Two boundary value control algorithms
For the heat equation on the finite domain using the unified transform method
W.M. van Wijk (TU Delft - Mechanical Engineering)
S. Wahls – Mentor (TU Delft - Team Shengling Shi)
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Abstract
In this work we investigate two boundary-value control algorithms for the heat equation on the finite interval. The algorithms we discuss here are based on the unified transform method (UTM), a method invented by A. S. Fokas to solve boundary value problems of partial differential equations. We first inspect the boundary-value control algorithm presented in Kalimeris et al.. This algorithm is originally constructed to find the Neumann boundary value on the right side for nullcontrol of the heat equation. In this work the algorithm has been expanded to allow arbitrary control objective, with either the Dirichlet or Neumann boundary values from both sides. Other improvements have also been made.
Furthermore, a second algorithm is constructed, which aims for a lower computational cost than the first algorithm. This second algorithm uses the same principles as the algorithm used in [10], but stems from another part of the derivation of the UTM. Both algorithms were tested with various control objectives, and show promising results.