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This paper proposes a novel prescribed-time cooperative guidance law (PTCGL) for multiple missiles cooperatively attacking a manoeuvring target. Guidance models in two directions are used and the acceleration saturations are also considered in both two directions. In line-of-sight (LOS) direction, by applying prescribed-time multi-agent consensus theory, the problem of the times-to-go () of multiple missiles converging to a same value is transformed into a stabilisation problem. Then the cooperative guidance law in LOS direction is designed based on the prescribed time integral sliding mode surface (PTISMS) and a new variable coefficient exponential reaching law, and a first-order auxiliary system is introduced to deal with the input saturation problem; based on a prescribed time linear sliding surface (PTLSMS), the cooperative guidance law in normal LOS direction is designed to ensure the LOS angle and LOS angle rate convergence within a prescribed time, and a second-order auxiliary system is designed to deal with the input saturation problem. Furthermore, the prescribed time convergence of the PTCGL is proved with the Lyapunov stability theory. Finally, numerical simulations demonstrate the effectiveness and advantages of the proposed PTCGL.

Prescribed-time cooperative guidance law against manoeuvring target with input saturation