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Title data
Grüne, Lars ; Guglielmi, Roberto:
Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems.
Bayreuth
,
2017
. - 20 S.
![[thumbnail of LQ_dissipativity_turnpike.pdf]](https://epub.uni-bayreuth.de/style/images/fileicons/application_pdf.png) |
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Project information
| Project title: |
Project's official title Project's id Analyse der Regelgüte für verteilte und multikriterielle Modellprädiktive Regelung — Die Rolle von Paretofronten, multikriterieller Dissipativität und mehrfachen Gleichgewichten 244602989 |
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| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract
We investigate turnpike behaviour of discrete time optimal control problems with linear dynamics and linear-quadratic cost functions including state and control constraints. We give necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. As important tools we use the concepts of strict dissipativity and a new property called strict pre-dissipativity of a system at an equilibrium point and link these properties to the turnpike behaviour of the optimal control problem. Moreover, we give further conditions to ensure that the turnpike behavior is of exponential type, i.e., the optimal trajectories are exponentially close to a steady-state of the system for all but finitely many time instants whose number is bounded independently of the optimization horizon.
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