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

## TL;DR

This paper introduces a specialized branch-and-bound algorithm for mixed-integer model predictive control that leverages problem structure and warm-starting to improve computational efficiency in real-time applications.

## Contribution

It presents a novel structure-exploiting branch-and-bound algorithm tailored for MI-MPC, incorporating warm-start strategies based on previous solutions.

## Key findings

- Enhanced computational performance over existing solvers
- Effective exploitation of problem structure and warm-starting
- Successful application to automotive and aerospace case studies

## Abstract

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.