Robust Adaptive Backstepping Control Over Native Spaces

This paper presents the first robust adaptive backstepping control system for dynamical systems whose functional uncertainties are assumed to lie in a user-defined native space (also known as reproducing kernel Hilbert space). This work generalizes classical adaptive backstepping control systems and their non-adaptive counterparts by freeing the user from providing a parametric representation of the functional uncertainties. Such representations are usually in the form of regressor vectors, or some equivalent structure, to be provided a priori or reconstructed online, and without employing conservative upper bounds on the functional uncertainties. The adaptive laws for the proposed control system are shown to form a distributed parameter system (DPS) evolving over the native space. Finite-dimensional approximations of such adaptive laws enable their applications to problems of practical interest, as shown by the proposed numerical examples.