An indirect numerical method for a time-optimal state-constrained control problem in a steady two-dimensional fluid flow

This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements underlying the control of Autonomous Underwater Vehicles in realistic scenarii. The key contribution consists in devising a computational indirect method which becomes effective in the numerical computation of extremals to optimal control problems with state constraints by using the maximum principle in Gamkrelidze's form in which the measure Lagrange multiplier is ensured to be continuous. The specific problem of time-optimal control of an Autonomous Underwater Vehicle in a bounded space set, subject to the effect of a flow field and with bounded actuation, is used to illustrate the proposed approach. The corresponding numerical results are presented and discussed

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 via 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. The property of regularity 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 in computing the entire field of extremals for the problem in question. Several examples of vector fields are considered to illustrate the computational approach.Comment: 23 page