Games in Aerospace: Homing missile guidance

Abstract

The development of a homing missile guidance law against an intelligent adversary requires the solution to a differential game. First, we formulate the deterministic homing guidance problem as a linear dynamic system with an indefinite quadratic performance criterion (LQ). This formulation allows the navigation ratio to be greater than three, which is obtained by the onesided linear-quadratic regulator and appears to be more realistic. However, this formulation does not allow for saturation in the actuators. A deterministic game allowing saturation is formulated and shown to be superior to the LQ guidance law, even though there is no control penalty. To improve the performance of the quadratic differential game solution in the presence of saturation, trajectoryshaping feature is added. Finally, if there are uncertainties in the measurements and process noise, a disturbance attenuation function is formulated that is converted into a differential game. Since only the terminal state enters the cost criterion, the resulting estimator is a Kalman filter, but the guidance gains are a function of the assumed system variances.