Controlling nonlinear dynamical systems into arbitrary states using machine learning

TL;DR

This paper introduces a data-driven machine learning control method that can steer nonlinear dynamical systems into arbitrary states, including periodic and chaotic behaviors, with high accuracy and minimal data requirements.

Contribution

It presents a novel ML-based control scheme capable of directing complex nonlinear systems into any desired dynamical state, expanding control possibilities.

Findings

Successfully controlled Lorenz and Rössler systems to various states

Achieved accurate targeting of periodic, intermittent, and chaotic behaviors

Demonstrated minimal data needs for effective control

Abstract

We propose a novel and fully data driven control scheme which relies on machine learning (ML). Exploiting recently developed ML-based prediction capabilities of complex systems, we demonstrate that nonlinear systems can be forced to stay in arbitrary dynamical target states coming from any initial state. We outline our approach using the examples of the Lorenz and the R\"ossler system and show how these systems can very accurately be brought not only to periodic but also to e.g. intermittent and different chaotic behavior. Having this highly flexible control scheme with little demands on the amount of required data on hand, we briefly discuss possible applications that range from engineering to medicine.