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-based 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. First, the network is augmented with new inputs to account for the initial state of the system and the control action. Then, 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. The complete response is formed by setting the initial state of the next interval to the terminal state of the previous one. The new methodology enables the optimal control of dynamic systems, making feasible to integrate a priori knowledge from experts and data collected from plants in control applications. We showcase our method in the control of two nonlinear dynamic systems: the Van der Pol oscillator and the four-tank system.

翻译：物理知情神经网络(PINNs)在深神经网络的学习中强制引入已知物理法则,确保它们尊重过程的物理,同时减少对标签数据的需求。对于普通差异方程式(ODEs)所代表的系统,常规PINN具有连续的时间输入变量和输出,对应的 ODE 的解决方案。以其原始形式,PINN 不允许控制投入,也不能在不严重降解预测的情况下模拟长距离输入。在这方面,这项工作提出了一个称为物理化神经网控制的新框架(PIN),它提出了一个新的基于PIN的架构,可以控制问题,并能够模拟不事先固定的更远的时间范围。首先,网络增加了新的投入,以考虑到系统的初始状态和控制动作。随后,全时范围的反应是分裂的,每个更小的间隔都是以初始状态和控制动作的固定值为条件的解决方案。完全的响应是,将下一个基于PINN的PIN基础结构结构结构结构的架构设置为下一个不初始状态,可以控制问题,并且能够模拟更远的时间范围的时间范围,将我们收集的数据系统从以前的动态控制方法整合到前一个。