Basis Functions for the Exact Control of the Heat Equation

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Abstract
The problem of using boundary control to drive the one-dimensional heat equation exactly to a given terminal condition in a finite time T is considered. The control function is described in terms of a set of finite dimensional basis functions which have certain optimality properties. An efficient algorithm for the evaluation of these basis functions and the control is presented and the use of the control is demonstrated using numerical examples. The controls resulting from this algorithm are likely to be most useful as initial approximations to the control in, for example, quadratic cost control problems.

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