Minimal Energy Control of an ESN Pattern Generator

In this report we present a method of adding a feedback control mechanism to an echo state network (ESN) pattern generator in order to modulate its output patterns with the purpose of tracking slowly varying control targets, e.g. shift, amplitude, or frequency of an oscillatory pattern. A proofof-principle case study is presented where a basic ESN is trained to produce a stable sinewave oscillation with fixed shift, amplitude and frequency. With the controller in place, the system demonstrates that the shift, amplitude and frequency of the produced sine waveform can be modulated simultaneously by suitably generated slow varying control signals inserted into the network. Furthermore, an equilibration procedure is introduced to relearn ESN weights such that the equilibrated ESN pattern generator can approximately reproduce the reservoir dynamics across the controllable range, with the feedback control loop switched off. As a result, when reconnecting the feedback control loop to the equilibrated ESN, the energy of the control signals are many orders of magnitude smaller compared to the native system.