Zusammenfassung
Die optimale Steuerung und Regelung hybrider Systeme ist herausfordernd, da sie sprunghafte Änderungen von Zustandsgrößen und die Kombinatorik ereignisdiskreten Verhaltens in die Optimierung von kontinuierlicher Dynamik einbringt. Dieser Beitrag gibt zunächst einen Überblick über die wichtigsten Lösungsverfahren für verschiedene Problemausprägungen. Anschließend wird für den Fall zeitdiskreter hybrider Systeme mit kontinuierlichen und diskreten Stelleingriffen eine neue Lösungsmethode vorgestellt, worin die optimale Lösung durch Verwendung von approximierten Kostenschranken und Nachbarschaftsbeziehungen explorierter Zustände mit relativ geringem Rechenaufwand angenähert wird.
Abstract
The optimal control of hybrid systems is challenging as it adds resets of state variables as well as the combinatorics of discrete-event behavior to the optimization of continuous dynamics. This contribution first provides an overview of the most important methods for different variants of the hybrid optimal control problem. For a problem instance of discrete-time hybrid systems with continuous and discrete controls, the paper then proposes a new technique. In there, the optimal solution is approximated with relatively low computational effort by use of approximated cost bounds and an adjacancy criterion for explored states.
Funding source: European Commission
Award Identifier / Grant number: 643921
Funding statement: Diese Untersuchung wurde zum Teil durch die Europäische Kommission im Rahmen des Projekts UnCoVerCPS (Bewilligung Nr. 643921) gefördert.
About the authors
M. Sc. Zonglin Liu ist wissenschaftlicher Mitarbeiter im Fachgebiet für Regelungs- und Systemtheorie am Fachbereich Elektrotechnik / Informatik an der Universität Kassel. Im Rahmen seiner Forschungstätigkeiten untersucht er Verfahren zur optimalen und prädiktiven Regelung von cyberphysischen Systemen mit Unsicherheiten.
Prof. Dr.-Ing. Olaf Stursberg ist Professor und Fachgebietsleiter für Regelungs- und Systemtheorie im Fachbereich Elektrotechnik / Informatik an der Universität Kassel. Seine Hauptarbeitsgebiete schließen Methoden zur Regelung und Analyse hybrider Systeme, zur optimalen und prädiktiven Regelung vernetzter und hierarchischer Systeme sowie Verfahren zur Regelung stochastischer und unsicherer Systeme ein.
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