This work presents a methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated in four different study cases: the Lorenz system, a modified version of the Kuramoto-Sivashinsky equation, a streamwise-periodic two-dimensional channel flow, and a confined cylinder flow. Neural networks are trained as models to capture the complex system dynamics and estimate equilibrium points through a Newton method, enabled by back-propagation. These neural network surrogate models (NNSMs) are leveraged to train a second neural network, which is designed to act as a stabilizing closed-loop controller. The training process employs a recurrent approach, whereby the NNSM and the neural network controller are chained in closed loop along a finite time horizon. By cycling through phases of combined random open-loop actuation and closed-loop control, an …