Model predictive control for linear uncertain systems using integral quadratic constraints

TL;DR

This paper introduces a tube-based model predictive control method for linear systems with dynamic uncertainties modeled by integral quadratic constraints, ensuring robust stability and constraint satisfaction.

Contribution

It extends IQC-based stability analysis to external inputs and develops a less conservative robust MPC scheme for uncertain linear systems.

Findings

Achieves robust constraint satisfaction under dynamic uncertainties.

Demonstrates reduced conservatism compared to existing robust MPC methods.

Ensures input-to-state stability despite disturbances.

Abstract

In this work, we propose a tube-based MPC scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of $\rho$-hard IQCs for exponential stability analysis to external inputs. This result yields that the error between the true uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In the proposed tube-based MPC scheme, the state of this error bounding system is predicted along with the nominal model and used as a scaling parameter for the tube size. We prove that this method achieves robust constraint satisfaction and input-to-state stability despite dynamic uncertainties and additive bounded disturbances. A numerical example demonstrates the reduced conservatism of this IQC approach compared to state-of-the-art robust MPC approaches for dynamic uncertainties.