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R. J. Williams and D. Zipser, “A Learning Algorithm for Continually Running Fully Recurrent Neural Networks,” Neural Computation, Vol. 1, No. 2, 1989, pp.270-280. doi:10.1162/neco.1989.1.2.270

has been cited by the following article:

• TITLE: Stable Adaptive Neural Control of a Robot Arm

  AUTHORS: Salem Zerkaoui, Saeed M. Badran

  KEYWORDS: Adaptive Control; Neural Networks; Multivariable Systems; Stability; Robustness; Lyapunov Function; Manipulator Robot

  JOURNAL NAME: Intelligent Control and Automation, Vol.3 No.2, May 23, 2012

  ABSTRACT: In this paper, stable indirect adaptive control with recurrent neural networks (RNN) is presented for square multivariable non-linear plants with unknown dynamics. The control scheme is made of an adaptive instantaneous neural model, a neural controller based on fully connected “Real-Time Recurrent Learning” (RTRL) networks and an online parameters updating law. Closed-loop performances as well as sufficient conditions for asymptotic stability are derived from the Lyapunov approach according to the adaptive updating rate parameter. Robustness is also considered in terms of sensor noise and model uncertainties. This control scheme is applied to the manipulator robot process in order to illustrate the efficiency of the proposed method for real-world control problems.