Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networks

Junsei Ito, Yasuaki Wasa

TL;DR

This work addresses data-driven control for nonlinear dynamics by embedding Physics-Informed Neural Networks into a model predictive control framework to adaptively tune PID gains in real time. Gains are optimized via gradients obtained from automatic differentiation of PINN-based dynamics within a zero-order hold MPC horizon, with regularization to prevent overfitting. The approach is validated through two case studies, a 2-DOF manipulator and a mass-spring-damper system, demonstrating improved transient performance and gravity compensation, as well as a stability-aware variant that enforces closed-loop stability through a barrier-based constraint. The results suggest practical impact for industrial settings where accurate physics-informed models enable robust, adaptive control under nonlinearities and constraints, while also highlighting areas for future work in guaranteeing stability and extending to output-feedback scenarios.

Abstract

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.

Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networks

TL;DR

This work addresses data-driven control for nonlinear dynamics by embedding Physics-Informed Neural Networks into a model predictive control framework to adaptively tune PID gains in real time. Gains are optimized via gradients obtained from automatic differentiation of PINN-based dynamics within a zero-order hold MPC horizon, with regularization to prevent overfitting. The approach is validated through two case studies, a 2-DOF manipulator and a mass-spring-damper system, demonstrating improved transient performance and gravity compensation, as well as a stability-aware variant that enforces closed-loop stability through a barrier-based constraint. The results suggest practical impact for industrial settings where accurate physics-informed models enable robust, adaptive control under nonlinearities and constraints, while also highlighting areas for future work in guaranteeing stability and extending to output-feedback scenarios.

Abstract

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.

Paper Structure

This paper contains 17 sections, 35 equations, 38 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Original Control Problem
  4. Physics-Informed Neural Networks for Control
  5. PINNs-based Adaptive PID Control
  6. PID Gain Optimization Problem
  7. Implementation
  8. Case Study 1: 2-DOF Robot Manipulator
  9. Properties on steady-state PID control
  10. Evaluation on PINNs-based model
  11. Application to Regulation Problem
  12. Application to Servo Problem
  13. Case Study 2: Mass-Spring-Damper System
  14. Evaluation on PINNs-based model
  15. Application to Servo Problem
  16. ...and 2 more sections

Figures (38)

  • Figure 1: Sketch of PINNs-based model predictive control.
  • Figure 2: Block diagram of PINNs-based MPC.
  • Figure 3: A 2-DOF manipulator system.
  • Figure 4: Evolution of loss functions during training.
  • Figure 5: Control input signals for the test dataset.
  • ...and 33 more figures

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3