This paper investigates the problem of distributed co-operative guidance law design for multiple anti-ship missiles in the three-dimensional (3-D) space hitting simultaneously the same target with considering the desired terminal impact angle constraint. To address this issue, the problem formulation including 3-D nonlinear mathematical model description, and communication topology are built firstly. Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight (LOS) which satisfies the impact time constraint. However, the normal accelerations are designed to guarantee the convergence of the LOS angular rate. Furthermore, consider the terminal impact angle constraints, a nonsingular terminal sliding mode (NTSM) control is introduced, and a finite time convergent control law of normal acceleration is proposed. The convergence of the proposed guidance law is proved by using the second Lyapunov stability method, and numerical simulations are also conducted to verify its effectiveness. The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

中文翻译：

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反舰导弹三维碰撞角约束分布式协同制导律

本文研究了在考虑期望的终端冲击角约束的同时在三维（3-D）空间中同时击中同一目标的多种反舰导弹的分布式合作制导律设计问题。为了解决这个问题，首先建立了包括3-D非线性数学模型描述和通信拓扑的问题表述。然后，使用可用信息构造共识变量，并且可以在建议的加速命令下沿满足冲击时间约束的视线（LOS）达成共识。但是，正常加速度旨在确保LOS角速率的收敛。此外，考虑到终端冲击角约束，引入了非奇异终端滑模（NTSM）控制，提出了正常加速度的有限时间收敛控制律。利用第二种Lyapunov稳定性方法证明了所提出的制导律的收敛性，并进行了数值模拟以验证其有效性。结果表明，如果通信拓扑的连接时间长于所需的收敛时间，则提出的协同制导律可以在有限的时间内调节碰撞时间误差和碰撞角度误差。