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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 1-2/2016

01-06-2016 | Original Research

Boundary control of nonlinear elastic systems

Author: K. D. Do

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2016

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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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Metadata
Title
Boundary control of nonlinear elastic systems
Author
K. D. Do
Publication date
01-06-2016
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2016
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-015-0907-5

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