Robust MPC via min-max differential inequalities

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Title: Robust MPC via min-max differential inequalities
Authors: Villanueva, ME
Quirynen, R
Diehl, M
Chachuat, B
Houska, B
Item Type: Journal Article
Abstract: This paper is concerned with tube-based model predictive control (MPC) for both linear and nonlinear, input-affine continuous-time dynamic systems that are affected by time-varying disturbances. We derive a min-max differential inequality describing the support function of positive robust forward invariant tubes, which can be used to construct a variety of tube-based model predictive controllers. These constructions are conservative, but computationally tractable and their complexity scales linearly with the length of the prediction horizon. In contrast to many existing tube-based MPC implementations, the proposed framework does not involve discretizing the control policy and, therefore, the conservatism of the predicted tube depends solely on the accuracy of the set parameterization. The proposed approach is then used to construct a robustMPCscheme based on tubes with ellipsoidal cross-sections. This ellipsoidal MPC scheme is based on solving an optimal control problem under linear matrix inequality constraints. We illustrate these results with the numerical case study of a spring-mass-damper system.
Issue Date: 16-Jan-2017
Date of Acceptance: 8-Nov-2016
ISSN: 0005-1098
Publisher: Elsevier
Start Page: 311
End Page: 321
Journal / Book Title: Automatica
Volume: 77
Copyright Statement: © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Commission of the European Communities
Funder's Grant Number: EP/J006572/1
Keywords: 01 Mathematical Sciences
09 Engineering
08 Information And Computing Sciences
Industrial Engineering & Automation
Publication Status: Published
Appears in Collections:Faculty of Engineering
Chemical Engineering

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