Neighboring optimal terminal control with discontinuous forcing functions.

Abstract

The paper deals with an extension of the optimal guidance methods of Kelley and Breakwell to systems containing a bang-bang control component. The method consists of a rescaling of the time variable, which allows for small changes in the switching times, to compensate for the presence of initial errors and disturbing forces. Two example problems are analyzed which indicate that the linear or first-order approximation to the optimal guidance law is in good agreement with the exact law, provided that the disturbances and initial errors are small and the guidance logic is computed at a time slightly removed from the switching time. It is shown that a feedback mechanization is possible on time intervals that do not contain switches. In the vicinity of a switching time, however, a control scheme using the optimal guidance methods must operate on an open-loop basis.

Optimal Space Trajectories—A Review of Published Work

“…The use of linear guidance theory for the problem of closed-loop operation as developed in refs. 69 and 80 is modified to allow for a discontinuous control variable' 132 '. Other papers to note are refs.…”

Neighboring optimal control for fixed-time multi-burn orbital transfers

“…However, difficulties arize when we consider to minimize the fuel consumption for a low-thrust orbital transfer because the corresponding optimal control function exhibits a bang-bang behavior if the prescribed transfer time is bigger than the minimum transfer time for the same boundary conditions [28]. Considering the control function as a discontinuous scalar, the corresponding neighboring optimal feedback control law was studied by Mcintyre [30] and Mcneal [41]. Then, Foerster et al [42] extended the work of Mcintyre and Mcneal to problems with discontinuous vector control functions.…”