Estimation and approximation in nonlinear dynamic systems using quasilinearization

TL;DR

This paper introduces a smoothing method using quasilinearized ODE penalties to accurately estimate states and parameters of nonlinear differential systems from noisy data, simplifying the optimization process.

Contribution

It presents a novel quasilinearized spline-based framework that reduces nonlinear estimation to a conditionally linear problem, facilitating parameter estimation and constraint imposition.

Findings

Effective in real and simulated data applications

Simplifies nonlinear estimation to linear optimization problems

Allows easy selection of ODE compliance parameters

Abstract

Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a quasilinearized ODE-based penalty in order to approximate the state functions and estimate the parameters defining nonlinear differential systems from noisy data. Within the quasilinearized spline based framework, the estimation process reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are easily applicable and conditions on the state function(s) can be eventually imposed using soft or hard constraints. The approach is illustrated on real and simulated data.