An optimal discrete control strategy for interplanetary guidance

The problem of guiding one state of a linear dynamical system to a prescribed rms terminal accuracy in the presence of injection, measurement, as well as engine-mechanization errors with a minimum average effort, is considered. Orbit corrections are assumed to be mechanized in the form of discrete velocity increments whose areas are proportional to the predicted miss distance. Equations are derived for computing the feedback gains as a function of the correction times. It is then shown how the spacings between successive corrections can be optimized. This is done by outlining a computation procedure based on the theory of dynamic programming. The optimum solution includes the effect of the loss of information caused by the mechanization error. The results are applied to a simple but illustrative example that approximates the terminal phase of an interplanetary trip. A numerical study is made relating the number of corrections and the required amount of propellant for various terminal accuracies and mechanization errors with typical initial errors. The computer results make evident the improvement of the multiple correction strategy over the design of using only one correction, and seem to indicate that the improvement obtained using more than three to four corrections is negligible. Moreover, it shows that there is an optimum number of corrections for a given size of mechanization error.