Minimizing the natural fuel requirement for nuclear reactor power systems: A nonstandard optimal control problem

Abstract

A class of model problems in nuclear reactor economics is defined and shown to be equivalent to a linear optimal control problem to which present versions of the maximum principle apparently cannot be applied. It is shown that the search for an optimal control can be restricted tocontrols of maximum fuel utilization (Comfu), and that theComfu's are in a one-to-one correspondence with the functions which satisfy certain inequalities and are solutions of a nonlinear Volterra integral equation containing the value of the cost functional as a parameter. In the general case, one can establish an iterative procedure, involving solution of the integral equation at each iteration, for approximating the optimalComfu. For some important special cases, a point on the solution corresponding to the optimalComfu is knowna priori, and thus the optimalComfu can be obtained by solving the integral equation only once. Some possible generalizations of the original economic model are also discussed.