Sparse identification and parameter estimation of nonlinear dynamical systems using SINDy-MHE framework

Abstract

Modelling and parameter estimation of nonlinear dynamical systems can be difficult in the presence of strong, unknown nonlinearities, measurement noise, disturbances, partial observability, and unknown physical parameters. Traditional physics-based models usually require an abundance of prior knowledge, whereas purely data-driven black-box methods lack robustness and interpretability. This study addresses these challenges by proposing a unified framework that integrates sparse identification of nonlinear dynamical systems (SINDy) with moving horizon estimation (MHE) for joint system identification and parameter estimation. Firstly, SINDy is applied offline to extract a parsimonious and interpretable model of system dynamics from time-series data by discovering a comparatively small set of governing equations with good physical interpretability. An MHE framework is then integrated within the identified SINDy model, enabling explicit handling of constraints and online estimation of system state and unknown parameters under noisy and partial observability conditions. The performance of the proposed framework is validated with two nonlinear systems: a magnetic levitation system and a hydraulically actuated four-bar mechanism. In both case studies, this approach shows resilience to noise and modelling errors, leveraging optimization-based estimation of MHE to compensate for SINDy's inherent sensitivity to measurement uncertainty, accurately identifying system dynamics and estimating unknown parameters. The results illustrate that the proposed framework is a reliable and robust approach providing effective joint system identification and parameter estimation for nonlinear dynamical systems.