A Dynamic Mode Decomposition Approach to Parameter Identification

TL;DR

This paper introduces a data-driven method using Dynamic Mode Decomposition for identifying system parameters in nonlinear control systems, demonstrated on a Duffing oscillator.

Contribution

It proposes a novel approach combining system identification and parameter estimation through predictive modeling with DMD, applicable to control-affine nonlinear systems.

Findings

Accurately recovered system trajectories and parameters from data

Validated method on a Duffing oscillator with unknown parameters

Demonstrated effectiveness with open-loop excitation data

Abstract

This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action measurements and various known values at the parameters of interest. The predictive model is then used in conjunction with state-action data corresponding to unknown values of the parameters to estimate the said unknown value. Numerical experiments on the controlled Duffing oscillator with unknown damping, stiffness, and nonlinearity coefficients demonstrate accurate recovery of both the system trajectories and the unknown parameter values from data collected under open-loop excitation.