A physics-informed neural networks–based adaptive control for a class of nonlinear systems with nonparametric uncertainties

This article addresses the trajectory tracking control problem for a class of nonlinear systems subject to nonparametric uncertainties. Traditional adaptive methods struggle with such uncertainties due to inadequate regression models, while conventional black-box neural networks suffer from poor generalization and physical inconsistency beyond the training distribution. To overcome these limitations, a physics-informed neural networks–based adaptive nonrecursive control framework is proposed. The core innovation lies in using the physics-informed neural networks mechanism to estimate the nonparametric uncertainty by embedding the system dynamics as a constraint in the loss function, ensuring physically consistent and highly generalizable uncertainty estimation even with sparse data. Furthermore, the physics-informed neural networks–based estimated uncertainty is directly fed into an adaptive nonrecursive controller to dynamically adjust the scaling gain, thereby achieving a composite estimation and control design that mitigates the analytical complexity growth and noise amplification in recursive methods. Rigorous stability analysis validates the uniformly bounded tracking error.