ABSTRACT Online learning‐based control has emerged as a viable alternative to the derivation of control algorithms based on modern control theory. Gaussian process (GP) regression, with its probabilistic inference properties, is a particularly potent branch of many learning‐based algorithms and is applicable to nonparametric dynamics modeling. This paper focuses on the online safety‐critical actor‐critic control paradigm from real‐time measured datasets for control‐affine systems with additive uncertainty or disturbance. Firstly, the nonparametric modeling properties of GP regression are presented, and the Lipschitz constant of the regression model is analyzed, which ensures error convergence and smoothness of the GP model. Subsequently, an actor‐critic control law is constructed employing an online Hellinger metric‐based GP inference model. The critic network is utilized to perform online estimation of the value function, while the actor network is synchronously updated to approximate the optimal control law. To encode safety specifications, control barrier functions (CBFs) are incorporated in the proposed control framework as a safety filter with minimal shift. The closed‐loop stability is analyzed using Lyapunov's direct method. Ultimately, the efficacy of the proposed method is assessed through comparative simulations.
Peng et al. (2026) studied this question.