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This paper studies a vertical powered descent problem in the context ofplanetary landing, considering glide-slope and thrust pointing constraints andminimizing any final cost. In a first time, it proves the Max-Min-Max orMax-Singular-Max form of the optimal control using the Pontryagin MaximumPrinciple, and it extends this result to a problem formulation considering theeffect of an atmosphere. It also shows that the singular structure does notappear in generic cases. In a second time, it theoretically analyzes theoptimal trajectory for a more specific problem formulation to show that therecan be at most one contact or boundary interval with the state constraint oneach Max or Min arc.

Structure of optimal control for planetary landing with control and state constraints