  Physics-informed neural networks (PINNs) impose known physical laws into the
learning of deep neural networks, making sure they respect the physics of the
process while decreasing the demand of labeled data. For systems represented by
Ordinary Differential Equations (ODEs), the conventional PINN has a continuous
time input variable and outputs the solution of the corresponding ODE. In their
original form, PINNs do not allow control inputs, neither can they simulate for
variable long-range intervals without serious degradation in their predictions.
In this context, this work presents a new framework called Physics-Informed
Neural Nets for Control (PINC), which proposes a novel PINN-based architecture
that is amenable to control problems and able to simulate for longer-range time
horizons that are not fixed beforehand, making it a very flexible framework
when compared to traditional PINNs. Furthermore, this long-range time
simulation of differential equations is faster than numerical methods since it
relies only on signal propagation through the network, making it less
computationally costly and, thus, a better alternative for simulation of models
in Model Predictive Control. We showcase our proposal in the control of two
nonlinear dynamic systems: the Van der Pol oscillator and the four-tank system.
