Reduced-order methods for nonlinear model predictive control

• Applicant: Professor Dr. Stefan Volkwein
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2015 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 274852524

• Final Report Year: 2021

Final Report Abstract

The overall aim of the project was the development of efficient controllers for the energy efficient HVAC of buildings. These controllers should be able to incorporate possible changes e.g. in outside temperature (due to weather changes). This problem is very challenging because the underlying physics leads to complex, large-scale problems which have to be solved numerically very often. To overcome these difficulties we develop an algorithmic optimal control strategy, where the interplay between the optimization methods and the simplification of the physical model (by linearization and reduced-order approaches) was done in an efficient and certified way.

Publications

• Closed-loop performance analysis for economic model predictive control of time-varying systems. In Proceedings of the 56th IEEE Conference on Decision and Control — CDC 2017, pages 5563–5569, Melbourne, Australia, 2017
  L. Grüne and S. Pirkelmann
  
• Flachheitsbasierte beschränkte Optimalsteuerung für Diffusions-Reaktionssysteme. In Tagungsband GMA-Fachausschuss 1.40 ”Theoretische Verfahren der Regelungstechnik”, pages 89–104, Anif (A), Sep. 20–22 2017
  J. Andrej and T. Meurer
  
• Flatness-based constrained optimal control of reaction-diffusion systems. In Proc. American Control Conference (ACC), pages 2539–2544, June 2018
  J. Andrej and T. Meurer
  
• Flatness-based model predictive control of linear diffusionconvection-reaction processes. In 2018 IEEE Conference on Decision and Control (CDC), pages 527–532, Dec. 2018
  T. Meurer and J. Andrej
  
• Reduced-order greedy controllability of finite dimensional linear systems. IFAC-PapesOnline, 51:296–301, 2018
  G. Fabrini, L. Iapichino, and S. Volkwein
  
• Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. In G. Feichtinger, R. M. Kovacevic, and G. Tragler, editors, Control systems and mathematical methods in economics: Essays in Honor of Vladimir M. Veliov, volume 687 of Lecture Notes in Econom. and Math. Systems, pages 195–218. Springer, Cham, 2018
  L. Grüne, S. Pirkelmann, and M. Stieler
  
• Coupling MPC and HJB for the computation of POD-based feedback laws. Lecture Notes in Computational Science and Engineering, 126:941–949, 2019
  G. Fabrini, M. Falcone, and S. Volkwein
  
• Economic model predictive control for time-varying system: Performance and stability results. Opt. Control Appl. Meth., 41(1):42– 64, 2019. Special Issue: MPC for Energy Systems: Economic and Distributed Approaches
  L. Grüne and S. Pirkelmann
  
• Numerical verification of turnpike and continuity properties for time-varying pdes. In Proceedings of NOLCOS 2019, volume 52 of IFAC-PapersOnLine, pages 7–12, Vienna, Austria, 2019
  L. Grüne and S. Pirkelmann
  
• POD-based economic model predictive control for heatconvection phenomena. Lecture Notes in Computational Science and Engineering, 126:663–670, 2019
  L. Mechelli and S. Volkwein
  
• Multiobjective model predictive control of a parabolic advection-diffusion-reaction equation. Lecture Notes in Computational Science and Engineering, 8:777, 2020
  S. Banholzer, G. Fabrini, L. Grüne, and S. Volkwein
  
• POD-based augmented Lagrangian method for state constrained heat-convection phenomena. In J. Fehr and B. Haasdonk, editors, IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, May 22–25, 2018. Springer International Publishing, Cham, 2020
  J. S. Jehle, L. Mechelli, and S. Volkwein
  
• POD-based economic optimal control for heat-convection phenomena. In M. Falcone, R. Ferretti, L. Grüne, and W. M. McE-neaney, editors, Numerical Methods for Optimal Control Problems, volume 29 of Springer INdAM Series. Springer, Cham, 2020
  L. Mechelli and S. Volkwein
  
• Parallelized POD-based suboptimal economic model predictive control of a stateconstrained Boussinesq approximation, 2021. in: Journal Computers and Mathematics with Applications
  J. Andrej, L. Grüne, L. Mechelli, T. Meurer, S. Pirkelmann, and S. Volkwein
  
• Performance estimates for economic model predictive control and their application in POD-based implementations. Mathematical Control and Related Fields, 11:579–599, 2021
  L. Grüne, L. Mechelli, S. Pirkelmann, and S. Volkwein