Controlling nonlinear dynamical systems into previously unseen target states using resource-efficient machine learning

Abstract

Controlling nonlinear dynamical systems is a fundamental challenge in engineering and science, crucial for maintaining stability, optimizing performance, and enabling adaptability across a broad spectrum of applications. In aerospace engineering e.g. the precise control of air- and spacecraft or satellites is vital while energy-efficient solutions are a must in these deployments. Here, we report on novel developments of control strategies based on reservoir computing that fulfill a predefined control objective, with which the dynamical systems are controlled in extrapolated and previously unseen target states. We present a model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly dif- ferent and complex dynamics. This is achieved by combining previous work on controlling chaotic systems to arbitrary states and extrapolating the system behavior into unseen parameter regions using machine learning. Specifically, we use reservoir computing (RC) as it combines superior prediction results with little CPU-needs for training. Since only the parameters in the output layer are to be optimized there is a wealth of conceivable physical systems that can act as reservoir and lead to novel, energy-efficient computing methods. By extending the applicability of machine learning-based control mechanisms to previously inaccessible target dynamics, this methodology opens the door to transformative new applications while maintaining exceptional efficiency. Our results highlight reservoir computing as a powerful alternative to traditional methods for dynamic system control.