Title : ( Time optimal control problem of the heat equation with thermal source )
Authors: Sohrab Effati , Alireza Nazemi , Hassan Shabani ,
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Abstract
To obtain a control function which puts the heat equation with thermal source in an unknown minimum time into a stationary regime is considered. Using an embedding method, the problem of finding the time optimal control is reduced to one consisting of minimizing a linear form over a set of positive measures. The resulting problem can be approximated by a finite-dimensional linear programming (LP) problem. The nearly optimal control is constructed from the solution of the final LP problem. To find the lower bound of the optimal time, a search algorithm is proposed. Some examples demonstrate the effectiveness of the method.
Keywords
heat equation; moment problem; measure theory; time optimal control; linear programming.
@article{paperid:1035485,
author = {Effati, Sohrab and Alireza Nazemi and Hassan Shabani},
title = {Time optimal control problem of the heat equation with thermal source},
journal = {IMA Journal of Mathematical Control and Information},
year = {2013},
volume = {31},
number = {3},
month = {August},
issn = {0265-0754},
pages = {385--402},
numpages = {17},
keywords = {heat equation; moment problem; measure theory; time optimal control; linear programming.},
}
%0 Journal Article
%T Time optimal control problem of the heat equation with thermal source
%A Effati, Sohrab
%A Alireza Nazemi
%A Hassan Shabani
%J IMA Journal of Mathematical Control and Information
%@ 0265-0754
%D 2013
