A Hybrid Perspective on Suboptimal Mixed-Integer Quadratic Programming

TL;DR

This paper presents a hybrid framework for solving suboptimal mixed-integer quadratic programs recursively, combining MIQP and hybrid systems theory to design feedback controllers with guaranteed stability for dynamical systems.

Contribution

It introduces a novel hybrid approach that encodes suboptimality via solver parameters, providing theoretical stability guarantees and practical validation through simulations.

Findings

Framework guarantees stability of feedback control.

Validated through MIQP model predictive control simulations.

Encodes suboptimality as bounded perturbations.

Abstract

This work solves suboptimal mixed-integer quadratic programs recursively for feedback control of dynamical systems. The proposed framework leverages parametric mixed-integer quadratic programming (MIQP) and hybrid systems theory to model a recursive MIQP feedback controller and a feedback controlled dynamical system. The proposed hybrid framework theoretically encodes the suboptimal part via solver parameters as bounded perturbations from the optimal solution set. The stability of the proposed hybrid framework is theoretically guaranteed and validated through MIQP model predictive control simulations with multiple solver parameters.