Distributed dissipativity and graph theoretic properties in distributed economic MPC

• Applicant: Professor Dr.-Ing. Frank Allgöwer
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2013 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 244600449

• Final Report Year: 2024

Final Report Abstract

We developed distributed economic model predictive control (MPC) schemes for a group of dynamic systems that are connected through shared objectives. One focus was on systems that pursue individual interests but also need to coordinate towards a cooperative goal, which requires a trade-off between egoistic and cooperative behavior. The cooperative goal is, however, not known in advance, but is negotiated online. The systems receive in each time step only the current state of this negotiation, which may not yet reflect the resulting cooperative objective. Our developed distributed economic MPC schemes lead to a solution such that the individual systems’ economic objectives are minimized during a transient phase and the cooperative goal is satisfied by eventually deviating from this egoistic behavior. We rigorously show that the schemes achieve the desired properties, and complete important steps towards deriving transient performance estimates. Another focus was on deriving structured dissipativity from local properties of systems interconnected by costs. Such a dissipativity property, depending on the structure of the system interconnection, plays an essential role in the resulting closed-loop system behavior, if distributed economic MPC is applied. We derived conditions on when local dissipativity is preserved under suitable cost coupling. Furthermore, we introduced the concept of approximate dissipativity. This allows for a derivation of performance and stability properties also for those cases, where these strong conditions do not hold, and for interconnections in which systems join and leave online. We designed tailored distributed economic MPC schemes that exploit this property. In addition, we draw on graph theoretic properties of the interconnection structure to analyze the resulting approximate dissipativity and estimate the impact of a system joining the network, when no recomputation and reconfiguration of the MPC scheme is performed. Finally, we applied the distributed economic MPC schemes to application examples, including power systems and supply chain management. The scientific output of this project amounts to 27 publications, of which 9 are journal papers, 17 are peer-reviewed conference papers, and one is a dissertation, constituting a major contribution to research in distributed economic MPC.

Publications

• Real time economic dispatch for power networks: A distributed economic model predictive control approach. 2017 IEEE 56th Annual Conference on Decision and Control (CDC), 6340-6345.
  Kohler, Johannes; Muller, Matthias A.; Li, Na & Allgower, Frank
  
• Transient performance of economic model predictive control with average constraints. 2017 IEEE 56th Annual Conference on Decision and Control (CDC), 5557-5562.
  Kohler, Philipp N.; Muller, Matthias A. & Allgower, Frank
  
• A distributed economic MPC framework for cooperative control under conflicting objectives. Automatica, 96, 368-379.
  Köhler, Philipp N.; Müller, Matthias A. & Allgöwer, Frank
  
• Graph topology and subsystem centrality in approximately dissipative system interconnections. 2019 IEEE 58th Conference on Decision and Control (CDC), 7441-7447.
  Kohler, Philipp N.; Muller, Matthias A. & Allgower, Frank
  
• A distributed optimization algorithm for Nash bargaining in multi-agent systems. IFAC-PapersOnLine, 53(2), 2684-2689.
  Camisa, Andrea; Köhler, Philipp N.; Müller, Matthias A.; Notarstefano, Giuseppe & Allgöwer, Frank
  
• Distributed Model Predictive Control for Consensus of Constrained Heterogeneous Linear Systems. 2020 59th IEEE Conference on Decision and Control (CDC), 1248-1253.
  Hirche, Matthias; Kohler, Philipp N.; Muller, Matthias A. & Allgower, Frank
  
• Distributed economic model predictive control for cooperative supply chain management using customer forecast information. IFAC Journal of Systems and Control, 15, 100125.
  Köhler, Philipp N.; Müller, Matthias A.; Pannek, Jürgen & Allgöwer, Frank
  
• Approximate Dissipativity of Cost-Interconnected Systems in Distributed Economic MPC. IEEE Transactions on Automatic Control, 68(4), 2170-2182.
  Köhler, Philipp N.; Müller, Matthias A. & Allgöwer, Frank
  
• Distributed Model Predictive Control for Periodic Cooperation of Multi-Agent Systems. IFAC-PapersOnLine, 56(2), 3158-3163.
  Köhler, Matthias; Müller, Matthias A. & Allgöwer, Frank
  
• Transient Performance of MPC for Tracking. IEEE Control Systems Letters, 7(2023), 2545-2550.
  Köhler, Matthias; Krügel, Lisa; Grüne, Lars; Müller, Matthias A. & Allgöwer, Frank
  
• Distributed MPC for Self-Organized Cooperation of Multiagent Systems. IEEE Transactions on Automatic Control, 69(11), 7988-7995.
  Köhler, Matthias; Müller, Matthias A. & Allgöwer, Frank