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Immersion and invariance‐based extended state observer design for a class of nonlinear systems
Author(s) -
HosseiniPishrobat Mehran,
Keighobadi Jafar,
Pirastehzad Armin,
Javad Yazdanpanah Mohammad
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5607
Subject(s) - control theory (sociology) , observer (physics) , nonlinear system , manifold (fluid mechanics) , convergence (economics) , mathematics , immersion (mathematics) , state observer , computer science , mathematical analysis , control (management) , engineering , artificial intelligence , physics , mechanical engineering , quantum mechanics , economics , economic growth
This article presents a novel geometric framework for the design of extended state observers (ESOs) using the immersion and invariance (I&I) method. The ESO design problem of a class of uncertain lower‐triangular nonlinear systems is considered for joint state and total disturbance observation. This problem is formulated as designing a dynamical system, as the observer, along with an appropriately defined manifold in the system‐observer extended state‐space. The ESO convergence translates into the attractivity of this manifold; that is, the convergence of the system‐observer trajectories to a small boundary layer around the manifold. The design of both reduced‐order and full‐order ESOs is studied using the I&I formulation. Moreover, an optimization method based on linear matrix inequalities is proposed to establish the convergence of ESOs. It is shown that the I&I‐based method leads to a unifying framework for the design and analysis of ESOs with linear, nonlinear, and time‐varying gains. Detailed simulations are provided to show the efficacy of the proposed ESOs.