Optimal linear-quadratic missile guidance laws with penalty on command variability

This paper proposes a new approach to the derivation of homing guidance laws for interceptor missiles that makes use of linear-quadratic optimal control in a different manner than the traditional approaches. Instead of looking only for the minimization of the miss distance and the integral square of the guidance command, the new criterion penalizes also the "variability" of the guidance command. The solution has the familiar structure of traditional linear-quadratic guidance laws, of a zero-effort-miss term multiplied by a, possibly time-varying, gain. Still it differs in one essential feature: The navigation gain does not only depend on the time to go, but also on the total time of flight. The new guidance law also has an additional design parameter that can be profitably used to avoid acceleration saturation.