Tube-based model predictive control (MPC) methods leverage tubes to bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. This paper presents a novel tube-based MPC formulation based on system level disturbance reachable sets (SL-DRS), which leverage the affine system level parameterization (SLP). We show that imposing a finite impulse response (FIR) constraint on the affine SLP guarantees containment of all future deviations in a finite sequence of SL-DRS. This allows us to formulate a system level tube-MPC (SLTMPC) method using the SL-DRS as tubes, which enables concurrent optimization of the nominal trajectory and the tubes, while using a positively invariant terminal set. Finally, we show that the SL-DRS tubes can also be computed offline.
@article{arxiv.2111.03564,
title = {System Level Disturbance Reachable Sets and their Application to Tube-based MPC},
author = {Jerome Sieber and Andrea Zanelli and Samir Bennani and Melanie N. Zeilinger},
journal= {arXiv preprint arXiv:2111.03564},
year = {2021}
}