Pade-approximation as a "bridge" between two parametric boundary asymptotics

For classical optimal control problem with free right end point and two groups of motions in one of which velocity has both large and small values is constructed approximate analytic expressions for optimal control based on Pade-approximation. It is instinctively clear that weakly controllable systems and systems with hign-gain coefficient are connected by some parametric "bridge" even though the contrary valuations of parameter. Copyright (C) 2001 IFAC.