Optimal chattering solutions for longitudinal vibrations of a nonhomogeneous bar

2013/02/16 by Larissa Manita, Manita, Larissa
Mathematics · Physics and Astronomy · #49K20 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:49K20

paper · pdf · doi:10.48550/arxiv.1302.4001

12 pages

arxiv created 2013/02/16 · arxiv updated 2013/02/19

Abstract

We consider a control problem for longitudinal vibrations of a nonhomogeneous bar with clamped ends. The vibrations of the bar are controlled by an external force which is distributed along the bar. For the minimization problem of mean square deviation of the bar we prove that the optimal control has an infinite number of switchings in a finite time interval, i.e., the optimal control is the chattering control.

Related

• Optimal Motions of an Elastic Structure under Finite-Dimensional Distributed Control
• Regularization of chattering phenomena via bounded variation control
• Optimal Control of Longitudinal Motions for an Elastic Rod with Distributed Forces
• A bang-bang solution with infinitely many switching points for a parabolic boundary control problem with terminal observation
• Optimal control problems with oscillations, concentrations and discontinuities