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 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.