Data-driven control of echo state-based recurrent neural networks with robust stability guarantees

In this work we propose a new data-based approach for robust controller design for a rather general class of recurrent neural networks affected by bounded measurement noise. We first identify the model set compatible with available data in a selected model class via set membership (SM). Then, incremental input-to-state stability and desired performances for the closed loop system are enforced robustly to all models in the identified model set via a linear matrix inequality (LMI) optimization problem. Numerical results show the effectiveness of the comprehensive method.