A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Informed Neural Networks (Control PINNs) that simultaneously solve for a given system state, and for the optimal control signal, in a one-stage framework that conforms to the underlying physical laws. Prior approaches use a two-stage framework that first models and then controls a system in sequential order. In contrast, a Control PINN incorporates the required optimality conditions in its architecture and in its loss function. The success of Control PINNs is demonstrated by solving the following open-loop optimal control problems: (i) an analytical problem, (ii) a one-dimensional heat equation, and (iii) a two-dimensional predator-prey problem.

翻译：科学和工程方面的一个基本问题是设计最佳控制政策,引导特定系统实现预期结果,这项工作提议在符合基本物理法则的一阶段框架内,同时解决特定系统状态和最佳控制信号的同步控制物理成形神经网络(Control PINN),在符合基本物理法则的一阶段框架内,控制物理成形神经网络(Control PINN)的成功表现为:(一) 分析问题,(二) 一维热方程式,(三) 二维掠食者先行问题。