Control of nonlinear systems with actuator dynamics governed by quasilinear first order hyperbolic PDEs (EN)

Μπεκιαρης-Λυμπερης Νικολαος (EL)

Bekiaris-Liberis Nikolaos (EN)

Krstić, Miroslav (EN)

Πολυτεχνείο Κρήτης (EL)

Technical University of Crete (EN)

We present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by quasilinear transport 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). (EN)

conferenceItem

poster

Predictor feedback (EN)

Hyperbolic PDEs (EN)

PDE-ODE cascades (EN)

Πολυτεχνείο Κρήτης

Ιδρυματικό Αποθετήριο Πολυτεχνείου Κρήτης

School of Mineral Resources Engineering - Journal Publications

Αγγλική γλώσσα

2018

http://purl.tuc.gr/dl/dias/5F38152B-80DC-422D-B019-7BDF0AF0BFC410.23919/ECC.2018.8550318

Institute of Electrical and Electronics Engineers (EN)