Regression Methods for Inverse Learning Control of Unknown Nonlinear Systems based on Echo State Networks

Control of nonlinear systems require some explicit representation of the nominal plant dynamics. However, for highly complex systems obtaining such mathematical form may not be possible. In these situations, researchers have applied online learning techniques in order to achieve the control objective. Echo state networks (ESN), that are a class of recurrent neural networks, have provided promising results in this online learning area. However, the online learning of ESNs has been restricted to using recursive least squares (RLS) which has its own drawbacks such as numerical instability due to round-off errors, slow tracking capability for time-varying parameters, and high sensitivity to initial conditions of the algorithm. In this work, we investigate various algorithms that can be used for the online training of ESNs. The algorithms are evaluated numerically based on the tracking performance for a given reference trajectory and their computational complexity.