  This paper presents an adaptive control approach for uncertain nonlinear
systems subject to safety constraints that allows for modularity in the
selection of the parameter estimation algorithm. Such modularity is achieved by
unifying the concepts of input-to-state stability (ISS) and input-to-state
safety (ISSf) via control Lyapunov functions (CLFs) and control barrier
functions (CBFs), respectively. In particular, we propose a class of
exponential ISS-CLFs and ISSf high order CBFs that can be combined with a
general class of parameter estimation algorithms akin to those found in the
literature on concurrent learning adaptive control. We demonstrate that the
unification of ISS and ISSf in an adaptive control setting allows for
maintaining a single set of parameter estimates for both the CLF and CBF that
can be generated by a class of update laws satisfying a few general properties.
The modularity of our approach is demonstrated via numerical examples by
comparing performance in terms of stability and safety across different
parameter estimation algorithms.
