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

2025-10-06

AI Summary

To address the poor stability and weak adaptability of conventional PID controllers in nonlinear systems, this paper proposes a physics-informed neural network (PINN)-based adaptive PID control method. The approach embeds a PINN within a closed-loop control framework, leveraging automatic differentiation to precisely compute system gradients and jointly integrating model predictive control with gradient-based optimization to minimize, online, a weighted cost function comprising tracking error and control effort—thereby enabling real-time adaptation of PID gains. Its key innovation lies in the first-ever construction of an adaptive PID architecture that deeply fuses data-driven learning with first-principles modeling, simultaneously ensuring superior dynamic response, steady-state accuracy, and robustness. Numerical experiments demonstrate that the proposed method significantly outperforms both conventional PID and purely data-driven approaches in time-domain tracking precision and frequency-domain disturbance rejection, while exhibiting strong resilience to model mismatch and external disturbances.

Technology Category

• Search and Optimization: Learning to Search
• Multiagent Systems: Adversarial Agents
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Adaptive PID control design using Physics-Informed Neural Networks
• Optimizing PID gains through automatic differentiation of PINNs
• Ensuring stability while handling system nonlinearities in control

Innovation

• Adaptive PID control using Physics-Informed Neural Networks
• Automatic differentiation enables model predictive control
• Systematic framework integrates neural networks into control