Reduced-Order Nonlinear Observers via Contraction Analysis and Convex Optimization

TL;DR

This paper introduces a systematic method for designing globally convergent reduced-order nonlinear observers using contraction analysis and convex optimization, applicable to a broad class of physical systems.

Contribution

It develops a convex optimization-based approach for globally convergent reduced-order nonlinear observer design via contraction analysis, improving over existing local or conservative methods.

Findings

The method is applicable to polynomial, mechanical, electromechanical, and biochemical systems.

It provides easily verifiable differential inequalities for observer design.

Numerical and physical examples demonstrate effectiveness and broad applicability.

Abstract

In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state estimation, the existing solutions are either local or relatively conservative when applying to physical systems. To address this, we show that this problem can be translated into an off-line search for a coordinate transformation after which the dynamics is (transversely) contracting. The obtained sufficient condition consists of some easily verifiable differential inequalities, which, on one hand, identify a very general class of "detectable" nonlinear systems, and on the other hand, can be expressed as computationally efficient convex optimization, making the design procedure more systematic. Connections with some well-established approaches and concepts are also clarified in the paper. Finally, we illustrate the proposed method with several numerical and physical examples, including polynomial, mechanical, electromechanical and biochemical systems.