  This paper presents adaptive robust quadratic program (QP) based control
using control Lyapunov and barrier functions for nonlinear systems subject to
time-varying and state-dependent uncertainties. An adaptive estimation law is
proposed to estimate the pointwise value of the uncertainties with
pre-computable estimation error bounds. The estimated uncertainty and the error
bounds are then used to formulate a robust QP, which ensures that the actual
uncertain system will not violate the safety constraints defined by the control
barrier function. Additionally, the accuracy of the uncertainty estimation can
be systematically improved by reducing the estimation sampling time, leading
subsequently to reduced conservatism of the formulated robust QP. The proposed
approach is validated in simulations on an adaptive cruise control problem and
through comparisons with existing approaches.
