# Nonlinear Feedback Control and Artificial Intelligence Computational Methods applied to a Dissipative Dynamic Contact Problem

### Daniela Danciu, Andaluzia Cristina Matei, Sorin Daniel Micu, Ionel Rovenţa

#### Abstract

In this paper we consider a vibrational percussion system described by a one-dimensional hyperbolic partial differential equation with boundary dissipation at one extremity and a normal compliance contact condition at the other extremity. Firstly, we obtain the mathematical model using the Calculus of variations and we prove the existence of weak solutions. Secondly, we focus on the numerical approximation of solutions by using a neuromathematics approach – a well-structured numerical technique which combines a specific approach of Method of Lines with the paradigm of Cellular Neural Networks. Our technique ensures from the beginning the requirements for convergence and stability preservation of the initial problem and, exploiting the local connectivity of the approximating system, leads to a low computational effort. A comprehensive set of numerical simulations, considering both contact and non-contact cases, ends the contribution.

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#### Paper Citation

#### in Harvard Style

Danciu D., Matei A., Micu S. and Rovenţa I. (2014). **Nonlinear Feedback Control and Artificial Intelligence Computational Methods applied to a Dissipative Dynamic Contact Problem** . In *Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-039-0, pages 528-539. DOI: 10.5220/0005055005280539

#### in Bibtex Style

@conference{icinco14,

author={Daniela Danciu and Andaluzia Cristina Matei and Sorin Daniel Micu and Ionel Rovenţa},

title={Nonlinear Feedback Control and Artificial Intelligence Computational Methods applied to a Dissipative Dynamic Contact Problem},

booktitle={Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2014},

pages={528-539},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005055005280539},

isbn={978-989-758-039-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Nonlinear Feedback Control and Artificial Intelligence Computational Methods applied to a Dissipative Dynamic Contact Problem

SN - 978-989-758-039-0

AU - Danciu D.

AU - Matei A.

AU - Micu S.

AU - Rovenţa I.

PY - 2014

SP - 528

EP - 539

DO - 10.5220/0005055005280539