Stable Training Method for Echo State Networks Running in Closed-Loop Based on Particle Swarm Optimization Algorithm

Authors:
Qingsong Song;Zuren Feng;Yonggang Wang
Affiliations:
System Engineering Institute, Xi'an Jiaotong University, Xi'an, China 710049;System Engineering Institute, Xi'an Jiaotong University, Xi'an, China 710049;System Engineering Institute, Xi'an Jiaotong University, Xi'an, China 710049
Venue:
ICONIP '09 Proceedings of the 16th International Conference on Neural Information Processing: Part II
Year:
2009

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Abstract

Echo state network (ESN) is a new paradigm for using recurrent neural networks (RNNs) with a simpler training method, where an RNN is generated randomly and only a readout is trained. ESN method has quickly become popular in modeling for nonlinear dynamic systems. However, the classical training method for ESNs can not ensure the dynamics asymptotic stability any more if the trained ESNs run in a closed-loop self-generative mode. The reason is analyzed at first. We then consider the ESN training problem as an optimization problem with a nonlinear constraint, and take a particle swarm optimization (PSO) algorithm solve it. In the simulation experiments, the ESNs are trained as "figure-eight" trajectory generators. The results show that the proposed PSO-based training method can effectively ensure the dynamics asymptotic stability as well as the precision of generating trajectories of the trained ESNs.