Abstract
In model predictive control, the control action is found at each sampling time by solving an online optimization problem. Computationally, this step is very demanding, especially if compared to the evaluation of traditional control laws. This has limited the application of model predictive control to systems with slow dynamics for many years. Recently, several methods have been proposed in the literature which promise a substantial reduction of the computation time by either running the computation in parallel (distributed model predictive control) or exploiting the problem structure (fast model predictive control). A combination of these methods has not yet been considered in the literature. To achieve this goal, different optimization techniques need to be employed at once. The order of how these methods are applied matters. This paper considers fast distributed model predictive control combining the alternating direction method of multipliers (ADMM), the interior point method (IPM) and the Riccati iteration for a particular class of multi-agent systems for which the order of the methods can be arbitrarily changed. This leads to two different solver schemes where a trade-off arises between computation time and number of communications required to reach consensus. A simplified problem involving the formation control of a fleet of vehicles is considered at the end.
Zusammenfassung
Bei der modellprädiktiven Regelung wird die Stellgröße in jedem Abtastschritt durch Lösen eines Optimierungsproblems ermittelt. Das Lösen des Optimierungsproblems ist überaus rechenintensiv und damit äußerst zeitaufwändig, insbesondere im Vergleich zu klassischen Regelungsmethoden. Die modellprädiktive Regelung war dadurch über lange Jahre auf Systeme mit langsamer Dynamik beschränkt. In letzter Zeit wurden in der Literatur verschiedene Methoden vorgeschlagen, die eine maßgebliche Verringerung der Rechenzeit versprechen, entweder durch eine Ausführung der Berechnungen in parallelisierter Form (verteilte modellprädiktive Regelung) oder durch eine Ausnutzung der Struktur des Optimierungsproblems (schnelle modellprädiktive Regelung). Eine Kombination dieser Methoden wurde bislang noch nicht betrachtet. Für eine solche Kombination müssen verschiedene Optimierungsmethoden miteinander verknüpft werden. Hierbei ist insbesondere die Reihenfolge, in welcher die Optimierungsmethoden angewendet werden, von Bedeutung. Dieser Beitrag stellt ein Verfahren für die schnelle verteilte modellprädiktive Regelung basierend auf einer Kombination der Methode der alternierenden Richtung der Multiplikatoren, des Innere-Punkte-Verfahrens und der Riccati-Iteration für eine spezifische Klasse von Multiagentensystemen vor, bei denen die Reihenfolge der Methoden beliebig verändert werden kann. Dies führt zu zwei verschiedenen Lösungsschemata, mit denen ein Kompromiss zwischen Rechen- und Kommunikationsaufwand ermöglicht wird. Das Verfahren wird für die Formationsregelung einer Fahrzeugflotte am Ende des Beitrags veranschaulicht.
About the authors
M.Sc. Giuliano Costantini is researcher in the Division of Electromobility at the University of Kaiserslautern. His research interests include numerical optimization methods, networked systems, distributed control, model predictive control, and their application to vehicular systems.
apl. Prof. Dr.-Ing. Daniel Görges is research group leader at the German Research Center for Artificial Intelligence (DFKI). His research interests include methods for model predictive control, distributed control and learning control and their applications in vehicular systems, transportation systems, mechatronic systems, and power systems.
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