Distributed Prescribed-Time Observer for Nonlinear Systems in Block-Triangular Form

TL;DR

This paper introduces a distributed observer for nonlinear block-triangular systems that guarantees state estimation convergence at a user-defined time using time-varying gains, validated through theoretical proofs and simulations.

Contribution

It presents a novel prescribed-time observer design for nonlinear systems in block-triangular form, ensuring finite-time convergence regardless of initial conditions.

Findings

Convergence to zero estimation error at prescribed time.

Effective observer design for systems with limited local observability.

Validation through rigorous simulations and theoretical proofs.

Abstract

This paper proposes a distributed prescribed-time observer for nonlinear systems representable in a block-triangular observable canonical form. Using a weighted average of neighbor estimates exchanged over a strongly connected digraph, each observer estimates the system state despite the limited observability of local sensor measurements. The proposed design guarantees that distributed state estimation errors converge to zero at a user-specified convergence time, irrespective of observers' initial conditions. To achieve this prescribed-time convergence, distributed observers implement time-varying local output injection gains that monotonically increase and approach infinity at the prescribed time. The theoretical convergence is rigorously proven and validated through numerical simulations, where some implementation issues due to increasing gains have also been clarified.