Adaptive Control Barrier Functions for Safety-Critical Systems
This work addresses safety-critical control for systems with uncertainties, but it is incremental as it builds on existing high-order CBF methods.
The paper tackles the problem of ensuring safety in control systems with time-varying bounds and noise by introducing adaptive control barrier functions (AdaCBFs), resulting in improved feasibility and application to a cruise control scenario with varying conditions.
Recent work showed that stabilizing affine control systems to desired (sets of) states while optimizing quadratic costs and observing state and control constraints can be reduced to quadratic programs (QP) by using control barrier functions (CBF) and control Lyapunov functions. In our own recent work, we defined high order CBFs (HOCBFs) to accommodating systems and constraints with arbitrary relative degrees, and a penalty method to increase the feasibility of the corresponding QPs. In this paper, we introduce adaptive CBF (AdaCBFs) that can accommodate time-varying control bounds and dynamics noise, and also address the feasibility problem. Central to our approach is the introduction of penalty functions in the definition of an AdaCBF and the definition of auxiliary dynamics for these penalty functions that are HOCBFs and are stabilized by CLFs. We demonstrate the advantages of the proposed method by applying it to a cruise control problem with different road surfaces, tires slipping, and dynamics noise.