Closed-Form Impact-Angle-Control Guidance of Nose-Dive Missiles for Maximum Terminal Speed

Abstract

This paper addresses an impact angle control guidance problem for nose-dive missiles to achieve the maximum terminal speed against a fixed target in the same vertical plane. By modeling the aerodynamic drag as a drag polar, we set up the nonlinear system equations needed to pursue an analytic closed-form solution. This paper shows that maximizing the terminal speed is equivalent to minimizing a weighted quadratic cost of the curvature of trajectory, and can be used as an equivalent problem to the original problem. Applying Pontryagin's maximum principle to the equivalent problem, we obtained a closed-form optimal guidance law, described in terms of air density parameters as well as heading error angle, flight path angle, range-to-go, and time-varying speed.