Robust Observer Design for Lipschitz Nonlinear Systems With Parametric Uncertainty. Wang, Y. & Bevly, D. M. In Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing; System Identification (Estimation for Automotive Applications, Modeling, Therapeutic Control in Bio-Systems); Variable Structure/Sliding-Mode Control; Vehicles and Human Robotics; Vehicle Dynamics and Control; Vehicle Path Planning and Collision Avoidance; Vibrational and Mechanical Systems; Wind Energy Systems and Control, pages V003T35A006, Palo Alto, California, USA, October, 2013. American Society of Mechanical Engineers. ![Robust Observer Design for Lipschitz Nonlinear Systems With Parametric Uncertainty [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex This paper discusses optimal and robust observer design for the Lipschitz nonlinear systems. The stability analysis for the Lure problem is first reviewed. Then, a two-DOF nonlinear observer is proposed so that the observer error dynamic model can be transformed to an equivalent Lure system. In this framework, the difference of the nonlinear parts in the vector fields of the original system and observer is modeled as a nonlinear memoryless block that is covered by a multivariable sector condition or an equivalent semi-algebraic set defined by a quadratic polynomial inequality. Then, a sufficient condition for asymptotic stability of the observer error dynamics is formulated in terms of the feasibility of polynomial matrix inequalities (PMIs), which can be solved by Lasserre’s moment relaxation. Furthermore, various quadratic performance criteria, such as H2 and H∞, can be easily incorporated in this framework. Finally, a parameter adaptation algorithm is introduced to cope with the parameter uncertainty.
@inproceedings{wang_robust_2013,
address = {Palo Alto, California, USA},
title = {Robust {Observer} {Design} for {Lipschitz} {Nonlinear} {Systems} {With} {Parametric} {Uncertainty}},
isbn = {978-0-7918-5614-7},
url = {https://asmedigitalcollection.asme.org/DSCC/proceedings/DSCC2013/56147/Palo%20Alto,%20California,%20USA/228856},
doi = {10.1115/DSCC2013-4104},
abstract = {This paper discusses optimal and robust observer design for the Lipschitz nonlinear systems. The stability analysis for the Lure problem is first reviewed. Then, a two-DOF nonlinear observer is proposed so that the observer error dynamic model can be transformed to an equivalent Lure system. In this framework, the difference of the nonlinear parts in the vector fields of the original system and observer is modeled as a nonlinear memoryless block that is covered by a multivariable sector condition or an equivalent semi-algebraic set defined by a quadratic polynomial inequality. Then, a sufficient condition for asymptotic stability of the observer error dynamics is formulated in terms of the feasibility of polynomial matrix inequalities (PMIs), which can be solved by Lasserre’s moment relaxation. Furthermore, various quadratic performance criteria, such as H2 and H∞, can be easily incorporated in this framework. Finally, a parameter adaptation algorithm is introduced to cope with the parameter uncertainty.},
urldate = {2024-06-20},
booktitle = {Volume 3: {Nonlinear} {Estimation} and {Control}; {Optimization} and {Optimal} {Control}; {Piezoelectric} {Actuation} and {Nanoscale} {Control}; {Robotics} and {Manipulators}; {Sensing}; {System} {Identification} ({Estimation} for {Automotive} {Applications}, {Modeling}, {Therapeutic} {Control} in {Bio}-{Systems}); {Variable} {Structure}/{Sliding}-{Mode} {Control}; {Vehicles} and {Human} {Robotics}; {Vehicle} {Dynamics} and {Control}; {Vehicle} {Path} {Planning} and {Collision} {Avoidance}; {Vibrational} and {Mechanical} {Systems}; {Wind} {Energy} {Systems} and {Control}},
publisher = {American Society of Mechanical Engineers},
author = {Wang, Yan and Bevly, David M.},
month = oct,
year = {2013},
pages = {V003T35A006},
}
Downloads: 0
{"_id":"54b6yYFps9fBwHWr3","bibbaseid":"wang-bevly-robustobserverdesignforlipschitznonlinearsystemswithparametricuncertainty-2013","author_short":["Wang, Y.","Bevly, D. M."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","address":"Palo Alto, California, USA","title":"Robust Observer Design for Lipschitz Nonlinear Systems With Parametric Uncertainty","isbn":"978-0-7918-5614-7","url":"https://asmedigitalcollection.asme.org/DSCC/proceedings/DSCC2013/56147/Palo%20Alto,%20California,%20USA/228856","doi":"10.1115/DSCC2013-4104","abstract":"This paper discusses optimal and robust observer design for the Lipschitz nonlinear systems. The stability analysis for the Lure problem is first reviewed. Then, a two-DOF nonlinear observer is proposed so that the observer error dynamic model can be transformed to an equivalent Lure system. In this framework, the difference of the nonlinear parts in the vector fields of the original system and observer is modeled as a nonlinear memoryless block that is covered by a multivariable sector condition or an equivalent semi-algebraic set defined by a quadratic polynomial inequality. Then, a sufficient condition for asymptotic stability of the observer error dynamics is formulated in terms of the feasibility of polynomial matrix inequalities (PMIs), which can be solved by Lasserre’s moment relaxation. Furthermore, various quadratic performance criteria, such as H2 and H∞, can be easily incorporated in this framework. Finally, a parameter adaptation algorithm is introduced to cope with the parameter uncertainty.","urldate":"2024-06-20","booktitle":"Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing; System Identification (Estimation for Automotive Applications, Modeling, Therapeutic Control in Bio-Systems); Variable Structure/Sliding-Mode Control; Vehicles and Human Robotics; Vehicle Dynamics and Control; Vehicle Path Planning and Collision Avoidance; Vibrational and Mechanical Systems; Wind Energy Systems and Control","publisher":"American Society of Mechanical Engineers","author":[{"propositions":[],"lastnames":["Wang"],"firstnames":["Yan"],"suffixes":[]},{"propositions":[],"lastnames":["Bevly"],"firstnames":["David","M."],"suffixes":[]}],"month":"October","year":"2013","pages":"V003T35A006","bibtex":"@inproceedings{wang_robust_2013,\n\taddress = {Palo Alto, California, USA},\n\ttitle = {Robust {Observer} {Design} for {Lipschitz} {Nonlinear} {Systems} {With} {Parametric} {Uncertainty}},\n\tisbn = {978-0-7918-5614-7},\n\turl = {https://asmedigitalcollection.asme.org/DSCC/proceedings/DSCC2013/56147/Palo%20Alto,%20California,%20USA/228856},\n\tdoi = {10.1115/DSCC2013-4104},\n\tabstract = {This paper discusses optimal and robust observer design for the Lipschitz nonlinear systems. The stability analysis for the Lure problem is first reviewed. Then, a two-DOF nonlinear observer is proposed so that the observer error dynamic model can be transformed to an equivalent Lure system. In this framework, the difference of the nonlinear parts in the vector fields of the original system and observer is modeled as a nonlinear memoryless block that is covered by a multivariable sector condition or an equivalent semi-algebraic set defined by a quadratic polynomial inequality. Then, a sufficient condition for asymptotic stability of the observer error dynamics is formulated in terms of the feasibility of polynomial matrix inequalities (PMIs), which can be solved by Lasserre’s moment relaxation. Furthermore, various quadratic performance criteria, such as H2 and H∞, can be easily incorporated in this framework. Finally, a parameter adaptation algorithm is introduced to cope with the parameter uncertainty.},\n\turldate = {2024-06-20},\n\tbooktitle = {Volume 3: {Nonlinear} {Estimation} and {Control}; {Optimization} and {Optimal} {Control}; {Piezoelectric} {Actuation} and {Nanoscale} {Control}; {Robotics} and {Manipulators}; {Sensing}; {System} {Identification} ({Estimation} for {Automotive} {Applications}, {Modeling}, {Therapeutic} {Control} in {Bio}-{Systems}); {Variable} {Structure}/{Sliding}-{Mode} {Control}; {Vehicles} and {Human} {Robotics}; {Vehicle} {Dynamics} and {Control}; {Vehicle} {Path} {Planning} and {Collision} {Avoidance}; {Vibrational} and {Mechanical} {Systems}; {Wind} {Energy} {Systems} and {Control}},\n\tpublisher = {American Society of Mechanical Engineers},\n\tauthor = {Wang, Yan and Bevly, David M.},\n\tmonth = oct,\n\tyear = {2013},\n\tpages = {V003T35A006},\n}\n\n\n\n","author_short":["Wang, Y.","Bevly, D. M."],"key":"wang_robust_2013","id":"wang_robust_2013","bibbaseid":"wang-bevly-robustobserverdesignforlipschitznonlinearsystemswithparametricuncertainty-2013","role":"author","urls":{"Paper":"https://asmedigitalcollection.asme.org/DSCC/proceedings/DSCC2013/56147/Palo%20Alto,%20California,%20USA/228856"},"metadata":{"authorlinks":{}}},"bibtype":"inproceedings","biburl":"https://bibbase.org/zotero-group/keb0115/5574615","dataSources":["oHndJaZA7ydhNbpvR","cN69sC6vEx9NJkKJi","kDK6fZ4EDThxNKDCP"],"keywords":[],"search_terms":["robust","observer","design","lipschitz","nonlinear","systems","parametric","uncertainty","wang","bevly"],"title":"Robust Observer Design for Lipschitz Nonlinear Systems With Parametric Uncertainty","year":2013}