Nonlinear Optimal Control Using Deep Reinforcement Learning

We propose a shift of paradigm for the control of fluid flows based on the application of deep reinforcement learning (DRL). This strategy is quickly spreading in the machine learning community and it is known for its connection with nonlinear control theory. The origin of DRL can be traced back to the generalization of the optimal control to nonlinear problems, leading-in the continuous formulation-to the Hamilton-Jacobi-Bellman (HJB) equation, of which DRL aims at providing a discrete, data-driven approximation. The only a priori requirement in DRL is the definition of an instantaneous reward as measure of the relevance of an action when the system is in a given state. The value function is then defined as the expected cumulative rewards and it is the objective to be maximized. The control action and the value function are approximated by means of neural networks. In this work, we clarify the connection between DRL and rediscuss our recent results for the control of the Kuramoto-Sivashinsky (KS) equation in one-dimension [4] by means of a parametric analysis.