Three-dimensional cooperative guidance law for multiple missiles with finite-time convergence

For the three-dimensional terminal guidance problem of multiple missiles cooperatively intercepting a maneuvering target, a novel finite-time cooperative guidance law with impact angle constraints is proposed. It is continuous and requires no information on target maneuvers. Firstly, the multiple missiles cooperative guidance model with impact angle constraints is constructed. We subsequently divide the process of cooperative guidance law design into two stages. In the first stage, based on the adaptive super-twisting algorithm and integral sliding mode, a new finite-time consensus protocol, i.e., the acceleration command on the line-of-sight direction, is designed to guarantee that all missiles reach the maneuvering target simultaneously. In the second stage, a new adaptive nonsingular fast terminal sliding mode control law, i.e., the acceleration command on the normal direction of the line-of-sight, is developed to ensure the finite-time convergence of the line-of-sight angular rate and line-of-sight angle between individual missile and the target. Furthermore, the detailed finite-time stability analysis is given based on the Lyapunov theory. Finally, numerical simulations demonstrate the effectiveness of the proposed cooperative guidance law.