High Order Robust Adaptive Control Barrier Functions and Exponentially Stabilizing Adaptive Control Lyapunov Functions

In practice, however, many safetycritical stability and safety of nonlinear control systems has received constraints have relative degrees larger than one (e.g., significant attention in recent years. In particular, the unification constraints on the configuration of a mechanical system of Control Lyapunov Functions (CLFs) [1], [2] and generally have at least relative degree two). The unification Control Barrier Functions (CBFs) [3], [4] has provided a of CLFs/CBFs with techniques from CL adaptive control was pathway towards safe and stable control of complex nonlinear also presented in [23], [24]; however, the resulting CLF controllers systems such as autonomous vehicles [5], [6], multiagent either only guarantee uniformly ultimately bounded systems [7], and bipedal robots [8]. Although powerful, stability or are limited to single-input feedback linearizable the guarantees afforded by these approaches are modelbased, systems. Importantly, the CL-based aCBF controllers from hence the success in transferring such guarantees [23], [24] do not provide strong safety guarantees since the to real-world systems is inherently tied to the fidelity of CBF-based control inputs are generated using the estimated the underlying system model. Inevitably, such models are dynamics without accounting for estimation errors, leading only an approximation of the true system due to parametric to potential safety violations that can be understood through uncertainties and unmodeled dynamics, thus there is strong the notion of input-to-state-safety [25].