Attractor Control Using Machine Learning

Ambrosys GmbH, Albert-Einstein-Str. 1-5, D-14469 Potsdam, GermanyLEMTA, 2 Avenue de la Fort de Haye F-54518 Vandoeuvre-ls-Nancy Cedex, France andUniversity of Potsdam, Karl-Liebknecht-Str. 24/25 D-14476 Potsdam, Germany(Dated: December 16, 2013)We propose a general strategy for feedback control design of complex dynamical systems exploit-ing the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems canhave a state space of arbitrary dimension with nite number of actuators (multiple inputs) and sen-sors (multiple outputs). The control law maps outputs into inputs and is optimized with respect toa cost function, containing physics via the dynamical or statistical properties of the attractor to becontrolled. 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 ofmachine learning. This machine learning control is successfully applied to the stabilization of non-linearly coupled oscillators and maximization of Lyapunov exponent of a forced Lorenz system. Weforesee potential applications to most nonlinear multiple inputs/multiple outputs control problems,particulary in experiments.

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