Abstract
This paper presents a heterogeneously parameterized tube-based model predictive control (MPC) design applicable to linear parameter-varying (LPV) systems. In a heterogeneous tube, the parameterizations of the tube cross sections and the associated control laws are allowed to vary along the prediction horizon. Two extreme cases that can be described in this framework are scenario MPC (high complexity, larger domain of attraction) and homothetic tube MPC with a simple time-invariant control parameterization (low complexity, smaller domain of attraction). In the proposed framework, these extreme parameterizations, as well as other parameterizations of intermediate complexity, can be combined within a single tube. By allowing for more flexibility in the parameterization design, one can influence the trade-off between computational cost and the size of the domain of attraction. Sufficient conditions on the parameterization structure are developed under which recursive feasibility and closed-loop stability are guaranteed. A specific parameterization that combines the principles of scenario and homothetic tube MPC is proposed and it is shown to satisfy the required conditions. The properties of the approach, including its capability of achieving improved complexity/performance trade-offs, are demonstrated using two numerical examples.
| Original language | English |
|---|---|
| Article number | 108622 |
| Number of pages | 13 |
| Journal | Automatica |
| Volume | 111 |
| DOIs | |
| Publication status | Published - 1 Jan 2020 |
Funding
In this paper, a framework for the construction of MPCschemes for LPV-SS models was developed, based on the construction of so-called heterogeneously parameterized tubes. Possibilities for future research include the extension of the framework to handle LPV models also affected by additive disturbances, the implementation of tube parameterizations based on ellipsoids, and the investigation of algorithmic approaches to systematically design heterogeneous parameterization structures. Jurre Hanema was born in 1990 in Heerenveen, The Netherlands. He obtained the BSc and MSc degrees in Electrical Engineering from Eindhoven University of Technology in 2012 and 2014, respectively. In 2014, Jurre joined the Control Systems Group at the Department of Electrical Engineering of the Eindhoven University of Technology as a doctoral candidate. During his PhD, he was supervised by Roland Tóth, Mircea Lazar, and Siep Weiland. His research deals with model predictive control of linear parameter-varying systems, focusing on tube-based approaches with the capability of exploiting available information on future scheduling trajectories (“anticipation”). He received the PhD degree (cum laude) in 2018 and is presently employed at ASML. Mircea Lazar was born in Iasi, Romania, 1978. He received the M.Sc. and Ph.D. degrees in control engineering from the Technical University Gh. Asachi of Iasi, Iasi, Romania, in 2002 and the Eindhoven University of Technology, Eindhoven, The Netherlands, in 2006, respectively. For his Ph.D. thesis he received the EECI (European Embedded Control Institute) Ph.D. Award in 2007. He is currently holding a position of an Associate Professor on Constrained Control of Complex Systems, part of the Control Systems group of the Electrical Engineering Faculty, Eindhoven University of Technology. His research interests include stability theory, distributed control, construction of Lyapunov functions and constrained control of nonlinear systems, including model predictive control. He has supervised 10 PhD students that received their title, out of which 2 received the Cum Laude distinction. Dr. Lazar is an active member of the IFAC Technical Committee 2.3 Nonlinear control systems. Roland Tóth was born in 1979 in Miskolc, Hungary. He received the B.Sc. degree in Electrical Engineering and the M.Sc. degree in Information Technology in parallel with distinction at the University of Pannonia, Veszprém, Hungary, in 2004, and the Ph.D. degree (cum laude) from the Delft Center for Systems and Control (DCSC), Delft University of Technology (TUDelft), Delft, The Netherlands, in 2008. He was a Post-Doctoral Research Fellow at DCSC, TUDelft, in 2009 and at the Berkeley Center for Control and Identification, University of California, Berkeley, in 2010. He held a position at DCSC, TUDelft, in 2011–12. Currently, he is an Associate Professor at the Control Systems Group, Eindhoven University of Technology (TU/e). He is an Associate Editor of the IEEE Transactions on Control Systems Technology. His research interests are in linear parameter-varying (LPV) and nonlinear system identification and control, machine learning for modeling and control, model predictive control and behavioral system theory. Dr. Tóth received the TUDelft Young Researcher Fellowship Award in 2010, the VENI award of The Netherlands Organisation for Scientific Research in 2011 and the Starting Grant of the European Research Council in 2016.
| Funders | Funder number |
|---|---|
| European Union's Horizon 2020 - Research and Innovation Framework Programme | 714663 |
| European Union's Horizon 2020 - Research and Innovation Framework Programme | |
| Nederlandse Organisatie voor Wetenschappelijk Onderzoek |
Keywords
- Constrained control
- Linear parameter-varying systems
- Robust model predictive control