System Level Disturbance Reachable Sets and their Application to Tube-based MPC

Jerome Sieber; Andrea Zanelli; Samir Bennani; Melanie N. Zeilinger

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arXiv · 2111.03564

System Level Disturbance Reachable Sets and their Application to Tube-based MPC

Jerome Sieber·Andrea Zanelli·Samir Bennani·Melanie N. Zeilinger

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Abstract

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.

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Jerome Sieber, Andrea Zanelli, Samir Bennani, Melanie N. Zeilinger. 2021-11-05. System Level Disturbance Reachable Sets and their Application to Tube-based MPC. https://arxiv.org/abs/2111.03564

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