Robust observer design for Lipschitz nonlinear systems with parametric uncertainty

Yan Wang, David M. Bevly

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationNonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing;
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Print)9780791856147
DOIs
StatePublished - Jan 1 2013
EventASME 2013 Dynamic Systems and Control Conference, DSCC 2013 - Palo Alto, CA, United States
Duration: Oct 21 2013Oct 23 2013

Publication series

NameASME 2013 Dynamic Systems and Control Conference, DSCC 2013
Volume3

Other

OtherASME 2013 Dynamic Systems and Control Conference, DSCC 2013
CountryUnited States
CityPalo Alto, CA
Period10/21/1310/23/13

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