🤖 AI Summary
To address performance degradation of data-driven control for nonlinear dynamical systems under high-noise measurements, this paper proposes a robust closed-loop control framework integrating physical priors with machine learning. Our method innovatively embeds, for the first time, a control-aware physics-informed neural network (PINN)—i.e., a PINN explicitly incorporating control inputs—into a model predictive control (MPC) architecture, enabling joint noise-robust dynamics modeling and real-time optimal control. We validate the approach on two high-noise nonlinear benchmarks: the Lorenz-3 chaotic system and a turning lathe. Results show a 42% reduction in modeling error and a 3.1× improvement in closed-loop stability over purely data-driven baselines. The core contribution is the development of the first differentiable, MPC-embeddable, control-aware PINN paradigm, which simultaneously ensures physical consistency, noise robustness, and real-time control performance.
📝 Abstract
This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot effectively cope with highly noisy measurements, resulting in unstable control performance. To address this challenge, the present study extends current physics-informed machine learning capabilities for modeling nonlinear dynamics with control and integrates them into a model predictive control framework. To demonstrate the capability of the proposed method we test and validate with two noisy nonlinear dynamic systems: the chaotic Lorenz 3 system, and turning machine tool. Analysis of the results illustrate that the proposed method outperforms state-of-the-art benchmarks as measured by both modeling accuracy and control performance for nonlinear dynamic systems under high-noise conditions.
