Parameter estimation of delay differential equations: An integration-free LS-SVM approach

Siamak Mehrkanoon*, Saeid Mehrkanoon, Johan A. K. Suykens

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


This paper introduces an estimation method based on Least Squares Support Vector Machines (LS-SVMs) for approximating time-varying as well as constant parameters in deterministic parameter-affine delay differential equations (DDEs). The proposed method reduces the parameter estimation problem to an algebraic optimization problem. Thus, as opposed to conventional approaches, it avoids iterative simulation of the given dynamical system and therefore a significant speedup can be achieved in the parameter estimation procedure. The solution obtained by the proposed approach can be further utilized for initialization of the conventional nonconvex optimization methods for parameter estimation of DDEs. Approximate LS-SVM based models for the state and its derivative are first estimated from the observed data. These estimates are then used for estimation of the unknown parameters of the model. Numerical results are presented and discussed for demonstrating the applicability of the proposed method. (C) 2013 Elsevier B. V. All rights reserved.

Original languageEnglish
Pages (from-to)830-841
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number4
Publication statusPublished - Apr 2014
Externally publishedYes


  • Delay differential equations
  • Parameter identification
  • Least squares support vector machines
  • Closed-form approximation


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