A Simple Robust MPC for Linear Systems with Parametric and Additive Uncertainty

TL;DR

This paper introduces a simple, computationally efficient robust MPC method for linear systems with parametric and additive uncertainties, ensuring constraint satisfaction and stability with significant speed improvements.

Contribution

The paper presents a novel robust MPC approach that separates constraint tightening based on horizon length and over-approximates uncertainties for efficiency.

Findings

Achieves up to 15x faster online computation compared to tube MPC.

Maintains 98% of the tube MPC's region of attraction.

Guarantees recursive feasibility and stability of the closed-loop system.

Abstract

We propose a simple and computationally efficient approach for designing a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertainty is modeled as an additive disturbance and an additive error on the system dynamics matrices. Set based bounds for each component of the model uncertainty are assumed to be known. We separate the constraint tightening strategy into two parts, depending on the length of the MPC horizon. For a horizon length of one, the robust MPC problem is solved exactly, whereas for other horizon lengths, the model uncertainty is over-approximated with a net-additive component. The resulting MPC controller guarantees robust satisfaction of state and input constraints in closed-loop with the uncertain system. With appropriately designed terminal components and an adaptive horizon strategy, we prove the controller's recursive feasibility and stability of the origin. With numerical simulations, we demonstrate that our proposed approach gains up to 15x online computation speedup over a tube MPC strategy, while stabilizing about 98$\%$ of the latter's region of attraction.