Lossless convexification of optimal control problems with annular control constraints

Abstract

This paper presents new mathematical results for lossless convexification of optimal control problems with a non-convex annular control constraint. The problem is relevant because it is representative of a rocket landing problem. It was studied previously with an assumption at the final point (e.g., free final time), and it was shown that controllability is a sufficient condition to solve the problem as a sequence of convex programs. Herein, a sufficient condition is given for certain fixed time problems to be solvable as a single convex program. The main result is that controllability is also a sufficient condition for solving the general fixed time problem as a sequence of convex programs.