Parameters identification of Van der Pol–Duffing oscillators via particle swarm optimization and differential evolution

Abstract

Many of the proposed approaches for non-linear systems control are developed under the assumption that all involved parameters are known in advance. Unfortunately, their estimation is not so simple because the nature of the non-linear behaviors is very complex in the most part of the cases. In view of this complication, parameters identification of non-linear oscillators has attracted increasing interests in various research fields: from a pure mathematical point-of-view, parameters identification can be formalized as a multi-dimensional optimization problem, typically over real bounded domains. In doing this, the use of the so-called non-classical methods based on soft computing theories seems to be promising because they do not require a priori information and the robustness of the identification against the noise contamination is satisfactory. However, further studies are required to evaluate the general effectiveness of these methodologies. In this sense, the paper addresses the consistency of two classes of soft computing based methods for the identification of Van der Pol–Duffing oscillators. A large numerical investigation has been conducted to evaluate the performances of six differential evolution algorithms (including a modified differential evolution algorithm proposed by the authors) and four swarm intelligence based algorithms (including a chaotic particle swarm optimization algorithm). Single well, double well and double-hump oscillators are identified and noisy system responses are considered in order to evaluate the robustness of the identification processes. The investigated soft computing techniques behave very well and thus they are suitable for practical applications.