Adaptive control for multi-scale stochastic dynamical systems with stochastic next generation reservoir computing

TL;DR

This paper introduces a stochastic reservoir computing controller that ensures stable, adaptive control of complex multiscale stochastic systems, validated through theoretical proofs and real-world EEG data applications.

Contribution

It presents the first stochastic NG-RC controller with rigorous stability guarantees for multiscale stochastic systems, integrating stochastic analysis with reservoir computing.

Findings

Proves asymptotic stability via stochastic LaSalle theorem.

Demonstrates convergence in a stochastic Van-der-Pol system.

Successfully modulates epileptic EEG dynamics.

Abstract

The rapid advancement of neuroscience and machine learning has established data-driven stochastic dynamical system modeling as a powerful tool for understanding and controlling high-dimensional, spatio-temporal processes. We introduce the stochastic next-generation reservoir computing (NG-RC) controller, a framework that integrates the computational efficiency of NG-RC with stochastic analysis to enable robust event-triggered control in multiscale stochastic systems. The asymptotic stability of the controller is rigorously proven via an extended stochastic LaSalle theorem, providing theoretical guarantees for amplitude regulation in nonlinear stochastic dynamics. Numerical experiments on a stochastic Van-der-Pol system subject to both additive and multiplicative noise validate the algorithm, demonstrating its convergence rate across varying temporal scales and noise intensities. To bridge theoretical insights with real-world applications, we deploy the controller to modulate pathological dynamics reconstructed from epileptic EEG data. This work advances a theoretically guaranteed scalable framework for adaptive control of stochastic systems, with broad potential for data-driven decision making in engineering, neuroscience, and beyond.