Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning

• URL: http://arxiv.org/abs/2605.09772v1
• Date: Sun, 10 May 2026 21:33:37 GMT
• Title: Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning
• Abstract summary: This paper proposes a safe data-driven control framework for nonlinear systems with partially known dynamics.<n>Unmodeled nonlinear dynamics are captured by a Gaussian process residual learned in real time.<n> Numerical results validate the approach, demonstrating safe and informative exploration under model uncertainty.
• Score: 7.223664911847993
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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