Linear and Nonlinear Event-Triggered Extended State Observers for Uncertain Stochastic Systems

TL;DR

This paper develops linear and nonlinear event-triggered extended state observers for uncertain stochastic systems with bounded noises, ensuring convergence and proposing triggers with positive minimum inter-event times, validated through simulations.

Contribution

It introduces novel event-triggered observers for uncertain stochastic systems, with rigorous convergence proofs and a comparison of linear versus nonlinear observer performance.

Findings

Nonlinear observer achieves higher estimation accuracy.

Nonlinear observer has higher triggering frequency.

Both observers ensure mean square and almost sure convergence.

Abstract

In this paper, linear and nonlinear event-triggered extended state observers are designed for a class of uncertain stochastic systems driven by bounded and colored noises. Two event-generators with an ensured positive minimum inter-event time for every sample path solution of the stochastic systems, are proposed for the designs of linear and nonlinear event-triggered extended state observers, respectively. The mean square and almost sure convergence of the estimation errors of unmeasured state and stochastic total disturbance including internal uncertainty and external stochastic noises is presented with rigorous theoretical proofs. Compared with the linear event-triggered extended state observer, the theoretical results show that the nonlinear one via homogeneity possesses higher estimation accuracy but is at the price of higher triggering frequency. Some numerical simulations are performed to authenticate the theoretical results.