Scalable synthesis of safety certificates from data with application to learning-based control

The control of complex systems faces a trade-off between high performance and\nsafety guarantees, which in particular restricts the application of\nlearning-based methods to safety-critical systems. A recently proposed\nframework to address this issue is the use of a safety controller, which\nguarantees to keep the system within a safe region of the state space. This\npaper introduces efficient techniques for the synthesis of a safe set and\ncontrol law, which offer improved scalability properties by relying on\napproximations based on convex optimization problems. The first proposed method\nrequires only an approximate linear system model and Lipschitz continuity of\nthe unknown nonlinear dynamics. The second method extends the results by\nshowing how a Gaussian process prior on the unknown system dynamics can be used\nin order to reduce conservatism of the resulting safe set. We demonstrate the\nresults with numerical examples, including an autonomous convoy of vehicles.\n