Optimal Distribution of the Resistivity of the Working Medium in the Channel of a Magnetohydrodynamic Generator
In this chapter, we apply the results obtained earlier to the problem of the optimal distribution of the resistivity of a conducting medium in the channel of a magnetohydrodynamic (MHD) generator. This problem has independent applied significance and simultaneously enables us to give a detailed illustration of the necessary conditions for optimality. Indeed, in a large number of cases the example illustrates many important facts that enable one to draw conclusions about the classical or generalized nature of an optimal solution, if one exists. It may happen that the originally chosen class of admissible controls does not contain an optimal control; in these cases, the necessary conditions indicate a natural way to relax the problem, i.e., a way of extending the class of admissible controls to guarantee the existence of an optimal control.
KeywordsAdmissible Control Current Line Working Medium Discontinuity Line Isoperimetric Problem
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