DocumentCode :
3466934
Title :
Optimal control of non-homogeneous wave equation
Author :
Sklyar, G.M. ; Szkibiel, G.
Author_Institution :
Inst. of Math., Szczecin Univ., Szczecin, Poland
fYear :
2011
fDate :
22-25 Aug. 2011
Firstpage :
393
Lastpage :
397
Abstract :
While studying vibrations of non-homogeneous strings or chains a trigonometric non-Fourier moment problems arise. The existence of solutions of such problems is still researched by many authors. In current note, a particular solution, called optimal, i.e. the one with the least L2-norm is searched for. Proposed is an algorithm that allows to change an infinite system of equations into the linear one with only a finite number of equations. The mentioned algorithm is based on the fact, that in the case of a Fourier moment problem, the optimal solution is periodic and easy to construct. The optimal solution of a non-Fourier moment problem close to a Fourier one is approximated by a sequence of solutions with periodicity disturbed in a finite number of equations. It is proved that this sequence of approximations converges to the solution sought for. The note is concluded with the application of proposed algorithm.
Keywords :
approximation theory; optimal control; wave equations; nonhomogeneous chains; nonhomogeneous strings; nonhomogeneous wave equation; optimal control; trigonometric nonFourier moment problem; vibration; Approximation algorithms; Approximation methods; Boundary conditions; Eigenvalues and eigenfunctions; Equations; Optimal control; Propagation;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Methods and Models in Automation and Robotics (MMAR), 2011 16th International Conference on
Conference_Location :
Miedzyzdroje
Print_ISBN :
978-1-4577-0912-8
Type :
conf
DOI :
10.1109/MMAR.2011.6031379
Filename :
6031379
Link To Document :
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