An LQG guidance law with bounded acceleration command

This paper presents a novel missile guidance law derived by analyzing an interception scenario in the framework of an LQG terminal control problem with a bound on the acceleration command. For the derivation, the target maneuver is represented by an appropriate shaping filter and the nonlinear saturation function is represented by the equivalent random input describing function. Since the certainty equivalence property is not valid in the investigated problem the resulting controller depends on the conditional probability density function of the estimated states. The new guidance law has the same structure as the classical optimal guidance law that was derived without taking into account the saturation in the control. However the navigation gain, computed by solving numerically a TPBVP, has unique characteristics such as not diverging near the terminal time. Using Monte Carlo simulations it is shown that the homing performance of the new guidance law is better than that of the classical one; moreover, the control effort is drastically reduced. The results validate the new derivation approach.