Online adaptation of an Echo State Network based Controller for Brushless-DC Motors via Modified FORCE Recursive Least Squares

This paper addresses the growing role of Data Driven methods in industrial control, enabled by advances in sensor technology and Machine Learning toolkits. While neural networks have been successfully employed for plant identification, grey-box modelling, direct control synthesis, and pattern generation, their practical adoption remains limited by training costs and numerical stability issues. Echo State Networks (ESN) offer a compelling compromise: a fixed-weight reservoir captures rich nonlinear dynamics, and only a linear readout requires adaptation. However, existing ESN applications in control typically rely on offline training and still depend on a conventional controller to generate calibration data. To overcome these limitations, an ESN based closed loop controller has been introduced, whose output weights are updated online via a modified version of the First-Order Reduced and Controlled Error (FORCE) algorithm, a variant of Recursive Least Squares. During operation, the reservoir's spontaneous dynamics are tamed by feeding the network output back into its hidden units, ensuring a small error from the outset and requiring only modest weight adjustments thereafter. The results confirm that online adaptation preserves the computational efficiency of reservoir computing while extending its applicability to processes with uncertain or time-varying dynamics.