Singular perturbations and singular arcs--Part I

Singular perturbation theory is applied to obtain the asymptotic solution for the nearly singular optimal control of a constant linear system on a finite time interval In the limit as the control cost is reduced to zero, the initial control is found to have an impulse-like behavior, while the outer solution agrees asymptotically with the familiar solution for a singular arc. The detailed structure of the impulse is provided by the asymptotic solution.