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This article concerns the problem of computing solutions to optimal control problems with state constraints and whose trajectory is also affected by known flow vector fields. 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 that becomes effective in the numerical computation of extremals to optimal control problems with state constraints by using multipliers of the Maximum Principle in the form of Gamkrelidze whose measure component 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.

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