Introduction

We present in this appendix the tests of the external and internal algorithms conducted by Nicolas Seube at Thomson-SINTRA to control the tracking of an exosystem by an autonomous underwater vehicle (AUV). This system has three degrees of freedom (planar motion), six state variables (positions, heading, and their derivatives), and three controls (thruster forces). The dynamics of an AUV are highly nonlinear, coupled, and sometimes fully interacting, thus making it difficult to control by the usual methods. Moreover, the dynamics are poorly known, because only approximate hydrodynamic models are available for realworld vehicles. Finally, we need to involve the marine currents that can significantly perturb the dynamics of the AUV.

In addition, the problem of controlling an AUV cannot be linearized about a single velocity axis because all vehicle velocities usually have the same range; conventional linear control techniques clearly are unable to provide adequate performance by the control systems.

We shall present three different learning rules that address the problems of uniform minimization and adaptive learning by a set-valued feedback control map. The three classes of algorithms presented here have been tested in the case of the Japanese Dolphin AUV.

In particular, it is shown that the gradient step size is critical for the external rule, but is not critical for the uniform external algorithm. The latter could also be applied to pattern-classification problems, and may provide a plausible alternative method to stochastic gradient algorithms.