Open AccessObserver‐based output feedback compensator design for linear parabolic PDEs with local piecewise control and pointwise observation in space
Author(s) -
Liu YaQiang,
Wang JunWei,
Sun ChangYin
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.1358
Subject(s) - pointwise , control theory (sociology) , mathematics , observer (physics) , partial differential equation , piecewise , exponential stability , lyapunov function , controller (irrigation) , distributed parameter system , parabolic partial differential equation , nonlinear system , mathematical analysis , computer science , control (management) , physics , quantum mechanics , artificial intelligence , agronomy , biology
This study presents an observer‐based output feedback compensator design for a linear parabolic partial differential equation (PDE), where a finite number of actuators and sensors are active over partial areas and at specified points in the spatial domain, respectively. In the proposed design method, a Luenberger‐type PDE observer is first constructed by using the non‐collocated pointwise observation to exponentially track the PDE state. Based on the estimated state, a collocated local piecewise state feedback controller is then proposed. By employing a Lyapunov direct method, integration by parts, Wirtinger's inequality and first mean value theorem for definite integrals, sufficient conditions on the exponential stability of the resulting closed‐loop coupled PDEs are presented in terms of standard linear matrix inequalities. Furthermore, both open‐loop and closed‐loop well‐posedness analysis results are also established by the C 0 ‐semigroup method. Numerical simulation results are presented to show the effectiveness of the proposed design method.