  Tube-based model predictive control (MPC) is the principal robust control
technique for constrained linear systems affected by additive disturbances.
While tube-based methods that compute the tubes online have been successfully
applied to systems with additive disturbances, their application to systems
affected by additional model uncertainties is challenging. This paper
introduces a new tube-based MPC method - named filter-based system level
tube-MPC (SLTMPC) - which overapproximates both uncertainties with an online
optimized disturbance set, while simultaneously computing the tube controller
online. Extending prior work, we generalize the method to polytopic disturbance
sets and for the first time provide rigorous closed-loop guarantees for the
receding horizon controller. These guarantees are obtained by virtue of a new
terminal controller design and an online optimized terminal set. To reduce the
computational complexity of the proposed method, we additionally introduce an
asynchronous computation scheme that separates the optimization of the tube
controller and the nominal trajectory. Finally, we provide a comprehensive
numerical evaluation of the proposed methods to demonstrate their
effectiveness.
