Contracting Nonlinear Observers: Convex Optimization and Learning from Data

TL;DR

This paper introduces a convex optimization-based framework for designing nonlinear observers that are contracting, enabling data-driven learning and optimization of state estimators for continuous and discrete systems.

Contribution

It proposes a novel convex set construction for contracting nonlinear observers and a data-driven optimization method to improve their performance.

Findings

Convex sets of contracting observers are constructed for various system types.

The approach effectively minimizes state-estimation error bounds.

Numerical simulations verify the utility of the proposed methods.

Abstract

A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for one which minimizes a bound on state-estimation error on a simulated noisy data set. We construct convex sets of continuous-time and discrete-time observers, as well as contracting sampled-data observers for continuous-time systems. Convex bounds for learning are constructed using Lagrangian relaxation. The utility of the proposed methods are verified using numerical simulation.