Fuel-optimal program for atmospheric vertical powered landing

This paper studies the problem of vertical powered landing through a non-negligible density atmosphere. Several constraints are considered, one of them prevents hovering flight. The findings of the paper extend the results from the literature on atmosphere-free problems. The main contribution establishes the nature of the fuel-optimal control sequence. Sufficient and necessary conditions are provided that guarantee the Min-Max nature of the normal extremals. Abnormal extremals are also shown to be either Min or Max.