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.

翻译：Echo State 网络(ESN)是一种经常性神经网络,由神经元随机连接和循环连接的固定储油层组成,只有通过培训输出连接重量才能获得预期产出。第一级减少和控制错误(FORCE)的学习是一种在线监督的培训方法,可以将ESN的混乱活动改变为特定的活动模式。本文件提议一种基于循环最少的最小方形的复合FORCE学习方法,以培训初始活动自发混乱的ESN,采用动态递减器扩展和记忆数据利用的复合学习技术来增强参数趋同。拟议方法应用于预测Mackey-Glass系统产生的混乱时间序列的基准问题,而数字结果显示,与现有方法相比,它大大改进了学习和预测的性能。