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

Abstract

This article concerns a class of time-optimal state constrained control\nproblems with dynamics defined by an ordinary differential equation involving a\nthree-dimensional steady flow vector field. The problem is solved via an\nindirect method based on the maximum principle in Gamkrelidze's form. The\nproposed computational method essentially uses a certain regularity condition\nimposed on the data of the problem. The property of regularity guarantees the\ncontinuity of the measure multiplier associated with the state constraint, and\nensures the appropriate behavior of the corresponding numerical procedure\nwhich, in general, consists in computing the entire field of extremals for the\nproblem in question. Several examples of vector fields are considered to\nillustrate the computational approach.\n