A Modified Finite-Time Guidance Law with Impact Angle Constraint

A modified finite-time impact angle control guidance (IACG) law is developed. First, based on the biased proportional navigation guidance (PNG) approach, the finite-time convergent impact-angle error dynamic is deduced from the guidance model. Then, a modified IACG law considering finite-time convergence is designed by inserting a time-to-go term into the dominator of the biased term. Furthermore, the finite-time stability and the explicit settling time of the impact-angle error dynamic is derived via utilizing the approach of Lyapunov analysis. Unlike the conventional IACG laws achieving finite-time convergence, the advantage of this modified guidance law is that the settling time for the impact-angle error is always smaller than the final time. Hence, under different initial impact-angle errors, the modified guidance law assures achieving the impact-angle error convergence before interception. Besides, it is convenient to adjust parameters. Finally, some numerical simulations under various scenarios are provided to confirm the properties of the modified finite-time convergent guidance law.