Regularized Taylor Echo State Networks for Predictive Control of Partially Observed Systems

The existing neural networks suffer from partial observation while modeling and controlling dynamic systems. In this paper, a new linearized recurrent neural network, the Taylor expanded echo state network (TESN), is proposed for predictive control of partially observed dynamic systems. Two schemes of regularization, ridge regression and sparse regression, are imposed on TESNs to tackle the issue of ill-conditioned estimation. Furthermore, two estimators, lasso and elastic net, are investigated for sparse regression. Regularized learning is found to improve the estimation consistency of readout coefficients and, at the same time, suppress the accumulation of linearization residues in a prediction horizon. A series of experiments was carried out, and the results verified that regularized learning is contributive to TESNs in predictive control of partially observed dynamic systems.