Adaptive Safety for Uncertain Nonlinear Systems with Control Barrier Functions and Contraction Metrics

We present a framework for control of constrained nonlinear systems subject to structured parametric uncertainty. The approach extends the notion of adaptive safety to achieve forward invariance of a desired safe set through online parameter adaptation and data-driven model estimation. This adaptive safety paradigm is merged with a recent direct adaptive control algorithm for systems nominally contracting in closed-loop. Because the existence of a closed-loop contraction metric only requires stabilizability, the proposed unification is considerably more general than what currently exists, e.g., it can be applied to underactuated systems. Additionally, our framework is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain aerodynamics.