[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82071-en":3,"doc-seo-82071-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82071,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Observer Design for a Class of Systems Described by Differential-Algebraic Equations and Parameter Identification of an Unmeasured Disturbance","Observer design addresses estimation for a class of linear descriptor systems modeled by differential-algebraic equations under unknown unmatched disturbances. The goal is to estimate the state vector components and the parameters of an unknown disturbance that is not directly measured. Structural assumptions are imposed to build an observer for the dynamic state part. Using the state estimate, the disturbance signal is reconstructed and its parameters are identified. A new nonlinear disturbance parameterization enables linear regression for identification, and numerical simulations validate the approach.","Observer Design for a Class of Systems Described by Differential-Algebraic  \nEquations and Parameter Identification of an Unmeasured Disturbance Authors:  \nOlga Vladimirovna Oskina, postgraduate student, [ov_oskina@itmo.ru](ov_oskina@itmo.ru), ITMO University, Saint Petersburg, 197101, Russian Federation  \nAlexey Alekseevich Bobtsov, D.Sc., Professor, [bobtsov@itmo.ru](bobtsov@itmo.ru), ITMO University, Saint Petersburg, 197101, Russian Federation  \nAbstract: 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.  \nKeywords: differential-algebraic equations, descriptor systems, adaptive observer, DREM, gradient method, parameter identification  \nIntroduction. Differential-algebraic equations are a natural mathematical framework for describing systems in which, unlike systems of ordinary differential equations, it is necessary to account not only for dynamic processes but also for natural relationships among system variables, which are expressed as algebraic equations. In the literature, systems described by differential-algebraic equations are called descriptor systems. The theoretical basis for analyzing the considered class of systems is described in detail in [1-4] . A wide range of applications of such systems, including electrical  \ncircuits, mechanical systems and mechatronic devices, and chemical engineering processes, is presented in [5, 6] .  \nThe development of theoretically sound and practically applicable observer design methods for dynamic systems described by differential-algebraic equations remains an important research problem with significant practical relevance. In many practical problems, only part of the state variables is measured directly, whereas the remaining variables must be reconstructed from the available system output. The presence of external disturbances or parametric uncertainties introduces additional complexity. Therefore, observer design requires preliminary analysis of the algebraic component of the system, and the direct application of standard methods used for systems of ordinary differential equations is generally not possible. In [7], observers for linear time-varying descriptor systems are considered, and the fundamental importance of consistency between the observer and the structure of the descriptor model is shown. In [8], an observer is proposed that does not require reduction of the system to canonical form and guarantees finite-time convergence of the observation error to zero. The authors of [9,10] consider the problem of observer design for nonlinear descriptor systems using linear matrix inequalities and systematize different types of nonlinearities affecting the observer algorithm design. In [11], a GPEBO-based approach to adaptive observer design for linear time-varying descriptor systems is proposed. The authors of [11], as well as those of [12], consider systems subject to disturbances and note that many state estimation methods rely on a reduction to ordinary differential equations, which leads to a loss of full system information and affects the estimation accuracy. A related direction is the stabilization of a system in the presence of unmeasured matched and unmatched external d","cbCaicKnFIuSkyJG","https://ap.wps.com/l/cbCaicKnFIuSkyJG","pdf",413752,1,15,"English","en",105,"# Introduction\n# Problem Statement\n## System Model and Assumptions\n### Assumption 1\n### Assumption 2\n### Assumption 3","[{\"question\":\"What problem does the paper address in observer design?\",\"answer\":\"The paper studies observer design for linear descriptor systems described by differential-algebraic equations with unknown unmatched disturbances. It focuses on estimating the state vector and unknown disturbance parameters.\"},{\"question\":\"How is the disturbance handled when it is unmeasured?\",\"answer\":\"After constructing an observer for the dynamic part of the state vector using structural assumptions, the method reconstructs the disturbance signal from the obtained state estimate. It then performs parameter identification of the reconstructed disturbance.\"},{\"question\":\"What is the role of the proposed parameterization method?\",\"answer\":\"The paper proposes a new parameterization for a class of disturbance inputs that depend nonlinearly on unknown parameters. This choice makes it possible to obtain a linear regression with respect to the unknowns for efficient identification.\"}]",1784178038,38,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"observer-design-for-a-class-of-systems-described-by-differential-algebraic-equations-and-parameter-identification-of-an-unmeasured-disturbance","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/observer-design-for-a-class-of-systems-described-by-differential-algebraic-equations-and-parameter-identification-of-an-unmeasured-disturbance/82071/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address in observer design?","Question",{"text":75,"@type":76},"The paper studies observer design for linear descriptor systems described by differential-algebraic equations with unknown unmatched disturbances. It focuses on estimating the state vector and unknown disturbance parameters.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the disturbance handled when it is unmeasured?",{"text":80,"@type":76},"After constructing an observer for the dynamic part of the state vector using structural assumptions, the method reconstructs the disturbance signal from the obtained state estimate. It then performs parameter identification of the reconstructed disturbance.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the role of the proposed parameterization method?",{"text":84,"@type":76},"The paper proposes a new parameterization for a class of disturbance inputs that depend nonlinearly on unknown parameters. This choice makes it possible to obtain a linear regression with respect to the unknowns for efficient identification.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]