Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially varying coefficients. Thereby, the ODE is coupled to the PDE in-domain and at the uncontrolled boundary, whereas the ODE is coupled with the latte...

Full description

Saved in:
Bibliographic Details
Published inInternational journal of control Vol. 92; no. 10; pp. 2274 - 2290
Main Authors Deutscher, J., Gehring, N., Kern, R.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.10.2019
Taylor & Francis Ltd
Subjects
backstepping
Boundary conditions
boundary control
Control systems design
coupled PDE-ODE systems
Decoupling
Distributed-parameter systems
Feedback control
Hyperbolic systems
observers
Output feedback
State feedback
Online AccessGet full text

Cover

More Information
Summary:This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially varying coefficients. Thereby, the ODE is coupled to the PDE in-domain and at the uncontrolled boundary, whereas the ODE is coupled with the latter boundary. For the state feedback design, a two-step backstepping approach is developed, which yields the conventional kernel equations and additional decoupling equations of simple form. In order to implement the state feedback controller, the design of observers for the PDE-ODE systems in question is considered, whereby anti-collocated measurements are assumed. Exponential stability with a prescribed convergence rate is verified for the closed-system pointwise in space. The resulting compensator design is illustrated for a 4 × 4 heterodirectional hyperbolic system coupled with a third-order ODE modelling a dynamic boundary condition.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2018.1436770