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

TL;DR

This paper introduces a novel tube-based MPC approach using system level disturbance reachable sets (SL-DRS) and affine system level parameterization, enabling finite-horizon deviation containment and offline computation.

Contribution

It proposes a new SL-DRS based tube-MPC formulation with FIR constraints, allowing concurrent optimization and offline computation of tubes.

Findings

Guarantees containment of deviations within finite sequences

Enables offline computation of disturbance reachable sets

Uses affine system level parameterization for improved control

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.