On Robust Control With Uncertainties in the Regressor Matrix and Parameter Vector

Existing research results on regressor-based control use the linear parameterization of the dynamic equation into a known regressor matrix and an uncertain parameter vector. In this note, we show that the well-known robust controller that assumes a known regressor matrix can yield undesirable performance and poor robustness capabilities if there is uncertainty in the regressor matrix, especially when dealing with larger robots. The novelty of our result lies in accounting for uncertainties in both the regressor matrix and parameter vector, while ensuring that the uncertainty bound of our controller depends on a tuning parameter, which reflects the confidence in the regressor matrix accuracy, and the upper bound on the inertia parameters. Our controller, when compared against the controller that assumes a known regressor matrix, facilitates improved robustness while maintaining a smaller uniform ultimate boundedness radius.