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    Boundary control of nonlinear elastic systems

    Access Status
    Fulltext not available
    Authors
    Do, Khac Duc
    Date
    2015
    Type
    Journal Article
    
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    Citation
    Do, K.D. 2015. Boundary control of nonlinear elastic systems. Journal of Applied Mathematics and Computing. 51 (1): pp. 315-339.
    Source Title
    Journal of Applied Mathematics and Computing
    DOI
    10.1007/s12190-015-0907-5
    ISSN
    1598-5865
    School
    Department of Mechanical Engineering
    URI
    http://hdl.handle.net/20.500.11937/28811
    Collection
    • Curtin Research Publications
    Abstract

    This paper presents a design of boundary controllers for global stabilization of nonlinear elastic systems, which cover nonlinear elastic strings and membranes, under external bounded forces. The boundary controllers guarantee exponential convergence of the unique system solution to a ball centered at the origin. The Faedo–Galerkin approximation method is used to prove existence and uniqueness of the solution of the closed-loop system. The control design is based on the Lyapunov direct method, Gronwall’s, Poincare’s, and Holder’s inequalities, and Sobolev embedding theorems. Simulations illustrate the effectiveness of the proposed controllers.

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