Set-membership state estimation framework for uncertain linear differential-algebraic equations

TL;DR

This paper develops a set-membership framework for state estimation in uncertain linear differential-algebraic equations, introducing new concepts like minimax directional observability to improve estimation accuracy.

Contribution

It introduces a novel minimax estimation approach for uncertain linear DAEs, including new notions of observability and non-causality, with recursive estimators for continuous and discrete systems.

Findings

Explicit minimax estimators derived for uncertain linear DAEs

Introduction of minimax directional observability and non-causality index

Numerical example demonstrating advantages of the approach

Abstract

We investigate a state estimation problem for the dynamical system described by uncertain linear operator equation in Hilbert space. The uncertainty is supposed to admit a set-membership description. We present explicit expressions for linear minimax estimation and error provided that any pair of uncertain parameters belongs to the quadratic bounding set. We introduce a new notion of minimax directional observability and index of non-causality for linear noncausal DAEs. Application of these notions to the state estimation problem for linear uncertain noncausal DAEs allows to derive new minimax recursive estimator for both continuous and discrete time. We illustrate the benefits of non-causality of the plant applying our approach to scalar nonlinear set-membership state estimation problem. Numerical example is presented.