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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.
The need for robust control laws is especially important in safety-critical applications. We propose robust hybrid control barrier functions as a means to synthesize control laws that ensure robust safety. Based on this notion, we formulate an optimi
Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust feedback contr
In this paper, a distributed learning leader-follower consensus protocol based on Gaussian process regression for a class of nonlinear multi-agent systems with unknown dynamics is designed. We propose a distributed learning approach to predict the re
Motivated by the lack of systematic tools to obtain safe control laws for hybrid systems, we propose an optimization-based framework for learning certifiably safe control laws from data. In particular, we assume a setting in which the system dynamics
Modern nonlinear control theory seeks to develop feedback controllers that endow systems with properties such as safety and stability. The guarantees ensured by these controllers often rely on accurate estimates of the system state for determining co