An optimal guidance approximation theory

Synthesis of optimal guidance approximations is undertaken by means of a perturbation theory approach and a scheme for obtaining linear, quadratic and higher order feedback approximations to the optimal control presented. Mechanization is carried out in terms of state deviations from an optimal reference trajectory with the comparison point along the reference selected so that the state comparison is approximately transverse. A simple example is treated analytically, linear and quadratic feedback expressions obtained, and some digital computer simulation results presented which permit a comparison of system performance and accuracy between various approximations.