  Robust tube-based model predictive control (MPC) methods address constraint
satisfaction by leveraging an a-priori determined tube controller in the
prediction to tighten the constraints. This paper presents a system level
tube-MPC (SLTMPC) method derived from the system level parameterization (SLP),
which allows optimization over the tube controller online when solving the MPC
problem, which can significantly reduce conservativeness. We derive the SLTMPC
method by establishing an equivalence relation between a class of robust MPC
methods and the SLP. Finally, we show that the SLTMPC formulation naturally
arises from an extended SLP formulation and show its merits in a numerical
example.
