About identifiability and observability for a class of dynamical systems

TL;DR

This paper introduces a new method for identifying parameters and states in certain autonomous dynamical systems using low-order derivatives and linear algebra, enabling efficient reconstruction with minimal data.

Contribution

It presents a novel approach that leverages linear independence and low-order derivatives for parameter and state identification in specific dynamical systems.

Findings

Requires fewer derivatives than classical methods

Allows reconstruction with very limited data

Provides constructive procedures for parameter retrieval

Abstract

In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the linear independence between some functions depending on the observations and its derivatives. In particular, we show that, in some cases, only low-order derivatives are necessary, opposed to classical approaches that need more derivation. We also provide different constructive procedures to retrieve the unknowns, which are based on the resolution of some linear systems. Moreover, under some analytic conditions, these unknowns may be retrieved with very few data. We finally apply this approach to some illustrative examples.