Safe Adaptive Control for Uncertain Systems with Complex Input Constraints

In this paper, we propose a novel adaptive Control Barrier Function (CBF) based controller for nonlinear systems with complex, time-varying input constraints. Conventional CBF approaches often struggle with feasibility issues and stringent assumptions when addressing input constraints. Unlike these methods, our approach converts the input-constraint problem into an output-constraint CBF design. This transformation simplifies the Quadratic Programming (QP) formulation and enhances compatibility with the CBF framework. We design an adaptive CBF-based controller to manage the mismatched uncertainties introduced by this transformation. Our method systematically addresses the challenges of complex, time-varying, and state-dependent input constraints. The efficacy of the proposed approach is validated using numerical examples.