Lossless Convexification of Optimal Control Problems with Semi-continuous Inputs

Abstract

This paper presents a novel one-shot convex optimization method for finding globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the input norms to be either zero or lower-and upper-bounded. The non-convex problem is relaxed to a convex one whose optimal solution is proved to be optimal almost everywhere for the original problem, a procedure known as lossless convexification. The solution relies on second-order cone programming and demonstrates that a meaningful class of optimal control problems with binary variables can be solved reliably and in polynomial time. A rocket landing example with a coupled thrust-gimbal constraint corroborates the effectiveness of the approach.