# Online Simultaneous State and Parameter Estimation for Second-order Nonlinear Systems

## TL;DR

This paper introduces a novel online adaptive observer for second-order nonlinear systems that estimates states and parameters simultaneously without needing persistent excitation, using a Lyapunov-based approach.

## Contribution

It presents a concurrent learning-based method for real-time state and parameter estimation in nonlinear systems, reducing excitation requirements compared to traditional methods.

## Key findings

- Estimation errors are uniformly ultimately bounded.
- The method works with finite excitation intervals.
- No persistent excitation needed for convergence.

## Abstract

In this paper, a concurrent learning based adaptive observer is developed for a class of second-order nonlinear time-invariant systems with uncertain dynamics. The developed technique results in simultaneous online state and parameter estimation. A Lyapunov-based analysis is used to show that the state and parameter estimation errors are uniformly ultimately bounded. As opposed to persistent excitation which is required for parameter estimation in traditional adaptive control methods, the developed technique only requires excitation over a finite time interval.