Abstract
A vector-valued impulsive control problem is considered whose dynamics, defined by a differential inclusion, are such that the vector fields associated with the singular term do not satisfy the so called Frobenius condition. A concept of proper solution based on a reparametrization procedure is adopted which enables the derivation of optimality conditions of the Hamilton-Jacobi type. These conditions are obtained by taking a limit of those for an appropriate sequence of auxiliary "standard" optimal control problems approximating the original one. Copyright (C) 2001 IFAC.

Abstract
It is becoming more and more common to use Autonomous Underwater Vehicles to perform tasks underwater. The use of this vehicles is affordable and its use doesn't raise any significant risk nor does it requires any human intervention. The traditional applications for the use of such vehicles were related with bathymetric tasks. But nowadays AUVs are being more and more used for variety of missions in open water environments, including the inspection of underwater structures and environmental monitoring in diverse oceanographic expeditions. Following some previous work, this paper addresses the problem of bottom following by an Autonomous Underwater Vehicle in an environment which is not previously known. In particular, the focus is on integrating a reactive behaviour based on environment sensing, with the on-board navigation software of the MARES AUV. For this, a guidance algorithm will provide the necessary pitch and depth references to the control layer of the vehicle. While the altitude towards the seabed can be measured with an altimeter, the pitch reference values are based on realtime estimation of the slope of the seabed. By doing so, it is possible to control the vehicle in a way that it will always maintain a constant attitude towards the bottom, and the trajectory followed will remain parallel to bottom, regardless of it's profile. © 2012 IEEE.

Abstract
The following addresses the control of an Autonomous Surface Vehicle (ASV) to follow the trajectory made by an Autonomous Underwater Vehicle (AUV) when the last is performing any given pre-programmed mission. In fact, it has been proved to be of great interest to have an ASV that could follow on the surface and even catch up the trajectory performed by the AUV, when executing a given mission. In order to achieve this desired coordinated motion between AUV and ASV, it would make sense just to program each of the vehicles with the same mission. However, due to the nature of vehicles, missions and also due to the localization system used, with this kind of solution some problems would arise, namely related with timings and synchronization, which are indeed difficult to overcome. The solution proposed here tries to estimate the AUV position, by tapping the signals exchanged between the former and each of the beacons of the acoustic localization network, and control and actuate the ASV in accordance.

Abstract
The latest technological developments on electronics, mechanics, optics, and other areas have made possible the availability of low cost and high performance sensors for navigation. This opens doors to the development of high accuracy navigation systems to be used on low cost small size underwater vehicles. This paper describes th development and implementation of the navigation system for the remotely operated vehicle (ROV) of the IES Project.

Abstract

Abstract
We present an algorithm for optimal control problems producing a minimizing sequence of control processes which are solutions to the associated differential inclusion and that the limiting process satisfies necessary conditions of optimality of the Pontryagin type. Numerical experiments show a good robustness to control perturbations and a good precision near the optimal solution.