Physics-Informed Neural Nets for Control of Dynamical Systems

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep networks, making sure they respect physics process while decreasing demand labeled data. For systems represented by Ordinary Differential Equations (ODEs), conventional PINN has a continuous time input variable and outputs solution corresponding ODE. In their original form, PINNs do not allow control inputs neither can simulate for long-range intervals without serious degradation in predictions. this context, work presents new framework called Physics-Informed Neural Nets Control (PINC), which proposes novel PINN-based architecture that is amenable to \emph{control} problems able longer-range horizons are fixed beforehand. The account initial state system action. PINC, response over complete horizon split such each smaller interval constitutes ODE conditioned on values action interval. whole formed feeding back predictions terminal as next This proposal enables optimal dynamic systems, integrating priori knowledge from experts data collected plants applications. We showcase our two nonlinear systems: Van der Pol oscillator four-tank system.