Open AccessEstimating parameters of chaotic system with variational method
Author(s) -
Xiaoqun Cao,
Junqiang Song,
Wei Min Zhang,
Jun Zhao,
Lilun Zhang
Publication year - 2011
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.60.070511
Subject(s) - chaotic , lorenz system , chaotic systems , mathematics , chen , computer science , variational method , control theory (sociology) , statistical physics , physics , mathematical analysis , artificial intelligence , paleontology , biology , control (management)
In this paper a method is presented to estimate the unknown parameters of chaotic system based on the variational principle, which can be applied to all chaotic systems governed by the following equation:x= F(x,θ). Firstly,the equation of the chaotic system is included into the objective functional. Secondly, the universal formulas of the adjoint equation for chaotic systems and the functional gradient for unknown parameters are derived using the variational principle. Thirdly, the algorithm to estimate unknown parameters of chaotic system is designed according to above formulas. Finally, all unknown parameters of the typical Lorenz chaotic system and the hyperchaotic Chen system are estimated separately. Numerical simulations show that the effectiveness and the feasibility of the proposed method to estimate unknown parameters of chaotic systems.