  Echo state network (ESN), a kind of recurrent neural networks, consists of a
fixed reservoir in which neurons are connected randomly and recursively and
obtains the desired output only by training output connection weights.
First-order reduced and controlled error (FORCE) learning is an online
supervised training approach that can change the chaotic activity of ESNs into
specified activity patterns. This paper proposes a composite FORCE learning
method based on recursive least squares to train ESNs whose initial activity is
spontaneously chaotic, where a composite learning technique featured by dynamic
regressor extension and memory data exploitation is applied to enhance
parameter convergence. The proposed method is applied to a benchmark problem
about predicting chaotic time series generated by the Mackey-Glass system, and
numerical results have shown that it significantly improves learning and
prediction performances compared with existing methods.
