Reservoir computing for system identification and model predictive control.

Abstract

Model predictive control (MPC), widely used for real-time control of complex dynamical systems, operates by repeatedly solving an optimization problem over a receding time horizon. Its success hinges on dynamical models that are accurate yet efficient enough for rapid online computation. Frequently, the governing models of complex systems are either unknown or computationally inefficient, forcing MPC to rely on data-driven surrogate models. Echo state networks (ESNs), a class of recurrent neural networks trained through computationally efficient ridge regression, are well-suited for this role and have demonstrated strong forecasting capabilities in chaotic dynamical systems. Their architecture naturally supports rapid training and flexible adaptation to varying control inputs. In this work, we demonstrate that ESNs serve as effective data-driven surrogates for system dynamics under diverse control scenarios, outperforming competing architectures such as long short-term memory (LSTM) networks. On challenging control benchmarks, including the Lorenz system with control and fluid flow past a cylinder, MPC with ESN surrogates consistently achieves the control objective, whereas the next-best considered architecture, LSTM-based MPC, frequently fails. Even in cases where LSTM-based MPC succeeds, ESN-based MPC reduces average control cost by up to 10% and decreases variability by as much as 85%. Beyond performance, ESNs are significantly more sample-efficient and train over an order of magnitude faster than LSTMs. These results establish ESNs as accurate, efficient architectures for scalable data-driven MPC in complex systems with limited training data and unknown dynamics.