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The control of complex systems faces a trade-off between high performance andsafety guarantees, which in particular restricts the application oflearning-based methods to safety-critical systems. A recently proposedframework to address this issue is the use of a safety controller, whichguarantees to keep the system within a safe region of the state space. Thispaper introduces efficient techniques for the synthesis of a safe set andcontrol law, which offer improved scalability properties by relying onapproximations based on convex optimization problems. The first proposed methodrequires only an approximate linear system model and Lipschitz continuity ofthe unknown nonlinear dynamics. The second method extends the results byshowing how a Gaussian process prior on the unknown system dynamics can be usedin order to reduce conservatism of the resulting safe set. We demonstrate theresults with numerical examples, including an autonomous convoy of vehicles.

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