Adaptive safety with Control Barrier Functions and triggered Batch Least-Squares Identifier

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 laws designed to guarantee specific properties of the Lyapunov functions, may grow unboundedly under the effects of the relaxation term. The proposed adaptive law is designed by processing system inputs and outputs, to avoid unbounded estimates and overparameterization problems in the existing results. A safety-triggered 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.