Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning
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.
Cite
@article{arxiv.2605.09772,
title = {Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning},
author = {Stefano Tonini and Soroush Rastegarpour and Hamid Reza Feyzmahdavian and Nicola Bastianello and Karl Henrik Johansson},
journal= {arXiv preprint arXiv:2605.09772},
year = {2026}
}
Comments
Accepted in 23rd IFAC World Congress