Energy Optimal Xenon Shutdown

Pontryagin's optimum theory is applied to the problem of determining a flux shutdown program that limits xenon poisoning in a reactor while using the minimum nuclear energy or flux time. The analysis shows several points of difference from the time-optimal problem. Solutions are found for both the unrestricted problem and the problem where the xenon density is restricted within the control period to some maximum acceptable poisoning. The method of solution is new in utilizing a more straightforward optimum theorem and (of necessity) giving the full adjoint solutions. A full solution to the restrained problem shows that a free end-time optimum solution rises at zero flux to the xenon restraint value and follows this value to the target curve, ending the problem. Not only is the energy optimal problem of some practical interest but it makes an excellent illustration of the complications of the continuum solution in optimal control and the very practical need to consider only those solutions satisfying certain state restraints.