  The OGY method is one of control methods for a chaotic system. In the method,
we have to calculate a stabilizing periodic orbit embedded in its chaotic
attractor. Thus, we cannot use this method in the case where a precise
mathematical model of the chaotic system cannot be identified. In this case,
the delayed feedback control proposed by Pyragas is useful. However, even in
the delayed feedback control, we need the mathematical model to determine a
feedback gain that stabilizes the periodic orbit. To overcome this problem, we
propose a model-free reinforcement learning algorithm to the design of a
controller for the chaotic system. In recent years, model-free reinforcement
learning algorithms with deep neural networks have been paid much attention to.
Those algorithms make it possible to control complex systems. However, it is
known that model-free reinforcement learning algorithms are not efficient
because learners must explore their control policies over the entire state
space. Moreover, model-free reinforcement learning algorithms with deep neural
networks have the disadvantage in taking much time to learn their control
optimal policies. Thus, we propose a data-based control policy consisting of
two steps, where we determine a region including the stabilizing periodic orbit
first, and make the controller learn an optimal control policy for its
stabilization. In the proposed method, the controller efficiently explores its
control policy only in the region.
