Investigation of a perturbation method to solve essentially non-regular time-optimal control problems with state constraints

Abstract

A general time-optimal control problem in the presence of state constraints is investigated. From the application point of view, the relevance of this article resides in the necessity to deal with extremals which do not satisfy the typically required assumptions of regularity. In this case, some useful properties of the Lagrange multipliers may not be available if one undertakes the effort to solve this problem numerically in the framework of indirect approach, that is, by using the maximum principle. To overcome this difficulty, we develop a certain regularization technique by constructing regular approximations of the original problem. A regular problem is possible to solve numerically, thus, a solution to the ε-approximation can be considered as an approximate calculation of the original solution. One application of the proposed method to the problem of optimal control of a mobile robot is provided.