Boundary control of nonlinear elastic systems
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Authors
Do, Khac Duc
Date
2015Type
Journal Article
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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
ISSN
School
Department of Mechanical Engineering
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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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