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Stabilizing Model Predictive Control Synthesis using Integral Quadratic Constraints and Full-Block Multipliers*
  • Marcelo Menezes Morato,
  • Tobias Holicki,
  • Carsten W. Scherer
Marcelo Menezes Morato
Universidade Federal de Santa Catarina Centro Tecnologico

Corresponding Author:[email protected]

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Tobias Holicki
Universitat Stuttgart
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Carsten W. Scherer
Universitat Stuttgart
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In this paper, we discuss how to synthesize stabilizing Model Predictive Control (MPC) algorithms based on convexly parameterized Integral Quadratic Constraints (IQCs), with the aid of general multipliers. Specifically, we consider Lur’e systems subject to sector-bounded and slope-restricted nonlinearities. As the main novelty, we introduce point-wise IQCs with storage in order to accordingly generate the MPC terminal ingredients, thus enabling closed-loop stability, strict dissipativity with regard to the nonlinear feedback, and recursive feasibility of the optimization. Specifically, we consider formulations involving both static and dynamic multipliers, and provide corresponding algorithms for the synthesis procedures. The major benefit of the proposed approach resides in the flexibility of the IQC framework, which is capable to deal with many classes of uncertainties and nonlinearities. Moreover, for the considered class of nonlinearities, our method yields larger regions of attraction of the synthesized predictive controllers (with reduced conservatism) if compared to the standard approach to deal with sector constraints from the literature.
25 Feb 2023Submitted to International Journal of Robust and Nonlinear Control
25 Feb 2023Submission Checks Completed
25 Feb 2023Assigned to Editor
25 Feb 2023Review(s) Completed, Editorial Evaluation Pending
04 Mar 2023Reviewer(s) Assigned
21 May 2023Editorial Decision: Revise Minor
23 Jun 20231st Revision Received
24 Jun 2023Submission Checks Completed
24 Jun 2023Assigned to Editor
24 Jun 2023Review(s) Completed, Editorial Evaluation Pending
01 Jul 2023Reviewer(s) Assigned
07 Aug 2023Editorial Decision: Accept