Investigation and simulation of optimal midcourse guidance for air-to-ground missiles

Because the two-time-scale behavior in the optimal solution allows the state variables to be decomposed into four slow variables (down range, cross range, specific energy and heading angle) and two fast variables (altitude and flight-path angle), singular perturbation theory is used to present a new optimal midcourse guidance law for air-to-ground missiles incorporating terminal specific energy as the performance. It is found that fast subsystem of missiles' dynamics was exactly linearizable. So using the feedback linearization methodology from nonlinear geometric control theory, the new guidance law was obtained through constructing a composite optimal control law consisting of three parts: minimum energy feedback control for slow dynamics; a feedback boundary-layer optimal control for tracking the optimal reduced-order trajectory; and a right boundary-layer minimum energy control achieving the aim of turning the missiles onto a favorable collision course at the end of the midcourse phase and of reducing heading error at hand over. Simulation results of a certain type of air-to-ground missile are presented. It is shown that application of the new guidance law results in maximization of the final energy at the end of midcourse, smoother acceleration command time history, smaller heading error at hand over, smaller and smoother angle of attack, and smaller and smoother sideslip angle.