# Partition-based Feasible Integer Solution Pre-computation for Hybrid Model Predictive Control

## TL;DR

This paper introduces a partitioning algorithm for hybrid model predictive control that precomputes feasible integer solutions, enabling real-time warm-starts and suboptimal control schemes with proven convergence.

## Contribution

The paper presents a novel partition-based algorithm for precomputing feasible integer solutions in hybrid MPC, improving real-time applicability and solution feasibility guarantees.

## Key findings

- Effective on systems with up to six states.
- Enables real-time warm-starts for mixed-integer solvers.
- Provides a static, efficient query map for feasible solutions.

## Abstract

For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a static map from the current parameter to a suboptimal integer solution such that the remaining convex program is feasible. Convergence is proven with a new insight that the overlap among the feasible parameter sets of each integer solution governs the partition complexity. The partition is stored as a tree which makes querying the feasible solution efficient. The algorithm can be used to warm start a mixed integer solver with a real-time guarantee or to provide a reference integer solution in several suboptimal MPC schemes. The algorithm is tested on randomly generated systems with up to six states, demonstrating the effectiveness of the approach.