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- Title
Time optimal control problem of the heat equation with thermal source.
- Authors
Effati, Sohrab; Nazemi, Alireza; Shabani, Hassan
- 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.
- Subjects
OPTIMAL control theory; HEAT equation; EMBEDDINGS (Mathematics); LINEAR programming; MOMENT problems (Mathematics)
- Publication
IMA Journal of Mathematical Control & Information, 2014, Vol 31, Issue 3, p385
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/dnt016