Safety Critical Control of a System With Element-Wise Estimation of Unknown Time-Varying Parameters

This paper presents a method for guaranteeing the safety of a system with time-varying parameters. First, we extend Dynamic Regressor Extension and Mixing to estimate time-varying parameters with a finite-time update rule, and present a bound on the estimation error. In the case of a constant parameter, we provide an improved lower bound on the update gain compared with the literature. Lastly, the parameter error bound is used to provide a Robust adaptive Control Barrier Function for systems with time-varying parameters. We conduct a numerical simulation of a system with time-varying parameters. The presented estimation method estimates the parameters with a smaller mean-square error compared with methods from the literature. The presented control barrier function can keep the system safe despite parametric uncertainties.