Elsevier

Automatica

Volume 122, December 2020, 109179
Automatica

Brief Paper
A set-theoretic generalization of dissipativity with applications in Tube MPC

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Abstract

This paper introduces a framework for analyzing a general class of uncertain nonlinear discrete-time systems with given state-, control-, and disturbance constraints. In particular, we propose a set-theoretic generalization of the concept of dissipativity for systems that are affected by external disturbances. The corresponding theoretical developments build upon set based analysis methods and lay a general theoretical foundation for a rigorous stability analysis of economic tube model predictive controllers.

Keywords

Model predictive control
Robust control
Dissipativity

Cited by (0)

Mario Eduardo Villanueva is a postdoctoral researcher at the School of Information Science and Technology at ShanghaiTech University. He received an M.Sc. and Ph.D. in chemical engineering from Imperial College London in 2011 and 2016, respectively. He was a postdoctoral researcher at Texas A&M University in 2016. Mario Villanueva is the recipient of the 2016 Dudley Newitt Award (Imperial College London) and the 2018 as well as 2019 SIST Excellent Postdoc Award. His research interests include set based computing, robust and stochastic control, global optimization and system theoretic tools for data analysis.

Elena De Lazzari received her BS in Mechanical Engineering from the Politecnico di Milano (2015) and a Master’s degree in Mechanical Engineering from Delft University of Technology (2017). During 2017 she was a visiting student at ShanghaiTech University under the supervision of Prof. Boris Houska. During this time, her research was focused on set-based methods for robust control.

Matthias A. Müller received a Diploma degree in Engineering Cybernetics from the University of Stuttgart, Germany, and an M.S. in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign, US, both in 2009. In 2014, he obtained a Ph.D. in Mechanical Engineering, also from the University of Stuttgart, Germany, for which he received the 2015 European Ph.D. award on control for complex and heterogeneous systems. Since 2019, he is director of the Institute of Automatic Control and full professor at the Leibniz University Hannover, Germany. His research interests include nonlinear control and estimation, model predictive control, and data-/learning-based control, with application in different fields including biomedical engineering.

Boris Houska is an assistant professor at the School of Information Science and Technology at ShanghaiTech University. He received a diploma in mathematics from the University of Heidelberg in 2007, and a Ph.D. in Electrical Engineering from KU Leuven in 2011. From 2012 to 2013 he was a postdoctoral researcher at the Centre for Process Systems Engineering at Imperial College London. Boris Houska’s research interests include numerical optimization and optimal control, robust and global optimization, as well as fast model predictive control algorithms.

The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Franco Blanchini under the direction of Editor Ian R. Petersen.