针对导弹末制导攻击时间和角度约束问题，本文提出了一种能够运用在导弹速率变化背景下，具有较好精度和鲁棒性的时空约束制导律。首先，基于现有比例导引的剩余飞行轨迹长度和攻击角度预测估计表达式，求解满足时空约束的期望速度前置角。其次，将速度前置角误差作为滑模面，通过滑模控制方法在比例导引基础上构造偏置项函数，提出了速率可控下不存在指令奇异和突变的时空约束制导律，实现对导弹攻击时间和角度的同时控制。接着，提出关于攻击时间的期望速度前置角预测估计算法，将所提出时空约束制导律推广至导弹速率不可控的场景，并设计指令更新优化策略，避免因计算耗时影响控制指令周期更新。最后，数值仿真结果表明，所设计制导律在导弹速率变化和随机误差干扰下，依旧能按期望时间和角度到达目标，验证了该制导律在复杂环境下仍具备较高的制导精度与良好的鲁棒性。
This paper addresses the problem of simultaneously constraining impact time and impact angle during terminal missile guidance under varying missile speed. A spatio-temporal constraint guidance law with high accuracy and robustness is proposed for use when the missile’s speed varies. First, based on existing proportional-navigation expressions for the predicted remaining flight-path length and impact angle, the desired velocity-lead angle that satisfies the spatio-temporal constraints is solved. Second, the error in the velocity-lead angle is taken as a sliding surface and, by means of sliding-mode control, a bias term is constructed on top of the proportional-navigation law; this yields a spatio-temporal guidance law that, in the speed-controllable case, avoids command singularities and abrupt command changes and achieves simultaneous control of impact time and impact angle. Next, a predictive estimation algorithm for the desired velocity-lead angle with respect to impact time is presented to extend the pro-posed guidance law to scenarios with uncontrollable speed; an optimized command-update strategy is also designed to prevent computational latency from degrading the command update cycle. Finally, numerical simulations demonstrate that the proposed guidance law attains the desired impact time and impact angle under speed variations and stochastic disturbances, validating its high guidance accuracy and good robustness in complex environments.
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