Use of a non-linear clock in the perturbation analysis of time optimal control problems

摘要

The authors phrase a regular perturbation problem for a time optimal control problem in which the optimal controller is bang-bang. Formal procedures for computing the asymptotic series expansions of the variables and then establishing the uniform validity of these asymptotic series are given. The technique is based upon the idea of introducing a nonlinear change of variables which freezes the switch times and the terminal time of the perturbed problem, and allows for an asymptotic analysis in the new variables. This is necessitated by the fact that a perturbation analysis in the original variables does not, in general, exist because of the discontinuous nature of the control.