Adaptive Control Barrier Functions

Abstract

We have seen that the use of CBFs introduces a trade-off between guaranteeing safe system behavior on one hand and conservativeness in the choice of control on the other. The latter may in turn adversely affect system performance. In our effort to ensure the feasibility of safety-guaranteeing solutions to the basic OCP, the selection of CBFs may be overly conservative, an issue that we addressed in Chap. 4 by using the penalty method. This approach works well when the control bounds are fixed and the system behavior is assumed to be noise-free. In this chapter, we introduce adaptive CBFs to guarantee safety and feasibility under time-varying control bounds and noisy dynamics, which also addresses the conservativeness issue. We introduce two different forms of adaptive CBFs: parameter-adaptive CBFs and relaxation-adaptive CBFs in Sects. 6.2 and 6.3, respectively. The type of adaptivity we propose here for CBFs is different from traditional adaptive control and we begin by briefly discussing this distinction in Sect. 6.1. Simulation examples showing the applicability of the two methods developed in this chapter for the ACC case study considered throughout the book are presented in Sects. 6.2.3 and 6.3.3.