This article proposes a data-driven PID controller design based on the principle of adaptive gain optimization, leveraging Physics-Informed Neural Networks (PINNs) generated for predictive modeling purposes. The proposed control design method utilizes gradients of the PID gain optimization, achieved through the automatic differentiation of PINNs, to apply model predictive control using a cost function based on tracking error and control inputs. By optimizing PINNs-based PID gains, the method achieves adaptive gain tuning that ensures stability while accounting for system nonlinearities. The proposed method features a systematic framework for integrating PINNs-based models of dynamical control systems into closed-loop control systems, enabling direct application to PID control design. A series of numerical experiments is conducted to demonstrate the effectiveness of the proposed method from the control perspectives based on both time and frequency domains.

翻译：本文提出一种基于自适应增益优化原理的数驱PID控制器设计方法，该方法利用为预测建模目的生成的物理信息神经网络（PINNs）。所提出的控制设计方法利用通过PINNs自动微分实现的PID增益优化梯度，基于跟踪误差与控制输入的成本函数应用模型预测控制。通过优化基于PINNs的PID增益，该方法实现了能确保稳定性并兼顾系统非线性的自适应增益调节。所提方法具备将动态控制系统的PINNs模型集成至闭环控制系统的系统化框架，可直接应用于PID控制设计。通过一系列数值实验，从时域和频域的控制视角验证了所提方法的有效性。