A Combined Linear–Quadratic/Bounded Control Differential Game Guidance Law

Abstract

A new guidance law, based on the solution of a combined linear–quadratic and norm-bounded differential game, is proposed. It hinges on the insight that the hard constraints on the lateral acceleration are critical in the last part of the flight, and in contrast, at the early stages of the flight, it is important to avoid excessive speed loss due to induced drag. This yields a linear–quadratic differential game formulation for the initial stage and a norm-bounded differential game formulation for the last stage of the engagement. In an important particular case of players with ideal dynamics, the proposed guidance law is shown to be biased proportional navigation guidance with a deadzone. Due to its simple structure, the proposed guidance law is easy to implement in practice. The performance of the guidance law is illustrated using numerical simulations, and it is shown to perform better than comparable classical guidance laws.