Safe Robust Control of Nonlinear Systems with Uncertain Regressor and Parameter Vector

Regressor-based control of nonlinear systems uses a linear parameterization of the system dynamics. Most regressor-based controllers only consider uncertainties in the parameter vector, ignoring unmodeled dynamics and perturbations that might be present in the regressor matrix - factors that can significantly deteriorate the controller's performance. In this paper, we propose a novel robust control approach with safety guarantees that also accounts for uncertainties in both the regressor matrix and the parameter vector. We design a control law comprised of several signals that ensure uniform ultimate boundedness of the tracking error and forward invariance of a desired safe set via Control Barrier Functions. The controller's stability and safety are validated using numerical simulations, while Monte Carlo simulations demonstrate its robustness to random perturbations in the modeling uncertainties.