Wang, Yan (Auburn University), Bevly, David (Auburn University)

Robust Observer Design for Lipschitz Nonlinear Systems with Parametric Uncertainty

Scheduled for presentation during the Contributed session "Nonlinear Estimation and Control" (MoCT7), Monday, October 21, 2013, 16:00−16:20, Room 138

6th Annual Dynamic Systems and Control Conference, October 21-23, 2020, Stanford University, Munger Center, Palo Alto, CA

This information is tentative and subject to change. Compiled on June 30, 2025

Abstract

his 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_infinity, can be easily incorporated in this framework. Finally, a parameter adaptation algorithm is introduced to cope with the parameter uncertainty.