Learning control algorithm for nonlinear maps

Abstract

A feedback optimal control algorithm is developed for $N$-dimensional maps, which uses learning-based feedback optimal control techniques. The algorithm has two steps: (1) Learn the control of a reference map containing a stochastic term. (2) Apply the learned control to the laboratory system employing real time feedback. The stochastic component of the learning step is important to provide a close knit family of controls to handle laboratory uncertainty and noise. As an example, the formalism is applied to simulated two- and three-dimensional nonlinear laboratory maps in the presence of noise.