Observer design for systems with an energy-preserving non-linearity

TL;DR

This paper presents a convex programming-based method for designing convergent observers for non-linear systems with energy-preserving nonlinearities, demonstrated on the Lorenz attractor and shear fluid flow models.

Contribution

It introduces a novel convex programming approach for observer design in energy-preserving non-linear systems, enabling convergence verification.

Findings

Observer design method successfully applied to Lorenz attractor

Method verified on shear fluid flow model

Convex programming ensures observer convergence

Abstract

Observer design is considered for a class of non-linear systems whose non-linear part is energy preserving. A strategy to construct convergent observers for this class of non-linear system is presented. The approach has the advantage that it is possible, via convex programming, to prove whether the constructed observer converges, in contrast to several existing approaches to observer design for non-linear systems. Finally, the developed methods are applied to the Lorenz attractor and to a low order model for shear fluid flow.