Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910207501664256 |
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| author | Tonini, Stefano Rastegarpour, Soroush Feyzmahdavian, Hamid Reza Bastianello, Nicola Johansson, Karl Henrik |
| author_facet | Tonini, Stefano Rastegarpour, Soroush Feyzmahdavian, Hamid Reza Bastianello, Nicola Johansson, Karl Henrik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09772 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning Tonini, Stefano Rastegarpour, Soroush Feyzmahdavian, Hamid Reza Bastianello, Nicola Johansson, Karl Henrik Systems and Control Robotics Optimization and Control 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. |
| title | Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning |
| topic | Systems and Control Robotics Optimization and Control |
| url | https://arxiv.org/abs/2605.09772 |