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A real-time analogue recurrent neural network (RNN) can extract and learn the unknown dynamics (and features) of a typical control system such as a robot manipulator. The task at hand is a tracking problem in the presence of disturbances. With reference to the tasks assigned to an industrial robot, one important issue is to determine the motion of the joints and the effector of the robot. In order to model robot dynamics we use a neural network that can be implemented in hardware. The synaptic weights are modelled as variable gain cells that can be implemented with a few MOS transistors. The network output signals portray the periodicity and other characteristics of the input signal in unsupervised mode. For the specific purpose of demonstrating the trajectory learning capabilities, a periodic signal with varying characteristics is used. The developed architecture, however, allows for more general learning tasks typical in applications of identification and control. The periodicity of the input signal ensures convergence of the output to a limit cycle. Online versions of the synaptic update can be formulated using simple CMOS circuits. Because the architecture depends on the network generating a stable limit cycle, and consequently a periodic solution which is robust over an interval of parameter uncertainties, we currently place the restriction of a periodic format for the input signals. The simulated network contains interconnected recurrent neurons with continuous-time dynamics. The system emulates random-direction descent of the error as a multidimensional extension to the stochastic approximation. To achieve unsupervised learning in recurrent dynamical systems we propose a synapse circuit which has a very simple structure and is suitable for implementation in VLSI.