# Lossless Convexification of Optimal Control Problems with Semi-continuous Inputs

arXiv: https://arxiv.org/abs/1911.09013 · HTML: https://mlsanity.com/paper/1911.09013/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2019.

## Built on by (most cited first, 1 of 1)

- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)

## Abstract (arXiv)

This paper presents a novel convex optimization-based method for finding the 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. This paper is the first to allow individual input sets to overlap and to have different norm bounds, integral input and state costs, and convex state constraints that can be activated at discrete time instances. 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.