Institutional Repository
Technical University of Crete
Technical University of Crete
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| URI | http://purl.tuc.gr/dl/dias/C9A3AD9D-1D2A-47F2-9B5C-E7210F9B5712 | - |
| Identifier | https://doi.org/10.1016/j.automatica.2018.02.006 | - |
| Identifier | https://www.sciencedirect.com/science/article/pii/S0005109818300669 | - |
| Language | en | - |
| Extent | 15 pages | en |
| Title | Compensation of actuator dynamics governed by quasilinear hyperbolic PDEs | en |
| Creator | Bekiaris-Liberis Nikolaos | en |
| Creator | Μπεκιαρης-Λυμπερης Νικολαος | el |
| Creator | Krstić, Miroslav | en |
| Publisher | Elsevier | en |
| Description | Nikolaos Bekiaris-Liberis was supported by the funding from the European Commission’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 747898, project PADECOT. | en |
| Content Summary | We present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by a certain class of, quasilinear, first-order hyperbolic PDEs. Since for such PDE-ODE cascades the speed of propagation depends on the PDE state itself (which implies that the prediction horizon cannot be a priori known analytically), the key design challenge is the determination of the predictor state. We resolve this challenge and introduce a PDE predictor-feedback control law that compensates the transport actuator dynamics. Due to the potential formation of shock waves in the solutions of quasilinear, first-order hyperbolic PDEs (which is related to the fundamental restriction for systems with time-varying delays that the delay rate is bounded by unity), we limit ourselves to a certain feasibility region around the origin and we show that the PDE predictor-feedback law achieves asymptotic stability of the closed-loop system, providing an estimate of its region of attraction. Our analysis combines Lyapunov-like arguments and ISS estimates. Since it may be intriguing as to what is the exact relation of the cascade to a system with input delay, we highlight the fact that the considered PDE-ODE cascade gives rise to a system with input delay, with a delay that depends on past input values (defined implicitly via a nonlinear equation). The developed control design methodology is applied to the control of vehicular traffic flow at distant bottlenecks. | en |
| Type of Item | Peer-Reviewed Journal Publication | en |
| Type of Item | Δημοσίευση σε Περιοδικό με Κριτές | el |
| License | http://creativecommons.org/licenses/by/4.0/ | en |
| Date of Item | 2018-04-25 | - |
| Date of Publication | 2018 | - |
| Subject | Traffic flow control | en |
| Subject | Distributed parameter systems | en |
| Bibliographic Citation | N. Bekiaris-Liberis and M. Krstic, "Compensation of actuator dynamics governed by quasilinear hyperbolic PDEs," Automatica, vol. 92, pp. 29-40, Jun. 2018. doi: 10.1016/j.automatica.2018.02.006 | en |
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