Robust MPC for Linear Systems with Parametric and Additive Uncertainty: A Novel Constraint Tightening Approach

TL;DR

This paper introduces a new robust MPC method for uncertain linear systems that uses a constraint tightening strategy based on known bounds, ensuring constraint satisfaction and stability.

Contribution

It presents a novel optimization-based constraint tightening approach for robust MPC that guarantees constraint satisfaction and stability for systems with parametric and additive uncertainties.

Findings

Proves robust constraint satisfaction and stability of the proposed MPC.

Demonstrates effectiveness through a numerical example.

Abstract

We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system matrices and the additive uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With an appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC in closed-loop with the uncertain system, and Input to State Stability of the origin. We highlight the efficacy of our proposed approach via a numerical example.