Adaptive Deep Neural Network-Based Control Barrier Functions

Abstract: Safety constraints of nonlinear control systems are commonly enforced through the use of control barrier functions (CBFs). Uncertainties in the dynamic model can disrupt forward invariance guarantees or cause the state to be restricted to an overly conservative subset of the safe set. In this paper, adaptive deep neural networks (DNNs) are combined with CBFs to produce a family of controllers that ensure safety while learning the system's dynamics in real-time without the requirement for pre-training. By basing the least squares adaptation law on a state derivative estimator-based identification error, the DNN parameter estimation error is shown to be uniformly ultimately bounded. The convergent bound on the parameter estimation error is then used to formulate CBF-constraints in an optimization-based controller to guarantee safety despite model uncertainty. Furthermore, the developed method is extended for use under intermittent loss of state-feedback. A switched systems analysis for CBFs is provided with a maximum dwell-time condition during which the feedback can be unavailable. Comparative simulation results demonstrate the ability of the developed method to ensure safety in an adaptive cruise control problem and when feedback is lost, unlike baseline methods. Results show improved performance compared to baseline methods and demonstrate the ability of the developed method to ensure safety in feedback-denied environments.