Fast Switching in Mixed-Integer Model Predictive Control

TL;DR

This paper analyzes stability and control switching in mixed-integer model predictive control, proposing methods for fast switching and demonstrating their effectiveness through numerical experiments.

Contribution

It introduces a stability analysis framework for mixed-integer MPC with fast switching capabilities using convex relaxation and sum-up rounding techniques.

Findings

Nominal asymptotic stability achieved for relaxed system.

Sum-up rounding restores integer feasibility efficiently.

Numerical experiments confirm practical effectiveness of fast switching.

Abstract

We deduce stability results for finite control set and mixed-integer model predictive control with a downstream oversampling phase. The presentation rests upon the inherent robustness of model predictive control with stabilizing terminal conditions and techniques for solving mixed-integer optimal control problems by continuous optimization. Partial outer convexification and binary relaxation transform mixed-integer problems into common optimal control problems. We deduce nominal asymptotic stability for the resulting relaxed system formulation and implement sum-up rounding to restore efficiently integer feasibility on an oversampling time grid. If fast control switching is technically possible and inexpensive, we can approximate the relaxed system behavior in the state space arbitrarily close. We integrate input perturbed model predictive control with practical asymptotic stability. Numerical experiments illustrate practical relevance of fast control switching.