal of Guidance, Control, and Dynamics , 2016 , 39 ( 10 ): 2439 - 2447 . DOI: 10.2514/1.G001609 http://doi.org/10.2514/1.G001609 https://arc.aiaa.org/doi/10.2514/1.G001609 https://arc.aiaa.org/doi/10.2514/1.G001609

姜尚 , 陈锋 , 高伟鹏 , 等 . 弹群在复杂作战空间下的自适应分布式协同制导策略 [J ] . 兵工学报 , 2022 , 43 ( 增刊2 ): 97 - 106 .

JIANG S , CHEN F , GAO W P , et al . An adaptive distributed cooperative guidance strategy for projectile clusters in complex combat environment [J ] . Acta Armamentarii , 2022 , 43 ( S2 ): 97 - 106 . (in Chinese) DOI: 10.12382/bgxb.2022.B023 http://doi.org/10.12382/bgxb.2022.B023 An adaptive distributed cooperative guidance strategy is proposed to improve the penetration ability and damage effect of shipborne gun guided projectiles, and to enable multiple projectiles to organize and cooperate in complex combat environment by themselves. An extended state observer with fast and accurate observation performance is designed to overcome external interference and constraints in the measurement of line of sight and angular velocity caused by the spin of projectiles. To address the problem of uncertain communication delay, a distributed controller in the direction of the line of sight is designed based on the cooperative consistency theory and integral sliding mode, which could converge the attack time within a limited time period. To eliminate the tracking error of the line of sight angle and line of sight angular rate in a certain time period, adaptive controllers using a nonsingular terminal sliding mode are installed along the normal and lateral directions of the line of sight based on the remaining flight time. Based on the Lyapunov theory and the Lyapunov-Krasovskii functional, it is proved that system is uniformly and ultimately bounded. Compared with existing research, experimental results reveal that this strategy improves the cooperative guidance performance of a projectile cluster against moving targets in a complex combat environment.

MA M C , SONG S M . Three-dimensional prescribed performance cooperative guidance law with spatial constraint for intercepting manoeuvring targets [J ] . International Journal of Control , 2023 , 96 ( 3 ): 1424 - 1435 . DOI: 10.1080/00207179.2022.2051075 http://doi.org/10.1080/00207179.2022.2051075 https://www.tandfonline.com/doi/full/10.1080/00207179.2022.2051075 https://www.tandfonline.com/doi/full/10.1080/00207179.2022.2051075

赵启伦 , 陈建 , 董希旺 , 等 . 拦截高超声速目标的异类导弹协同制导律 [J ] . 航空学报 , 2016 , 37 ( 3 ): 936 - 948 . DOI: 10.7527/S1000-6893.2015.0235 http://doi.org/10.7527/S1000-6893.2015.0235 对于多导弹协同拦截高超声速目标的问题,设计了一种具有领弹-从弹拓扑结构的异类导弹协同制导律:配备有高性能导引头的领弹采用改进比例导引法拦截目标;未配备导引头的从弹利用通信手段,采用二阶一致性跟踪算法,对领弹进行跟踪。两类导弹同时命中目标,形成"多对一"的拦截态势。异构型的制导策略可以降低对导引设备的需求,具备较理想的作战效费比。领弹与从弹的弹道均源于改进比例导引法,具有较理想的弹道特性。给出了协同制导律在固定拓扑与切换拓扑下成立的充分条件。算例仿真验证了所提出的制导律能够实现对高超声速目标的协同拦截,具有良好的可行性。

ZHAO Q L , CHEN J , DONG X W , et al. Cooperative guidance law for heterogeneous missiles intercepting hypersonic weapon [J ] . Acta Aeronautica et Astronautica Sinica , 2016 , 37 ( 3 ): 936 - 948 . (in Chinese) DOI: 10.7527/S1000-6893.2015.0235 http://doi.org/10.7527/S1000-6893.2015.0235 To solve the cooperative interception problem of hypersonic weapons for multi-missiles, a cooperative guidance law based on leader-follower communication topologies for heterogeneous missiles is investigated. The leader missile is equipped with high-performance seeker to intercept the target under the modified proportional navigation guidance law. The follower missiles, not equipped with seekers, track the leader missile under the second-order consensus protocols by means of communication. Hitting the target at the same time, the two types of missiles form a several-for-one intercepting situation. The heterogeneous guidance strategy can reduce the needs for seekers, and has an ideal operational efficiency.The trajectories of the leader missile and follower missiles, which have better ballistic characteristics, derive from the modified proportional navigation guidance law. The sufficient conditions for the cooperative guidance law under the fixed topology and switched topology are presented. Numerical simulations demonstrate that the guidance law proposed could accomplish the cooperative interception of hypersonic target, and has a good feasibility.

于江龙 , 董希旺 , 李清东 . 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 ): 521 - 541 .

YU J L , DONG X W , LI Q D . Distributed cooperative encirclement hunting guidance method for intercepting maneuvering target [J ] . Acta Aeronautica et Astronautica Sinica , 2022 , 43 ( 9 ): 521 - 541 . (in Chinese)

李国飞 , 朱国梁 , 吕金虎 , 等 . 主-从多飞行器三维分布式协同制导方法 [J ] . 航空学报 , 2021 , 42 ( 11 ): 524926 . DOI: 10.7527/S1000-6893.2020.24926 http://doi.org/10.7527/S1000-6893.2020.24926 针对三维空间下的多飞行器协同打击问题，基于主飞行器和从飞行器架构提出了两种分布式协同制导方法，实现了所有飞行器最终对目标的同时命中。方法1在定义协调变量的基础上，通过对所选协调变量的一致性协同控制使从飞行器状态同步于主飞行器状态。方法2提出了分布式观测器对主飞行器的状态进行准确估计，各从飞行器通过跟踪观测的主飞行器状态信息实现命中时间的一致。理论分析表明，两种方法都可保证多飞行器同时命中目标。仿真结果验证了所提方法的正确性和有效性。

LI G F , ZHU G L , LÜ J H , et al . Three dimensional distributed cooperative guidance law for multiple leader-follower flight vehicles [J ] . Acta Aeronautica et Astronautica Sinica , 2021 , 42 ( 11 ): 524926 . (in Chinese)

LIU F , DONG X W , LI Q D , et al . Robust multi-agent differential games with application to cooperative guidance [J ] . Aerospace Science and Technology , 2021 , 111 : 106568 . DOI: 10.1016/j.ast.2021.106568 http://doi.org/10.1016/j.ast.2021.106568 https://linkinghub.elsevier.com/retrieve/pii/S1270963821000791 https://linkinghub.elsevier.com/retrieve/pii/S1270963821000791

KANG S , WANF J N , LI G , et al . Optimal cooperative guidance law for salvo attack: an MPC-based consensus perspective [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2018 , 54 ( 5 ): 2397 - 2410 . DOI: 10.1109/TAES.2018.2816880 http://doi.org/10.1109/TAES.2018.2816880 https://ieeexplore.ieee.org/document/8318665/ https://ieeexplore.ieee.org/document/8318665/

GARCIA E , CASBEER D W , PACHTER M . Cooperative strategies for optimal aircraft defense from an attacking missile [J ] . Journal of Guidance, Control, and Dynamics , 2015 , 38 ( 8 ): 1510 - 1520 . DOI: 10.2514/1.G001083 http://doi.org/10.2514/1.G001083 https://arc.aiaa.org/doi/10.2514/1.G001083 https://arc.aiaa.org/doi/10.2514/1.G001083

TAN L N . Distributed optimal integrated tracking control for separate kinematic and dynamic uncertain non-holonomic mobile mechanical multi-agent systems [J ] . IET Control Theory & Applications , 2017 , 11 ( 18 ): 3249 - 3260 . DOI: 10.1049/cth2.v11.18 http://doi.org/10.1049/cth2.v11.18 https://onlinelibrary.wiley.com/toc/17518652/11/18 https://onlinelibrary.wiley.com/toc/17518652/11/18

TAN L N . Distributed cooperative H ∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming [J ] . International Journal of Control , 2017 , 91 ( 4 ): 952 - 968 . DOI: 10.1080/00207179.2017.1300685 http://doi.org/10.1080/00207179.2017.1300685 https://www.tandfonline.com/doi/full/10.1080/00207179.2017.1300685 https://www.tandfonline.com/doi/full/10.1080/00207179.2017.1300685

TAN L N . Omnidirectional-vision-based distributed optimal tracking control for mobile multirobot systems with kinematic and dynamic disturbance rejection [J ] . IEEE Transactions on Industrial Electronics , 2018 , 65 ( 7 ): 5693 - 5703 . DOI: 10.1109/TIE.2017.2782245 http://doi.org/10.1109/TIE.2017.2782245 http://ieeexplore.ieee.org/document/8231207/ http://ieeexplore.ieee.org/document/8231207/

SUN J L , LIU C S . Auxiliary-system-based composite adaptive optimal backstepping control for uncertain nonlinear guidance systems with input constraints [J ] . ISA Transactions , 2020 , 107 : 294 - 306 . DOI: 10.1016/j.isatra.2020.07.042 http://doi.org/10.1016/j.isatra.2020.07.042 This paper addresses a missile-target interception guidance process considering acceleration saturation and target maneuver as a constrained nonlinear tracking issue. A dynamic auxiliary system is designed for compensating the effects of constrained input, and external disturbances are counteracted through designing a nonlinear disturbance observer (NDO). The feedforward+feedback composite architecture is built in which a feedforward backstepping control and a feedback optimal control is presented recurrently. Furthermore, the parameter adaptive updating laws are derived to estimate the unknown functions online. Subsequently, the boundedness of the closed-loop signals are guaranteed. The predefined cost function is also ensured to be minimized. Furthermore, the control input is prevented violating its boundary. The contrastive simulation results demonstrate that the robustness of the proposed method is more superior to the nonsingular terminal sliding mode (NTSM) and the proportional navigation (PN) methods.Copyright © 2020 ISA. Published by Elsevier Ltd. All rights reserved.

DUAN D D , LIU C S , SUN J L . Adaptive periodic event-triggered control for missile-target interception system with finite-horizon convergence [J ] . Transactions of the Institute of Measurement and Control , 2020 , 42 ( 10 ): 1808 - 1822 . DOI: 10.1177/0142331219897186 http://doi.org/10.1177/0142331219897186 http://journals.sagepub.com/doi/10.1177/0142331219897186 http://journals.sagepub.com/doi/10.1177/0142331219897186 In this paper, the optimal control problem for finite-time missile-target interception systems is posed in a finite-horizon two-player zero-sum (ZS) differential game framework using a periodic event-triggered (PET) scheme. To solve the optimal control problem, a time-varying Hamilton-Jacobi-Issac (HJI) equation and a time-dependent cost function are constructed to deal with finite-horizon constraints, and an event-based periodic adaptive dynamic programming (ADP) algorithm is employed to find the Nash equilibrium solution for the designed HJI equation. Comparing with the traditional continuous event-triggered (ET) scheme, the proposed PET scheme only verifies the event-triggered conditions at periodic sampling instants, which reduces resource consumption in monitoring and excludes the Zeno behavior. A single critic neural network (CNN) is used to implement the proposed event-based optimal control algorithm, which reduces approximate errors bust also simplifies structures. Further, an additional error term is added in the designed weight updating law to such that the terminal constraint is also minimized over time. By resorting to Lyapunov function approach, some sufficient conditions are derived to achieve the uniformly ultimately bounded (UUB) of the ET closed-loop system and the estimation weight error of CNN. Finally, a missile-target interception system is introduced to illustrate the efficiency of the presented methods.

ZHANG W G , YI W J . Composite adaptive dynamic programming for missile interception systems with multiple constraints and less sensor requirement [J ] . ISA Transactions , 2021 , 117 : 40 - 53 . DOI: 10.1016/j.isatra.2021.01.040 http://doi.org/10.1016/j.isatra.2021.01.040 The adaptive integrated guidance and control issue of missiles with less sensor requirement is investigated in the optimal stabilization problem of an uncertain nonlinear system subjected to state and input constraints. The nonlinear system with partially unmeasurable states is transformed into the non-strict feedback form, firstly. Then, an adaptive observer is designed to approximate the full states, where a disturbance estimator is incorporated to suppress the unmatched external disturbances. Next, by employing a Barrier Lyapunov Function (BLF) and an auxiliary system to tackle the multiple constraints, an adaptive feedforward controller is raised to reduce the stabilization issue of the nonlinear system in non-strict feedback form to the equivalent control problem of an affine nonlinear system. Subsequently, an optimal controller is derived by utilizing adaptive dynamic programming (ADP) theory. The system stability is rigorously proved by using Lyapunov theory. Finally, simulations are performed to validate the effectiveness of the proposed control strategy.Copyright © 2021 ISA. Published by Elsevier Ltd. All rights reserved.

SUN J L , LIU C S . Distributed fuzzy adaptive backstepping optimal control for nonlinear multimissile guidance systems with input saturation [J ] . IEEE Transactions on Fuzzy Systems , 2019 , 27 ( 3 ): 447 - 461 .

ZHANG Y X , LIANG X L , LI D Y , et al . Barrier Lyapunov function-based safe reinforcement learning for autonomous vehicles with optimized backstepping [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2022 (2022-07-12). https://doi.org/ 10.1109/TNNLS.2022.3186528 https://dx.doi.org/10.1109/TNNLS.2022.3186528 .

LI Y M , FAN Y L , LI K W , et al . Adaptive optimized backstepping control-based RL algorithm for stochastic nonlinear systems with state constraints and its application [J ] . IEEE Transactions on Cybernetics , 2022 , 52 ( 10 ): 10542 - 10555 . DOI: 10.1109/TCYB.2021.3069587 http://doi.org/10.1109/TCYB.2021.3069587 https://ieeexplore.ieee.org/document/9408226/ https://ieeexplore.ieee.org/document/9408226/

ZHANG J X , LI K W , LI Y M . Output-feedback based simplified optimized backstepping control for strict-feedback systems with input and state constraints [J ] . IEEE/CAA Journal of Automatica Sinica , 2021 , 8 ( 6 ): 1119 - 1132 . DOI: 10.1109/JAS.2021.1004018 http://doi.org/10.1109/JAS.2021.1004018 https://ieeexplore.ieee.org/document/9428654/ https://ieeexplore.ieee.org/document/9428654/

ZHANG W G , YI W J . Composite adaptive dynamic programming for missile interception systems with multiple constraints and less sensor requirement [J ] . ISA Transactions , 2021 , 117 : 40 - 53 . DOI: 10.1016/j.isatra.2021.01.040 http://doi.org/10.1016/j.isatra.2021.01.040 The adaptive integrated guidance and control issue of missiles with less sensor requirement is investigated in the optimal stabilization problem of an uncertain nonlinear system subjected to state and input constraints. The nonlinear system with partially unmeasurable states is transformed into the non-strict feedback form, firstly. Then, an adaptive observer is designed to approximate the full states, where a disturbance estimator is incorporated to suppress the unmatched external disturbances. Next, by employing a Barrier Lyapunov Function (BLF) and an auxiliary system to tackle the multiple constraints, an adaptive feedforward controller is raised to reduce the stabilization issue of the nonlinear system in non-strict feedback form to the equivalent control problem of an affine nonlinear system. Subsequently, an optimal controller is derived by utilizing adaptive dynamic programming (ADP) theory. The system stability is rigorously proved by using Lyapunov theory. Finally, simulations are performed to validate the effectiveness of the proposed control strategy.Copyright © 2021 ISA. Published by Elsevier Ltd. All rights reserved.

DONG C Y , LIU Y , WANG Q . Barrier Lyapunov function based adaptive finite-time control for hypersonic flight vehicles with state constraints [J ] . ISA Transactions , 2020 , 96 : 163 - 176 . DOI: S0019-0578(19)30272-1 http://doi.org/S0019-0578(19)30272-1 This paper investigates the finite-time tracking control problem of the hypersonic flight vehicle (HFV) with state constraints. Firstly, a control-oriented model is introduced to enable the application of adaptive backstepping scheme. To meet strict requirements in terms of working conditions of HFV, barrier Lyapunov function is adopted to constrain the tracking errors, while piecewise saturation function is constructed to restrict the virtual signals. To guarantee the finite-time convergent property of HFV dynamics, an adaptive scheme in accordance with finite-time stability theory is designed. Meanwhile, a sliding mode differentiator is employed to estimate the derivatives of the virtual control laws. Novel auxiliary systems are then designed to consider the side effects of the possible saturation and to maintain the finite-time convergent property. In the final stage, the effectiveness and performance of the proposed method is demonstrated by numerical simulations.Copyright © 2019 ISA. Published by Elsevier Ltd. All rights reserved.

DOU L Q , CAI S Y , ZHANG X Y , et al . Event-triggered-based adaptive dynamic programming for distributed formation control of multi-UAV [J ] . Journal of the Franklin Institute , 2022 , 359 ( 8 ): 3671 - 3691 . DOI: 10.1016/j.jfranklin.2022.02.034 http://doi.org/10.1016/j.jfranklin.2022.02.034 https://linkinghub.elsevier.com/retrieve/pii/S0016003222001491 https://linkinghub.elsevier.com/retrieve/pii/S0016003222001491

LONG T , CAO Y , SUN J L , et al . Adaptive event-triggered distributed optimal guidance design via adaptive dynamic programming [J ] . Chinese Journal of Aeronautics , 2022 , 35 ( 7 ): 113 - 127 .

VAMVOUDAKIS K G , MIRANDA M F , HESPANHA J P . Asymptotically stable adaptive-optimal control algorithm with saturating actuators and relaxed persistence of excitation [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2016 , 27 ( 11 ): 2386 - 2398 . This paper proposes a control algorithm based on adaptive dynamic programming to solve the infinite-horizon optimal control problem for known deterministic nonlinear systems with saturating actuators and nonquadratic cost functionals. The algorithm is based on an actor/critic framework, where a critic neural network (NN) is used to learn the optimal cost, and an actor NN is used to learn the optimal control policy. The adaptive control nature of the algorithm requires a persistence of excitation condition to be a priori validated, but this can be relaxed using previously stored data concurrently with current data in the update of the critic NN. A robustifying control term is added to the controller to eliminate the effect of residual errors, leading to the asymptotically stability of the closed-loop system. Simulation results show the effectiveness of the proposed approach for a controlled Van der Pol oscillator and also for a power system plant.

LI Y M , SUN K K , TONG S C . Observer-based adaptive fuzzy fault-tolerant optimal control for SISO nonlinear systems [J ] . IEEE Transactions on Cybernetics , 2019 , 49 ( 2 ): 649 - 661 . DOI: 10.1109/TCYB.2017.2785801 http://doi.org/10.1109/TCYB.2017.2785801 This paper investigates adaptive fuzzy output feedback fault-tolerant optimal control problem for a class of single-input and single-output nonlinear systems in strict feedback form. The considered nonlinear systems contain unknown nonaffine nonlinear faults and unmeasured states. Fuzzy logic systems are used to approximate cost function and unknown nonlinear functions, respectively. It is assumed that the states of the systems to be controlled are unmeasurable, thus an adaptive state observer is developed. To solve the nonaffine nonlinear fault control design problem, filtered signals are introduced into the adaptive backstepping control design procedures, and in the framework of adaptive critic technique and fault-tolerant control technique, a novel adaptive fuzzy fault-tolerant optimal control scheme is developed. The stability of the closed-loop system is proved by using Lyapunov stability theory. The simulation results verify the effectiveness of the proposed control strategy.

张帅 , 郭杨 , 王仕成 , 等 . 考虑探测效能的有限时间协同制导方法 [J ] . 兵工学报 , 2019 , 40 ( 9 ): 1849 - 1859 . DOI: 10.3969/j.issn.1000-1093.2019.09.010 http://doi.org/10.3969/j.issn.1000-1093.2019.09.010 针对多飞行器协同拦截机动目标问题，基于有限时间控制理论设计了一种考虑探测几何构形的协同制导方法。假设飞行器具有1阶动力学特性，根据质点相对运动方程和协同探测原理建立了考虑探测几何构形的协同拦截模型。基于微分不等式理论给出系统状态有限时间有界和输入输出有限时间稳定的充分条件，并在此基础上设计了有限时间协同制导方法。该方法用度量矩阵刻画系统状态和输出动态品质，能够同时保证制导系统状态和输出在有限时间内有界和稳定。仿真结果表明：在目标进行不同程度机动情况下，所提制导方法均能够保证视线分离角收敛到预置角度、视线角速率收敛到0 rad/s且加速度不超过最大物理限制；与比例导引与最优制导方法相比，有限时间协同制导方法在探测和制导环节均具有较大优势。

ZHANG S , GUO Y , WANG S C , et al . A finite-time cooperative guidance method considering cooperative detection efficiency [J ] . Acta Armamentarii , 2019 , 40 ( 9 ): 1849 - 1859 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.09.010 http://doi.org/10.3969/j.issn.1000-1093.2019.09.010 For the multiple missiles intercepting a maneuvering target cooperatively, a cooperative guidance method considering a cooperative detection geometry configuration is designed based on the finite-time control theory. For the first-order dynamics of the missiles, a cooperative interception model with detection geometry configuration is established according to the relative motion equations of particles and the principle of cooperative detection. The sufficient conditions for the finite time boundedness of system state and the finite time stability of system input and output are given based on the differential inequality theory. And on this basis, a finite time cooperative guidance method is designed. The proposed method uses the measurement matrix to characterize the dynamic quality of system state and output, and can ensure that the state and output of guidance system are bounded and stable within a finite time interval. The simulated results show that the proposed guidance method can ensure that the LOS separation angle converges to the preset angle, the LOS angular rate converges to zero, and the acceleration does not exceed the maximum physical limit when a target is maneuvering. Compared with proportional navigation and optimal guidance law, the proposed method has the advantages in cooperative detection and guidance. Key