Recursive set-membership state estimation for linear non-causal time-variant differential- algebraic equation with continuous time

TL;DR

This paper develops recursive set-membership state estimation methods for linear non-causal time-varying differential-algebraic equations with uncertain parameters, providing optimal and suboptimal algorithms and comparing their performance.

Contribution

It introduces a novel recursive minimax estimation approach for non-causal DAEs with set-based uncertainties, including optimal solutions for structured matrix cases.

Findings

Optimal and suboptimal algorithms are derived for different matrix structures.

Performance comparison shows effectiveness of the proposed methods.

Application to 2D time-varying DAE demonstrates practical utility.

Abstract

This paper describes a state estimation approach for non-causal time-varying linear descriptor equations with uncertain parameters. The uncertainty in the state equation and in the measurements is supposed to admit a set-membership description. The approach is based on the notion of the linear minimax estimation. Suboptimal minimax state estimation algorithm is introduced for DAEs with non-stationary rectangular matrices. Optimal algorithm is presented for DAEs with special structure of the matrices. A comparison of suboptimal and optimal algorithms is presented for 2D time-varying DAE with a singular matrix pencil.