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Feedback control of nonlinear hyperbolic PDE systems inspired by traffic flow models

Karafyllis, Iasson, Bekiaris-Liberis Nikolaos, Papageorgiou Markos

Πλήρης Εγγραφή


URI: http://purl.tuc.gr/dl/dias/0C605B68-6B82-4DE7-AB29-557E7EBF4D2A
Έτος 2018
Τύπος Δημοσίευση σε Περιοδικό με Κριτές
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Βιβλιογραφική Αναφορά I. Karafyllis, N. Bekiaris-Liberis and M. Papageorgiou, "Feedback control of nonlinear hyperbolic PDE systems inspired by traffic flow models," IEEE Trans. Automat. Contr., Early Access, 2018. doi: 10.1109/TAC.2018.2887141 https://doi.org/10.1109/TAC.2018.2887141
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Περίληψη

The paper investigates and provides results, including feedback control, for a nonlinear, hyperbolic, 1-D PDE system on a bounded domain. The considered model consists of two first-order PDEs with a dynamic boundary condition on the one end and actuation on the other. It is shown that, for all positive initial conditions, the system admits a globally defined, unique, classical solution that remains positive and bounded for all times; these properties are important, for example for traffic flow models. Moreover, it is shown that global stabilization can be achieved for arbitrary equilibria by means of an explicit boundary feedback law. The stabilizing feedback law depends only on collocated boundary measurements. The efficiency of the proposed boundary feedback law is demonstrated by means of a numerical example of traffic density regulation.

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