  Deep Reinforcement Learning (DRL) is applied to control a nonlinear, chaotic
system governed by the one-dimensional Kuramoto-Sivashinsky (KS) equation. DRL
uses reinforcement learning principles for the determination of optimal control
solutions and deep Neural Networks for approximating the value function and the
control policy. Recent applications have shown that DRL may achieve superhuman
performance in complex cognitive tasks.
  In this work, we show that using restricted, localized actuations, partial
knowledge of the state based on limited sensor measurements, and model-free DRL
controllers, it is possible to stabilize the dynamics of the KS system around
its unstable fixed solutions, here considered as target states. The robustness
of the controllers is tested by considering several trajectories in the
phase-space emanating from different initial conditions; we show that the DRL
is always capable of driving and stabilizing the dynamics around the target
states.
  The complexity of the KS system, the possibility of defining the DRL control
policies by solely relying on the local measurements of the system, and their
efficiency in controlling its nonlinear dynamics pave the way for the
application of RL methods in control of complex fluid systems such as turbulent
boundary layers, turbulent mixers or multiphase flows.
