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

TL;DR

This paper characterizes the structure of optimal control strategies for planetary landing with control and state constraints, extending classical results to atmospheric effects and analyzing boundary interactions.

Contribution

It proves the Max-Min-Max control structure for planetary landing problems and extends the analysis to atmospheric conditions, providing insights into boundary interactions.

Findings

Optimal control has a Max-Min-Max structure.

Singular control does not appear in generic cases.

At most one contact interval with state constraints per arc.

Abstract

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