Finite time convergence cooperative guidance law based on graph theory

A new cooperative guidance law with impact time and impact angle constraints is presented for multiple flight vehicles to against the stationary target. The proposed guidance law has two projection components: the one that along the line-of-sight (LOS) ensures that all flight vehicles reach the target simultaneously with impact time constraints, another one that normal the LOS guarantees the convergence of the LOS angular rate with terminal impact angle constraints. Using the second Lyapunov stability method, we prove that the time-to-go of all flight vehicles reach at agreement in finite time if the connecting time of the communication topology is larger than the required convergent time. Nonlinear simulations demonstrate the effectiveness of the proposed law.