Vector-Valued Native Space Embedding for Adaptive State Observation

This paper combines vector-valued reproducing kernel Hilbert space (vRKHS) embedding with robust adaptive observation, yielding an algorithm that is both non-parametric and robust. The main contribution of this paper lies in the ability of the proposed system to estimate the state of a plan model whose matched uncertainties are elements of an infinite-dimensional native space. The plant model considered in this paper also suffers from unmatched uncertainties. Finally, the measured output is affected by disturbances as well. Upper bounds on the state observation error are provided in an analytical form. The proposed theoretical results are applied to the problem of estimating the state of a rigid body.