Time Optimal Solution to the Reactivity-Xenon Shutdown Problem

A time optimal criterion for the reactivity-xenon shutdown problem has been formulated and solved by application of the theorems of optimal processes as developed by L. S. Pontryagin et al. We desire the minimum time trajectory between any point of operation in the xenon-iodine phase space to a zero-power shutdown curve subject to the constraint that neither the shutdown curve nor the trajectory to the shutdown curve allow the xenon concentration to exceed an arbitrarily specified maximum. The optimal solution is shown to usually require sequential operation at zero power, variable (decreasing) power, and finally full power. The exact power program is calculated for one example.