Singular perturbation midcourse guidance law based on dynamic inversion for air-to-air missile

A near optimal midcourse guidance law incorporating a linear combination of flight time and terminal specific energy as the performance index was derived using singular perturbation theory and dynamic inversion. Missile state functions were put into three time-scale system according to the time constants of state variables. The reduced-order model consists of down range, cross range and specific energy dynamic. Optimal solution of reduce-order system, so called outer solution of original system, was obtained using optimal control theory. Dynamic inversion was applied to boundary layer correction for a close-loop controller. The performance of the controller could be regulated in accordance with different requirement of rise, cruise and descent stage or other instance. Simulation result shows that this guidance law satisfies requirements on trajectory smoothness, flight time and terminal specific energy. At the end of midcourse stage, missile heading error was small enough to ensure smooth transition from midcourse guidance stage to terminal guidance stage.