Computationally Efficient System Level Tube-MPC for Uncertain Systems

TL;DR

This paper introduces a novel tube-based MPC method called filter-based system level tube-MPC (SLTMPC) that efficiently handles both additive disturbances and model uncertainties with online optimization and provides rigorous closed-loop guarantees.

Contribution

The paper presents a new MPC approach that overapproximates uncertainties, computes tubes online, and guarantees stability, with reduced computational complexity through asynchronous optimization.

Findings

Effective handling of additive disturbances and model uncertainties.

Provision of rigorous closed-loop guarantees.

Demonstrated computational efficiency and robustness through numerical evaluation.

Abstract

Tube-based model predictive control (MPC) is one of the principal robust control techniques for constrained linear systems affected by additive disturbances. While tube-based methods with online-computed tubes have been successfully applied to systems with additive disturbances, their application to systems affected by additional model uncertainties is challenging. This paper proposes a tube-based MPC method - named filter-based system level tube-MPC (SLTMPC) - which overapproximates both types of uncertainties with an online optimized disturbance set, while simultaneously computing the tube controller online. For the first time, we provide rigorous closed-loop guarantees for receding horizon control of such a MPC method. These guarantees are obtained by virtue of a new terminal controller design and an online optimized terminal set. To reduce the computational complexity of the proposed method, we additionally introduce an asynchronous computation scheme that separates the optimization of the tube controller and the nominal trajectory. Finally, we provide a comprehensive numerical evaluation of the proposed methods to demonstrate their effectiveness.