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LP Modelling for the Time Optimal Control Problem of the Heat Equation

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Journal of Mathematical Modelling and Algorithms

Abstract

To find a control function which puts the heat equation 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.

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Authors and Affiliations

  1. Department of Mathematics, School of Mathematical Sciences, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran

    A. R. Nazemi

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  1. A. R. Nazemi
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Nazemi, A.R. LP Modelling for the Time Optimal Control Problem of the Heat Equation. J Math Model Algor 10, 227–244 (2011). https://doi.org/10.1007/s10852-011-9151-7

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  • DOI: https://doi.org/10.1007/s10852-011-9151-7

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