Institutional Repository [SANDBOX]
Technical University of Crete
EN  |  EL

Search

Browse

My Space

Compensation of actuator dynamics governed by quasilinear hyperbolic PDEs

Bekiaris-Liberis Nikolaos, Krstić, Miroslav

Full record


URI: http://purl.tuc.gr/dl/dias/C9A3AD9D-1D2A-47F2-9B5C-E7210F9B5712
Year 2018
Type of Item Peer-Reviewed Journal Publication
License
Details
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 https://doi.org/10.1016/j.automatica.2018.02.006
Appears in Collections

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.

Available Files

Services

Statistics