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

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 (<inline-formula> <tex-math notation="LaTeX">$\delta ISS$ </tex-math></inline-formula>) 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 <inline-formula> <tex-math notation="LaTeX">$\delta ISS$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">$pH$ </tex-math></inline-formula> neutralization confirm the effectiveness of the proposed control scheme.

[1]  Jun Wang,et al.  Model Predictive Control of Unknown Nonlinear Dynamical Systems Based on Recurrent Neural Networks , 2012, IEEE Transactions on Industrial Electronics.

[2]  Paul-Gerhard Plöger,et al.  Echo State Networks for Mobile Robot Modeling and Control , 2003, RoboCup.

[3]  Anne Nagel,et al.  Model Predictive Control In The Process Industry , 2016 .

[4]  Herbert Jaeger,et al.  Optimization and applications of echo state networks with leaky- integrator neurons , 2007, Neural Networks.

[5]  Barak A. Pearlmutter.  Learning State Space Trajectories in Recurrent Neural Networks , 1989, Neural Computation.

[6]  Garrison W. Cottrell,et al.  2007 Special Issue: Learning grammatical structure with Echo State Networks , 2007 .

[7]  Stephen A. Billings,et al.  Please Scroll down for Article , 1992 .

[8]  Marcello Farina,et al.  Echo State Networks: analysis, training and predictive control , 2019, 2019 18th European Control Conference (ECC).

[9]  Herbert Jaeger,et al.  A tutorial on training recurrent neural networks , covering BPPT , RTRL , EKF and the " echo state network " approach - Semantic Scholar , 2005 .

[10]  Frank Allgöwer,et al.  Discrete-time Incremental ISS: A framework for Robust NMPC , 2013, 2013 European Control Conference (ECC).

[11]  James B. Rawlings,et al.  Discrete-time stability with perturbations: application to model predictive control , 1997, Autom..

[12]  Paul-Gerhard Plöger,et al.  Echo State Networks used for Motor Control , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[13]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[14]  Harald Haas,et al.  Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication , 2004, Science.

[15]  Dale E. Seborg,et al.  Modelling and Self-Tuning Control of a Multivariable pH Neutralization Process Part I: Modelling and Multiloop Control , 1989, 1989 American Control Conference.

[16]  Herbert Jaeger,et al.  The''echo state''approach to analysing and training recurrent neural networks , 2001 .

[17]  András Lörincz,et al.  Reinforcement Learning with Echo State Networks , 2006, ICANN.

[18]  Ulrich Parlitz,et al.  Gradient based hyperparameter optimization in Echo State Networks , 2019, Neural Networks.

[19]  Benjamin Schrauwen,et al.  Reservoir-based techniques for speech recognition , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.