Chaotic neural control.

We consider the problem of stabilizing unstable equilibria by discrete controls (the controls take discrete values at discrete moments of time). We prove that discrete control typically creates a chaotic attractor in the vicinity of an equilibrium. Artificial neural networks with reinforcement learning are known to be able to learn such a control scheme. We consider examples of such systems, discuss some details of implementing the reinforcement learning to controlling unstable equilibria, and show that the arising dynamics is characterized by positive Lyapunov exponents, and hence is chaotic. This chaos can be observed both in the controlled system and in the activity patterns of the controller.