Adaptive Control Barrier Functions

We have seenBarrier function that the use of CBFsControl barrier function introduces a trade-off between guaranteeing safe system behavior on one hand andConservativeness conservativenessConservative, conservativeness in the choice of control on the other. The latter may in turn adversely affect system performance. In our effort to ensure the feasibilityFeasibility ofSafety safety-guaranteeing solutions to the basic OCP, the selection of CBFsControl barrier function may be overly conservativeConservative, conservativeness, an issue that we addressed in Chap. 4 by using the penalty methodPenalty method. This approach works well when the control boundsControl bound are fixed and the system behavior is assumed to be noise-freeNoise. In this chapter, we introduce adaptive CBFsControl barrier function to guaranteeGuarantee safetySafety and feasibilityFeasibility under time-varyingTime-varying control boundsControl bound and noisy dynamicsDynamics, which also addresses theConservativeness conservativenessConservative, conservativeness issue. We introduce two different forms of adaptive CBFsControl barrier function: parameter-adaptive CBFsControl barrier function and relaxation-adaptive CBFsControl barrier function in Sects. 6.2 and 6.3, respectively. The type of adaptivity we propose here for CBFsControl barrier function is different from traditional adaptive controlAdaptive 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 ACCAdaptive cruise control case study considered throughout the book are presented in Sects. 6.2.3 and 6.3.3.