Analytical guidance laws and integrated guidance/autopilot for homing missiles

An approach to integrated guidance/autopilot design is considered in this study. It consists of two parts: 1) recognizing the importance of polar coordinates to describe the end game in terms of problem description and measurement acquisition, the terminal guidance problem is formulated in terms of polar coordinates; 2a) through the use of the state transition matrix of the intercept dynamics, a closed form solution for the transverse command acceleration is obtained; and 2b) through a commonly used approximation on time-to-go and a coordinate transformation, a family of proportional navigation optimal guidance laws is obtained in a closed form. A typical element of such a guidance law is combined with the autopilot dynamics to result in a feedback control law in terms of output variables