The low-thrust guidance problem is defined as the minimumudterminal variance (MTV) control of a space vehicle subjected to randomudperturbations of its trajectory. To accomplish this control task,udonly bounded thrust level and thrust angle deviations are allowed, andudthese must be calculated based solely on the information gained fromudnoisy, partial observations of the state. In order to establish theudvalidity of various approximations, the problem is first investigatedudunder the idealized conditions of perfect state information and negligibleuddynamic errors. To check each approximate model, an algorithmudis developed to facilitate the computation of the open loop trajectoriesudfor the nonlinear bang-bang system. Using the results of thisudphase in conjunction with the Ornstein-Uhlenbeck process as a model forudthe random inputs to the system, the MTV guidance problem is reformulatedudas a stochastic, bang-bang, optimal control problem. Since audcomplete analytic solution seems to be unattainable, asymptoticudsolutions are developed by numerical methods. However, it is shownudanalytically that a Kalman filter in cascade with an appropriate nonlinearudMTV controller is an optimal configuration. The resultingudsystem is simulated using the Monte Carlo technique and is comparedudto other guidance schemes of current interest.
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