Multiple shooting-Local Linearization method for the identification of dynamical systems

TL;DR

This paper introduces a novel method combining multiple shooting with local linearization for efficient and accurate parameter estimation in dynamical systems modeled by ODEs, especially under noisy data conditions.

Contribution

It proposes using local linearization within the multiple shooting framework to improve derivative evaluation and integration accuracy without increasing computational cost.

Findings

Accurately recovers true parameters in noisy data scenarios

Provides a stable and efficient derivative approximation method

Demonstrates effectiveness through numerical simulations

Abstract

The combination of the multiple shooting strategy with the generalized Gauss-Newton algorithm turns out in a recognized method for estimating parameters in ordinary differential equations (ODEs) from noisy discrete observations. A key issue for an efficient implementation of this method is the accurate integration of the ODE and the evaluation of the derivatives involved in the optimization algorithm. In this paper, we study the feasibility of the Local Linearization (LL) approach for the simultaneous numerical integration of the ODE and the evaluation of such derivatives. This integration approach results in a stable method for the accurate approximation of the derivatives with no more computational cost than the that involved in the integration of the ODE. The numerical simulations show that the proposed Multiple Shooting-Local Linearization method recovers the true parameters value under different scenarios of noisy data.