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

ABSTRACT 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.