Robust Nonlinear L2 Filtering of Uncertain Lipschitz Systems via Pareto Optimization

TL;DR

This paper introduces a robust nonlinear L2 filtering method for uncertain Lipschitz systems using Pareto optimization, ensuring stability and robustness against uncertainties with explicit bounds.

Contribution

It develops a novel LMI-based multiobjective optimization framework to design Hinfty filters that maximize Lipschitz constant and disturbance attenuation simultaneously.

Findings

Guarantees asymptotic stability with exponential convergence

Robust against nonlinear additive and parametric uncertainties

Provides explicit bounds on nonlinear uncertainties

Abstract

A new approach for robust Hinfty filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting Hinfty filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.