Observer Design for a Class of Systems Described by Differential-Algebraic Equations and Parameter Identification of an Unmeasured Disturbance

Abstract

This paper addresses the problem of observer design for a class of linear descriptor systems affected by a certain class of unknown unmatched disturbances. The objective is to estimate the components of the state vector, as well as the unknown parameters of the unmeasured disturbance. To solve this problem, structural assumptions are introduced under which an observer for the dynamic part of the state vector is constructed. Then, based on the obtained state estimate, the disturbance signal is reconstructed, and its unknown parameters are identified. A new parameterization method is proposed for a class of disturbance input signals that depend nonlinearly on unknown parameters, making it possible to obtain a linear regression in the corresponding unknowns. Numerical simulations are presented to demonstrate the effectiveness of the proposed procedures.