Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning

2026-05-10

AI Summary

This work proposes a safe, data-driven control method for nonlinear systems with only partially known dynamics, ensuring both stability and satisfaction of state and input constraints during online learning. Built upon a stabilizable linear approximation, the approach employs an online Gaussian process to estimate the unmodeled nonlinear residuals in real time. By integrating Lyapunov theory, it constructs a probabilistic control-invariant set with finite-sample safety guarantees. A convex quadratic program is solved at each step to maximize information gain while preserving safety, and the safe region is adaptively expanded as uncertainty diminishes. Numerical experiments demonstrate that the method enlarges the feasible safe set by approximately 30% under safe exploration, while reducing the root mean square error of the Gaussian process predictions from 1.11 to 0.03.

Abstract

This paper proposes a safe data-driven control framework for nonlinear systems with partially known dynamics. The method ensures stability and constraint satisfaction during online learning, assuming only a stabilizable linear approximation of the process is available. Unmodeled nonlinear dynamics are captured by a Gaussian process residual learned in real time. Safety is enforced through a probabilistic control-invariant set derived from Lyapunov theory, guaranteeing high-probability stability. A convex quadratic program computes control inputs that maximize information gain while respecting probabilistic safety constraints. The framework provides finite-sample safety guarantees and allows adaptive expansion of the invariant set as uncertainty decreases. Numerical results validate the approach, demonstrating safe and informative exploration under model uncertainty: the safe set expands by about 30% while the Gaussian process root-mean-square error drops from 1.11 to 0.03.

Problem

• safe exploration
• nonlinear systems
• online learning
• Gaussian process
• stability

Innovation

• safe exploration
• Gaussian process
• control-invariant set
• online learning
• nonlinear systems