Beyond Bounded Noise: Stochastic Set-Membership Estimation for Nonlinear Systems

TL;DR

This paper introduces a stochastic set-membership estimation method for nonlinear dynamical systems with unbounded noise, providing probabilistic guarantees and convergence analysis.

Contribution

It develops a novel procedure that constructs finite-sample uncertainty sets for system parameters under stochastic noise with unbounded support, applicable to nonlinear systems.

Findings

Provides high-probability bounds on true parameters

Establishes convergence conditions and rates

Demonstrates advantages over existing methods in numerical examples

Abstract

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample uncertainty set containing the true system parameters with high probability. Our approach can be natively applied to a wide class of nonlinear systems affected by sub-Gaussian noise. Our analysis provides conditions under which the proposed uncertainty set converges to the true system parameters and establishes an upper bound on the convergence rate. The proposed uncertainty set can be used directly for robust controller synthesis with probabilistic stability and performance guarantees. Concluding numerical examples demonstrate the advantages of the proposed formulation over established approaches.