This paper proposes a three-dimensional (3-D) robust nonlinear cooperative guidance law for multiple missiles to simultaneously attack a maneuvering target at desired impact angles. Since the flight time of terminal guidance is very short, the fast convergence of guidance errors is a vital demand, especially when the initial errors are huge and the target is maneuvering. By utilizing the theory of fixed time convergence, a distributed sliding surface that only utilizes the information from adjacent missiles is first designed, whose convergence time is independent of initial conditions. In order to avoid the performance degradation due to the estimation error of time-to-go, the consensus variables of the fixed-time sliding surface are chosen as range-to-go and radial relative velocity. Then, a robust cooperative guidance law along the line-of-sight (LOS) direction is proposed to bring the multi-missile system to reach the sliding surface in finite time. Thus, the simultaneous attack to a maneuvering target can be guaranteed. Next, the guidance laws in the elevation and azimuth direction of LOS are developed to ensure the fixed-time convergence of LOS angles. The fixed-time stability is proved through the Lyapunov theory and bi-homogenous property. Simulation results indicate that the impact time of each missile under the proposed guidance law is the same, without any deviation. Compared with the state-of-the-art methods, the convergence time of LOS angles is shortened by about 30%. In addition, the miss distance and errors of LOS angles can be reduced by more than 80%.

本文提出了一种针对多枚导弹的三维（3-D）鲁棒非线性合作制导律，以同时以期望的冲撞角度攻击机动目标。由于终端制导的飞行时间非常短，因此制导误差的快速收敛是至关重要的要求，尤其是在初始误差较大且目标机动的情况下。利用固定时间收敛理论，首先设计了仅利用相邻导弹信息的分布式滑动面，其收敛时间与初始条件无关。为了避免由于走时估计误差引起的性能下降，选择固定时间滑动面的共识变量作为走时范围和径向相对速度。然后，提出了一种沿视线（LOS）方向的鲁棒合作制导律，以使多导弹系统在有限的时间内到达滑面。因此，可以确保对机动目标的同时攻击。接下来，发展LOS的仰角和方位角的制导律，以确保LOS角的固定时间收敛。通过李雅普诺夫理论和双齐性证明了固定时间的稳定性。仿真结果表明，在拟议的制导律下，每枚导弹的撞击时间相同，没有偏差。与最新技术相比，LOS角的收敛时间缩短了约30％。此外，可将错过距离和LOS角误差减少80％以上。