Physics-Informed Neural Nets for Control of Dynamical Systems

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 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 \emph{control} problems and able to simulate for longer-range time horizons that are not fixed beforehand. The framework has new inputs to account for the initial state of the system and the control action. In PINC, the response over the complete time horizon is split such that each smaller interval constitutes a solution of the ODE conditioned on the fixed values of initial state and control action for that interval. The whole response is formed by feeding back the predictions of the terminal state as the initial state for the next interval. This proposal enables the optimal control of dynamic systems, integrating a priori knowledge from experts and data collected from plants into control applications. We showcase our proposal in the control of two nonlinear dynamic systems: the Van der Pol oscillator and the four-tank system.