Model Predictive Control Design for Dynamical Systems Learned by Echo State Networks

Abstract

The objective of this letter is to analyze the stability properties, the training procedure and the use in predictive control schemes of echo state networks (ESNs), a specific class of recurrent neural networks. First, a sufficient condition guaranteeing incremental input-to-state stability ( $\delta ISS$ ) of ESNs is derived. Then, an automatic procedure to optimally tune the parameters of the ESN in the training phase is presented, which allows to enforce $\delta ISS$ . Finally, the application of the ESN as a model of the plant for predictive control purposes is studied. In particular, an asymptotically convergent observer is designed, and a model predictive controller with guaranteed stabilizing properties is devised for the solution to regulation problems. Simulation results on a nonlinear process for $pH$ neutralization confirm the effectiveness of the proposed control scheme.