  In this paper, a triggered Batch Least-Squares Identifier (BaLSI) based
adaptive safety control scheme is proposed for uncertain systems with
potentially conflicting control objectives and safety constraints. A relaxation
term is added to the Quadratic Programs (QP) combining the transformed Control
Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs), to mediate the
potential conflict. The existing Lyapunov-based adaptive schemes designed to
guarantee specific properties of the Lyapunov functions, may grow unboundedly
under the effects of the relaxation term. The adaptive law is designed by
processing system inputs and outputs, to avoid unbounded estimates and
overparameterization problems in the existing results. A safetytriggered
condition is presented, based on which the forward invariant property of the
safe set is shown and Zeno behavior can be excluded. Simulation results are
presented to demonstrate the effectiveness of the proposed adaptive control
scheme.
