Attractor Control Using Machine Learning

Abstract

We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with finite number of actuators (multiple inputs) and sensors (multiple outputs). The control law maps outputs into inputs and is optimized with respect to a cost function, containing physics via the dynamical or statistical properties of the attractor to be controlled. Thus, we are capable of exploiting nonlinear mechanisms, e.g. chaos or frequency cross-talk, serving the control objective. This optimization is based on genetic programming, a branch of machine learning. This machine learning control is successfully applied to the stabilization of nonlinearly coupled oscillators and maximization of Lyapunov exponent of a forced Lorenz system. We foresee potential applications to most nonlinear multiple inputs/multiple outputs control problems, particulary in experiments.