# On modeling, analysis and simulation of optimal control problems for dynamic networks of Euler-Bernoulli and Rayleigh-beams

G. Leugering, W. Rathmann:
**On modeling, analysis and simulation of optimal control problems for dynamic networks of Euler-Bernoulli and Rayleigh-beams**

in:
*Control of nonlinear distributed parameter systems,*
*
Goong Chen, I. Lasiecka and Jianxin Zhou
(eds.)
*

*Lecture Notes in Pure and Applied Mathematics*

**218**, Dekker, New York, 2001, 199 - 232

ISBN/ISSN/ISMV Nummer: 0-8247-0564-5

MR Nummer:
1817183

Zentralblattnummer:
0991.49021

Keywords: network models; Euler-Bernoulli- and Rayleigh-beams; nonoverlapping domain decomposition procedure; convergence; optimal control

Mathematics Subject Classification Code: 49M27 (74K10 74M05 93C20)

## Abstract:

We consider a network of Euler-Bernoulli and Rayleigh beams. For the sake of simplicity, we concentrate on scalar displacements coupled to torsion. We show that the model is well-posed in appropriate ramification spaces. We then describe a dynamic nonoverlapping domain decomposition procedure of the network into its individual edges and provide a proof of convergence. Further, we formulate typical optimal control problems, related to exact controllability. The optimality system is solved using conjugate gradients. Various numerical examples illustrate the method.