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

2020/07/02 by Monimoy Bujarbaruah, Ugo Rosolia, Bujarbaruah, Monimoy +7
Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #Fault Detection and Control Systems #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2007.00930

openalex publication_date 2020/07/02 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

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.

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