MRAC With Adaptive Uncertainty Bounds via Operator-Valued Reproducing Kernels

This letter presents three novel model reference adaptive control (MRAC) systems for nonlinear plants in which the matched, nonparametric uncertainty is only known to reside in a vector-valued reproducing kernel Hilbert space (RKHS). The first MRAC system is based on an extension of the classical projection operator for robust MRAC systems and assures ultimate boundedness of the trajectory tracking error. This MRAC system allows the user to design part of the control input, known as the compensator. The second MRAC method modifies the previous one and, based on an estimate of the largest admissible uncertainty in the RKHS norm, employs a particular choice of the compensator to assure asymptotic convergence of the tracking error to zero. The last MRAC method uses the previous one and, leveraging the error bounding method framework, employs an additional learning law to assure asymptotic convergence of the tracking error without any information on the largest admissible uncertainty. While the conventional approaches to adaptive error bounding methods usually leave it to an analyst to derive the required error bounds on a case-by-case basis, the proposed approaches work for any functional uncertainty that is contained in any native space of vector-valued functions defined in terms of an operator kernel.