Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes

• URL: http://arxiv.org/abs/2010.05818v1
• Date: Mon, 12 Oct 2020 16:12:52 GMT
• Title: Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes
• Authors: Pushpak Jagtap, George J. Pappas, Majid Zamani
• Abstract summary: This paper focuses on the controller synthesis for unknown, nonlinear systems while ensuring safety constraints. In the learning step, we use a data-driven approach to learn the unknown control affine nonlinear dynamics together with a statistical bound on the accuracy of the learned model. In the second controller synthesis steps, we develop a systematic approach to compute control barrier functions that explicitly take into consideration the uncertainty of the learned model.
• Score: 17.870440210358847
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper focuses on the controller synthesis for unknown, nonlinear systems while ensuring safety constraints. Our approach consists of two steps, a learning step that uses Gaussian processes and a controller synthesis step that is based on control barrier functions. In the learning step, we use a data-driven approach utilizing Gaussian processes to learn the unknown control affine nonlinear dynamics together with a statistical bound on the accuracy of the learned model. In the second controller synthesis steps, we develop a systematic approach to compute control barrier functions that explicitly take into consideration the uncertainty of the learned model. The control barrier function not only results in a safe controller by construction but also provides a rigorous lower bound on the probability of satisfaction of the safety specification. Finally, we illustrate the effectiveness of the proposed results by synthesizing a safety controller for a jet engine example.

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