What is the formal name for a dynamical system whose dynamics are a function of its state $\bf x$ and control input $\bf u$, where the control input is a function of the state, i.e., $\bf u(x)$. In essence,
$$\dot{\bf x} = \bf f ( x, u ( x ) )$$
In my case, $\bf u(x)$ is represented by a nonlinear function, namely, a neural network.