Optimal control of system governed by the Gao beam equation

Jitka  Machalová; Horymír  Netuka

doi:10.3934/proc.2015.0783

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2015, Volume 2015: 783-792. Doi: 10.3934/proc.2015.0783 open access

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Optimal control of system governed by the Gao beam equation

Jitka Machalová^1, and
Horymír Netuka^1,

1.
Palacký University, Faculty of Science, Department of Mathematical Analysis and Applications of Mathematics, 17. listopadu 1192/12, Olomouc, 771 46

Received: August 31, 2014

Revised: March 31, 2015

Published: October 2015

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Abstract

In this contribution several optimal control problems are mathematically formulated and analyzed for a nonlinear beam which was introduced in 1996 by David Y. Gao. The beam model is given by a static nonlinear fourth-order differential equation with some boundary conditions. The beam is here subjected to a vertical load and possibly to an axial tension load as well. A cost functional is constructed in such a way that the lower its value is, the better model we obtain. Both existence and uniqueness are studied for the solution to the proposed control problems along with optimality conditions. Due to the fact that analytical solution is not available for the nonlinear Gao beam, a finite element approximation is provided for the proposed problems. Numerical results are compared with Euler-Bernoulli beam as well as the authors' previous considerations.

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Mathematics Subject Classification: Primary: 49J15, 65L60; Secondary: 49N10.

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References

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