Regular path-constrained time-optimal control problems in three-dimensional flow fields

This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved by virtue of an indirect method based on the maximum principle in Gamkrelidze's form. The proposed computational method essentially uses a certain regularity condition imposed on the data of the problem. A regularity assumption guarantees the continuity of the measure multiplier associated with the state constraint and ensures the appropriate behavior of the corresponding numerical procedure which, in general, consists of computing the entire field of extremals for the problem in question. Several examples of vector fields are considered to illustrate the computational approach. (c) 2020 European Control Association. Published by Elsevier Ltd. All rights reserved.