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

This paper studies a vertical powered descent problem in the context of planetary landing, considering glide-slope and thrust pointing constraints minimizing any final cost. In first time, it proves Max-Min-Max or Max-Singular-Max form optimal control using Pontryagin Maximum Principle, extends this result to formulation effect an atmosphere. It also shows that singular structure does not appear generic cases. second theoretically analyzes trajectory for more specific show there can be at most one contact boundary interval with state constraint on each Max Min arc.