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    Bounded bilinear control of coupled first-order hyperbolic PDE and infinite dimensional ODE in the framework of PDEs with memory

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    Type
    Article
    Authors
    Mechhoud, Sarra cc
    Laleg-Kirati, Taous-Meriem cc
    KAUST Department
    Electrical Engineering Program
    Computational Bioscience Research Center (CBRC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-08-08
    Online Publication Date
    2019-08-08
    Print Publication Date
    2019-09
    Permanent link to this record
    http://hdl.handle.net/10754/656773
    
    Metadata
    Show full item record
    Abstract
    In this work, we consider the problem of bounded bilinear tracking control of a system of coupled first-order hyperbolic partial differential equation (PDE) with an infinite dimensional ordinary differential equation (ODE). This coupled PDE-infinite ODE system can be viewed as a degenerate system of two coupled first-order hyperbolic PDEs, the velocity of the ODE part vanishing. First, we convert this PDE-infinite ODE system into a first-order hyperbolic PDE with memory and investigate the bounded bilinear control problem in this framework. We consider as manipulated variable the constrained wave propagation velocity, which makes the control problem bounded and bilinear, and we take the measurements at the boundaries. To account for the actuator's constraints, we develop conditions under which the bounded control law ensures stability and tracking performances. This leads to a specification of the state-space region that enforces the desired system's closed-loop behaviour. To overcome the lack of full-state measurements, we design an observer-based bounded output-feedback control law which guarantees the reference tracking and uniform asymptotic stability of the system in closed-loop. A strong motivation of our work is the control problem of the solar collector parabolic trough where the manipulated control variable (the pump volumetric flow rate) is bilinear with respect to the PDE-infinite ODE model, and the measurements are taken at the boundary (tube's outlet). Simulation results illustrate the efficiency of the proposed control strategy.
    Citation
    Mechhoud, S., & Laleg-Kirati, T.-M. (2019). Bounded bilinear control of coupled first-order hyperbolic PDE and infinite dimensional ODE in the framework of PDEs with memory. Journal of Process Control, 81, 223–231. doi:10.1016/j.jprocont.2019.06.006
    Sponsors
    Research reported in this publication has been supported by the King Abdullah University of Science and Technology (KAUST).
    Publisher
    Elsevier BV
    Journal
    Journal of Process Control
    DOI
    10.1016/j.jprocont.2019.06.006
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S0959152418302439
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jprocont.2019.06.006
    Scopus Count
    Collections
    Articles; Electrical and Computer Engineering Program; Computational Bioscience Research Center (CBRC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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