Three-dimensional adaptive fixed-time cooperative guidance law with impact time and angle constraints

This paper mainly addresses the simultaneous attack of multiple missiles against a maneuvering target in three-dimensional (3-D) space. Here, we show that a novel fixed-time fast nonsingular terminal slide mode surface (FNTSMS), which has the characteristics of nonsingularity, converges in fixed time. With the help of the fixed-time FNTSMS, fixed-time adaptive distributed guidance laws along and perpendicular to the line of sight (LOS) direction are proposed. This realizes the dynamic adjustment of the target parameters in guidance laws, reduces the energy consumption of the guidance process, and realizes the constraints of the impact time and angle simultaneously. Additionally, considering that the communication topology will cause topology switching failure, this paper proves through graph theory that the proposed adaptive guidance laws will not be affected by topology switching. Moreover, through relevant auxiliary transformations, guidance laws with control input delay are demonstrated. To close to the actual action process of the missile, the air resistance item is added to guidance laws and analyzed. In addition, the control input amplitude is restricted to meet the actual working conditions of the missile. Finally, simulations are conducted to demonstrate the performance of the guidance law and its robustness against the mutation of communication topology.