Further results on “Robust MPC using linear matrix inequalities”. (English)
Magni, Lalo (ed.) et al., Nonlinear model predictive control. Towards new challenging applications. Selected papers based on the presentations at the international workshop on assessment and future directions of nonlinear model predictive control (NMPC08), Pavia, Italy, September 5‒9, 2008. Berlin: Springer (ISBN 978-3-642-01093-4/hbk; 978-3-642-01094-1/ebook). Lecture Notes in Control and Information Sciences 384, 89-98 (2009).
Summary: This paper presents a novel method for designing the terminal cost and the Auxiliary Control Law (ACL) for robust MPC of uncertain linear systems, such that Input-to-State Stability (ISS) is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and $\mathcal{H}_\infty$ control design. This relation shows that the LMI-based optimal solution of the $\mathcal{H}_\infty$ synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.
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