A machine learning based control of chaotic systems

Abstract

In this work, inspired by symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is obtained from an approximation of the dynamical rule, here the strategy rest upon an approach of a function that, from the current state of the system, give the necessary perturbation to bring the system closer to a homoclinic orbit that naturally goes to the target. The proposed methodology is data-driven or can be developed in a model-based context and is illustrated with computer simulations of chaotic systems given by discrete maps, ordinary differential equations and coupled map networks. Results show the usefulness of the design of nonlinear control techniques based on machine learning and numerical approach of homoclinic orbits.