Time-to-go weighted optimal trajectory shaping guidance law

For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based on the time-to-go weighted function. Based on the same cost function, the closed-form solutions of the guidance law were derived when the initial displacement of missile, final impact angle, heading error and target maneuver was introduced into the lag-free guidance system. To validate the closed-form solutions, the simulation of the lag-free system was done and the simulation results exactly matched the closed-form solutions and only when the exponent is greater than zero, the final acceleration approaches to zero.