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    Output stabilization of boundary-controlled parabolic PDEs via gradient-based dynamic optimization

    228364_228364.pdf (1.991Mb)
    Access Status
    Open access
    Authors
    Ren, Z.
    Xu, C.
    Lin, Qun
    Loxton, Ryan
    Date
    2015
    Type
    Conference Paper
    
    Metadata
    Show full item record
    Citation
    Ren, Z. and Xu, C. and Lin, Q. and Loxton, R. 2015. Output stabilization of boundary-controlled parabolic PDEs via gradient-based dynamic optimization, in Proceedings of the 2015 American Control Conference, Jul 1-3 2015, pp. 4257-4262. Chicago: IEEE.
    Source Title
    Proceedings of the 2015 American Control Conference
    Source Conference
    2015 American Control Conference
    DOI
    10.1109/ACC.2015.7171998
    ISBN
    9781479986866
    School
    Department of Mathematics and Statistics
    Remarks

    Copyright © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

    URI
    http://hdl.handle.net/20.500.11937/15628
    Collection
    • Curtin Research Publications
    Abstract

    This paper proposes a new control synthesis approach for the stabilization of boundary-controlled parabolic partial differential equations (PDEs). In the proposed approach, the optimal boundary control is expressed in integral state feedback form with quadratic kernel function, where the quadratic’s coefficients are decision variables to be optimized. We introduce a system cost functional to penalize both state and kernel magnitude, and then derive the cost functional’s gradient in terms of the solution of an auxiliary “costate” PDE. On this basis, the output stabilization problem can be solved using gradient-based optimization techniques such as sequential quadratic programming. The resulting optimal boundary control is guaranteed to yield closed-loop stability under mild conditions. The primary advantage of our new approach is that the costate PDE is in standard form and can be solved easily using the finite difference method. In contrast, the traditional control synthesis approaches for boundary-controlled parabolic PDEs (i.e., the LQ control and backstepping approaches) require solving non-standard Riccati-type and Klein-Gorden-type PDEs.

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