Output feedback control of general linear heterodirectional hyperbolic ODE-PDE-ODE systems

Deutscher J, Gehring N, Kern R (2018)

Publication Status: Published

Publication Type: Journal article

Publication year: 2018

Journal

Automatica Elsevier

Publisher: PERGAMON-ELSEVIER SCIENCE LTD

Book Volume: 95

Pages Range: 472-480

DOI: 10.1016/j.automatica.2018.06.021

Abstract

This paper considers the backstepping design of observer-based compensators for general linear heterodirectional hyperbolic ODE-PDE-ODE systems, where the ODEs are coupled to the PDEs at both boundaries and the input appears in an ODE. A state feedback controller is designed by mapping the closed-loop system into a stable ODE-PDE-ODE cascade. This is achieved by representing the ODE at the actuated boundary in Byrnes-Isidori normal form. The resulting state feedback is implemented by an observer for a collocated measurement of the PDE state, for which a systematic backstepping approach is presented. The exponential stability of the closed-loop system is verified in the infinity-norm. It is shown that all design equations can be traced back to kernel equations known from the literature, to simple Volterra integral equations of the second kind and to explicitly solvable boundary value problems. This leads to a systematic approach for the boundary stabilization of the considered class of ODE-PDE-ODE systems by output feedback control. The results of the paper are illustrated by a numerical example. (C) 2018 Elsevier Ltd. All rights reserved.

Authors with CRIS profile

Joachim Deutscher Chair of Automatic Control

Involved external institutions

Technische Universität München (TUM) DE Germany (DE) Johannes Kepler Universität (JKU) Linz AT Austria (AT)

How to cite

APA:

Deutscher, J., Gehring, N., & Kern, R. (2018). Output feedback control of general linear heterodirectional hyperbolic ODE-PDE-ODE systems. Automatica, 95, 472-480. https://dx.doi.org/10.1016/j.automatica.2018.06.021

MLA:

Deutscher, Joachim, Nicole Gehring, and Richard Kern. "Output feedback control of general linear heterodirectional hyperbolic ODE-PDE-ODE systems." Automatica 95 (2018): 472-480.

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