Tractable robust MPC design based on nominal predictions

TL;DR

This paper introduces a new robust MPC formulation based on nominal predictions that is computationally tractable for large systems, ensures stability, and simplifies robust constraint satisfaction.

Contribution

It proposes a novel robust MPC design with tractable ingredients, reduced robustness requirements for the terminal set, and applicability to large-scale systems.

Findings

Proven input-to-state stability and robust constraint satisfaction.

Comparable complexity to non-robust MPC.

Successful application to a multivariable chemical plant.

Abstract

Many popular approaches in the field of robust model predictive control (MPC) are based on nominal predictions. This paper presents a novel formulation of this class of controller with proven input-to-state stability and robust constraint satisfaction. Its advantages are: (i) the design of its main ingredients are tractable for medium to large-sized systems, (ii) the terminal set does not need to be robust with respect to all the possible system uncertainties, but only for a reduced set that can be made arbitrarily small, thus facilitating its design and implementation, (iii) under certain conditions the terminal set can be taken as a positive invariant set of the nominal system, allowing us to use a terminal equality constraint, which facilitates its application to large-scale systems, and (iv) the complexity of its optimization problem is comparable to the non-robust MPC variant. We show numerical closed-loop results of its application to a multivariable chemical plant and compare it against other robust MPC formulations.