Robust and stochastic economic model predictive control

• Applicants: Professor Dr.-Ing. Frank Allgöwer; Professor Dr.-Ing. Matthias Müller
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2015 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 279734922

• Final Report Year: 2024

Final Report Abstract

In this project, we developed model predictive control (MPC) schemes for systems that are subject to disturbances or uncertainties. The main focus of the project was on economic MPC, where the goal is to find the operating behavior that yields the best performance for a given economic cost function. Nevertheless, some parts of the project also considered stabilizing MPC, where the goal is to stabilize a given desired reference trajectory, which is an intermediate step towards the economic case. In particular, we designed computationally efficient algorithms to control linear and nonlinear systems subject to deterministic or stochastic additive disturbances. We derived modifications of the cost function to consider average, worst-case, or expected performance criteria and we have shown how to reduce conservatism by adapting the controller if we collect online data to learn unknown parameters. We have shown that the potentially cumbersome design of terminal conditions is not needed if one is willing to sacrifice a bit of performance or use long prediction horizons. We have analyzed the asymptotic average performance of the economic MPC schemes as well as the transient non-averaged performance. For the stabilizing MPC schemes we have proven stability and for all developed schemes, we have shown constraint satisfaction and recursive feasibility. Finally, we have investigated a potential application of economic MPC to the job shop scheduling problem in Industry 4.0. These results not only answer the questions posed in the project proposal but in many places go far beyond the original objectives and received significant international attention as well as several awards. In total 4 PhD dissertations, 17 journal articles, and 18 peer-reviewed conference papers can be listed as scientific output of this project when seen over the two funding phases.

Publications

• Average Constraints in Robust Economic Model Predictive Control∗∗The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/2) at the University of Stuttgart. IFAC-PapersOnLine, 48(8), 44-49.
  Bayer, Florian A.; MUller, Matthias A. & Allgower, Frank
  
• Min-max economic model predictive control approaches with guaranteed performance. 2016 IEEE 55th Conference on Decision and Control (CDC), 3210-3215.
  Bayer, Florian A.; Muller, Matthias A. & Allgower, Frank
  
• Robust economic Model Predictive Control using stochastic information. Automatica, 74, 151-161.
  Bayer, Florian A.; Lorenzen, Matthias; Müller, Matthias A. & Allgöwer, Frank
  
• Constraint-Tightening and Stability in Stochastic Model Predictive Control. IEEE Transactions on Automatic Control, 62(7), 3165-3177.
  Lorenzen, Matthias; Dabbene, Fabrizio; Tempo, Roberto & Allgower, Frank
  
• Stabilizing stochastic MPC without terminal constraints. 2017 American Control Conference (ACC), 5636-5641.
  Lorenzen, Matthias; Muller, Matthias A. & Allgower, Frank
  
• Stochastic model predictive control without terminal constraints. International Journal of Robust and Nonlinear Control, 29(15), 4987-5001.
  Lorenzen, Matthias; Müller, Matthias A. & Allgöwer, Frank
  
• Economic Model Predictive Control for Robust Periodic Operation with Guaranteed Closed-Loop Performance. 2018 European Control Conference (ECC), 507-513.
  Wabersich, Kim P.; Bayer, Florian A.; Muller, Matthias A. & Allguwer, Frank
  
• On optimal system operation in robust economic MPC. Automatica, 88, 98-106.
  Bayer, Florian A.; Müller, Matthias A. & Allgöwer, Frank
  
• Linear robust adaptive model predictive control: Computational complexity and conservatism. 2019 IEEE 58th Conference on Decision and Control (CDC), 1383-1388.
  Kohler, Johannes; Andina, Elisa; Soloperto, Raffaele; Muller, Matthias A. & Allgower, Frank
  
• A robust adaptive model predictive control framework for nonlinear uncertain systems. International Journal of Robust and Nonlinear Control, 31(18), 8725-8749.
  Köhler, Johannes; Kötting, Peter; Soloperto, Raffaele; Allgöwer, Frank & Müller, Matthias A.
  
• Augmenting MPC Schemes With Active Learning: Intuitive Tuning and Guaranteed Performance. IEEE Control Systems Letters, 4(3), 713-718.
  Soloperto, Raffaele; Kohler, Johannes & Allgower, Frank
  
• Periodic optimal control of nonlinear constrained systems using economic model predictive control. Journal of Process Control, 92, 185-201.
  Köhler, Johannes; Müller, Matthias A. & Allgöwer, Frank
  
• Robust Economic Model Predictive Control without Terminal Conditions. IFAC-PapersOnLine, 53(2), 7097-7104.
  Schwenkel, Lukas; Köhler, Johannes; Müller, Matthias A. & Allgöwer, Frank
  
• A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems. IEEE Transactions on Automatic Control, 66(2), 794-801.
  Kohler, Johannes; Soloperto, Raffaele; Muller, Matthias A. & Allgower, Frank
  
• Model Predictive Control for Flexible Job Shop Scheduling in Industry 4.0. Applied Sciences, 11(17), 8145.
  Wenzelburger, Philipp & Allgöwer, Frank
  
• Robust and optimal predictive control of the COVID-19 outbreak. Annual Reviews in Control, 51(2021), 525-539.
  Köhler, Johannes; Schwenkel, Lukas; Koch, Anne; Berberich, Julian; Pauli, Patricia & Allgöwer, Frank
  
• Transient Performance of Tube-based Robust Economic Model Predictive Control. IFAC-PapersOnLine, 54(6), 28-35.
  Klöppelt, Christian; Schwenkel, Lukas; Allgöwer, Frank & Müller, Matthias A.
  
• Guaranteed Closed-Loop Learning in Model Predictive Control. IEEE Transactions on Automatic Control, 68(2), 991-1006.
  Soloperto, Raffaele; Muller, Matthias A. & Allgower, Frank