Title: Robust stability analysis of adaptive control based on recurrent ANN

Authors: Salem Zerkaoui, Fabrice Druaux, Edouard Leclercq, Dimitri Lefebvre

Addresses: Universite Le Havre – GREAH, 25 rue P. Lebon, 76063 Le Havre, France. ' Universite Le Havre – GREAH, 25 rue P. Lebon, 76063 Le Havre, France. ' Universite Le Havre – GREAH, 25 rue P. Lebon, 76063 Le Havre, France. ' Universite Le Havre – GREAH, 25 rue P. Lebon, 76063 Le Havre, France; IUT, Place Robert Schuman, BP 4006, 76610 Le Havre, France

Abstract: Adaptive control by means of neural networks for non-linear dynamical systems is an open issue. For real world applications, practitioners have to pay attention to external disturbances, parameters uncertainty and measurement noise, as long as these factors will influence the stability of the closed loop system. As a consequence, robust stability of the closed loop controlled by neural network is an important issue that must be considered. Our contribution concerns the robustness analysis and synthesis of adaptive indirect control scheme. This scheme is based on fully connected neural networks, and inspired from the standard real time recurrent learning. This analysis is concerned by combining Lyapunov approach and linearisation around the nominal parameters to establish analytical sufficient conditions for the global robust stability of adaptive neural network controller. Advantages of the proposed algorithm are suggested according to simulation examples.

Keywords: adaptive control; fully connected recurrent neural networks; real time recurrent learning; RTRL; Lyapunov function; robust stability; simulation.

DOI: 10.1504/IJMIC.2008.021771

International Journal of Modelling, Identification and Control, 2008 Vol.5 No.1, pp.14 - 26

Published online: 03 Dec 2008 *

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