Skip to Main Content
Optimal control of a class of high-order time delay systems is considered. The mathematical description of these systems is written in such a way that whenever a scalar parameter is perturbed, the dimensionality of the system is reduced (singular perturbation). Further, the time delayed variables also will disappear from the system equations. An asymptotic power series solution of the optimal control is then developed with respect to the scalar parameter. This asymptotic control is valid for the high-order time delay system, while it is calculated on the basis of only a reduced order ordinary system. At first a scalar example illustrates the method of constructing the asymptotic expansions. Then the method is applied to an eighth order nonlinear time delay model of a coupled-core nuclear reactor system by reducing it to a second order ordinary model. Computationally, the asymptotic approximation method is compared with the second variation method and is shown to be superior.