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Presentation of a theory developing a linear feedback guidance scheme to correct for inflight disturbances of a vehicle during the course of a space mission. The theory is predicated on the use of a nominal optimal trajectory. The scheme consists of a linear combination of (1) perturbations of the vehicle state from its nominal state, and (2) time-varying gains to determine the control correction required to satisfy the constraints of the trajectory in an optimal fashion. Exact knowledge of the state of the vehicle is assumed. An analysis of numerical results for an idealized rocket trajectory problem shows the linear feedback guidance scheme to be effective over a wide range of chosen perturbations.

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