Leader-follower spatial-temporal cooperative guidance law with gain-tunable prescribed-time convergence

To address the problem of cooperative engagement of multiple missiles against a maneuvering target in three-dimensional space, this paper proposes a cooperative guidance law with controllable convergence time, impact time, and impact angle. By constructing a novel gain-tunable prescribed-time stability criterion, the convergence time of the guidance law can be arbitrarily set under the premise of ensuring bounded gain without sacrificing convergence accuracy. This criterion introduces a gain-tunable mechanism, which accommodates both constant and time-varying gain designs, and significantly improves the accuracy of the prescribed convergence time. First, a prescribed-time disturbance observer is proposed, which can accurately estimate the target acceleration within the prescribed time without relying on any priori information of the maneuvering target. Second, in the Line-of-Sight (LOS) direction, a leader-follower architecture is adopted. An impact time control guidance law is designed for the leader missile to achieve active control of the impact time of the missile swarm. For the follower missiles, a distributed prescribed-time state observer suitable for the directed communication is designed, and combined with a prescribed-time state tracking controller to ensure that the follower missiles can quickly and accurately estimate and track the state of the leader within the prescribed time, thereby achieving attack synchronization of multiple missiles. Third, in the LOS normal direction, a prescribed-time LOS angle control guidance law is proposed to drive the LOS angles of each missile to converge to the desired values within the prescribed time. Finally, numerical simulations under multiple cases are conducted to verify the effectiveness and superiority of the proposed guidance law.