Vector-Valued Native Space Embedding for Adaptive State Observation

TL;DR

This paper introduces a novel vector-valued RKHS-based adaptive observation method capable of estimating states in complex systems with uncertainties and disturbances, providing analytical error bounds and demonstrating effectiveness on rigid body state estimation.

Contribution

It combines vRKHS embedding with robust adaptive observation to handle unmatched uncertainties and disturbances in state estimation, a novel approach in this context.

Findings

Provides analytical upper bounds on observation error

Successfully applied to rigid body state estimation

Handles both matched and unmatched uncertainties

Abstract

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.