Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning

TL;DR

This paper introduces a safe, data-driven control framework for nonlinear systems that uses online Gaussian process learning to ensure stability and safety during exploration, with theoretical guarantees and adaptive safety set expansion.

Contribution

It presents a novel control approach combining Gaussian processes with Lyapunov-based safety guarantees for real-time nonlinear system exploration.

Findings

Safe set expands by about 30% during learning.

Gaussian process RMSE decreases from 1.11 to 0.03.

Framework guarantees high-probability stability during online 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.