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In this paper, we propose a deep learning based control synthesis frameworkfor fast and online computation of controllers that guarantees the safety ofgeneral nonlinear control systems with unknown dynamics in the presence ofinput constraints. Towards this goal, we propose a framework for simultaneouslylearning the unknown system dynamics, which can change with time due toexternal disturbances, and an integral control law for trajectory trackingbased on imitation learning. Simultaneously, we learn corresponding safetycertificates, which we refer to as Neural Integral Control Barrier Functions(Neural ICBF's), that automatically encode both the state and input constraintsinto a single scalar-valued function and enable the design of controllers thatcan guarantee that the state of the unknown system will never leave a safesubset of the state space. Finally, we provide numerical simulations thatvalidate our proposed approach and compare it with classical as well as recentlearning based methods from the relevant literature.

Neural Differentiable Integral Control Barrier Functions for Unknown Nonlinear Systems with Input Constraints