2014/04/29 by Gianluca Frasso, Frasso, Gianluca, Jonathan Jaeger +3
Engineering · Mathematics · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Computer and information sciences #Methodology (stat.ME) #Stability and Controllability of Differential Equations #stat.ME
paper · pdf · doi:10.48550/arxiv.1404.7370
arxiv created 2014/04/29 · openalex publication_date 2014/04/29 · arxiv updated 2014/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.