Online Output-Feedback Parameter and State Estimation for Second Order Linear Systems

TL;DR

This paper introduces a concurrent learning-based adaptive observer for second-order linear systems that guarantees exponential convergence of states and parameters with finite-time excitation, validated through simulations.

Contribution

It presents a novel adaptive observer that achieves exponential convergence without persistent excitation, using finite-time excitation for second-order systems.

Findings

Exponential convergence of state and parameter estimates demonstrated.

Finite-time excitation suffices for convergence, unlike traditional methods.

Validated effectiveness through simulations in noise-free and noisy conditions.

Abstract

In this paper, a concurrent learning based adaptive observer is developed for a class of second-order linear time-invariant systems with uncertain system matrices. The developed technique yields an exponentially convergent state estimator and an exponentially convergent parameter estimator. As opposed to persistent excitation required for parameter convergence in traditional adaptive methods, excitation over a finite time-interval is sufficient for the developed technique to achieve exponential convergence. Simulation results in both noise-free and noisy environments are presented to validate the design.