System level disturbance reachable sets and their application to tube-based MPC

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 leve...

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Bibliographic Details
Published in:	European journal of control 2022-11, Vol.68, p.100680, Article 100680
Main Authors:	Sieber, Jerome, Zanelli, Andrea, Bennani, Samir, Zeilinger, Melanie N.
Format:	Article
Language:	eng
Subjects:	Controllers Deviation Dynamical systems Impulse response Methods Optimization Parameterization Predictive control Reachable sets Robust model predictive control System level parameterization Tube-based model predictive control Tubes
Online Access:	Get full text
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Summary:	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.
ISSN:	0947-3580 1435-5671