# A Structure Exploiting Branch-and-Bound Algorithm for Mixed-Integer Model Predictive Control

arXiv: https://arxiv.org/abs/1903.09117 · HTML: https://mlsanity.com/paper/1903.09117/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2019.

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

- [Learning-Guided Rolling Horizon Optimization for Long-Horizon Flexible Job-Shop Scheduling](https://mlsanity.com/paper/2502.15791/) (2025)

## Abstract (arXiv)

Mixed-integer model predictive control (MI-MPC) requires the solution of a mixed-integer quadratic program (MIQP) at each sampling instant under strict timing constraints, where part of the state and control variables can only assume a discrete set of values. Several applications in automotive, aerospace and hybrid systems are practical examples of how such discrete-valued variables arise. We utilize the sequential nature and the problem structure of MI-MPC in order to provide a branch-and-bound algorithm that can exploit not only the block-sparse optimal control structure of the problem but that can also be warm started by propagating information from branch-and-bound trees and solution paths at previous time steps. We illustrate the computational performance of the proposed algorithm and compare against current state-of-the-art solvers for multiple MPC case studies, based on a preliminary implementation in MATLAB and C code.