Asymptotic tracking for systems with structured and unstructured uncertainties

Abstract—The control of systems with uncertain nonlinear dynamics has been a decades-long mainstream area of focus. The general trend for previous control strategies developed for uncertain nonlinear systems is that the more unstructured the system uncertainty, the more control effort (i.e., high gain or high-frequency feedback) is required to cope with the uncertainty, and the resulting stability and performance of the system is di-minished (e.g., uniformly ultimately bounded stability). This brief illustrates how the amalgamation of an adaptive model-based feedforward term (for linearly parameterized uncertainty) with a robust integral of the sign of the error (RISE) feedback term (for additive bounded disturbances) can be used to yield an asymptotic tracking result for Euler–Lagrange systems that have mixed unstructured and structured uncertainty. Experimental results are provided that illustrate a reduced root-mean-squared tracking error with reduced control effort. Index Terms—Adaptive control, friction, Lyapunov methods, nonlinearities, robustness