Optimization of self-adaptive synchronization and parameters estimation in chaotic Hindmarsh-Rose neuron model

Abstract

Optimization of self-adaptive synchronization is investigated to estimate a group of five unknown parameters in one certain chaotic neuron model, which is described by the Hindmarsh-Rose. Two controllable gain coefficients are introduced into the Lyapunov function, which is necessary to get the form of parameter observers and controllers for parameter estimation and synchronization, to adjust the transient period for complete synchronization and parameter identification. It is found that the identified results for the minimal parameter （three orders of magnitude less than the maximal parameter） oscillate with time （the estimated results for this parameter is not exact） while the four remaining parameters are estimated very well when one controller and five parameter observers are used to work on the driven system （response system）. To the best of our knowledge, it could result from the great difference of five target parameters （values）. As a result, this problem could be solved when two controllers and five parameter observers are used to change the driven system and all the unknown parameters are identified with high precision. Furthermore, longer transient period for parameter estimation and complete synchronization is required when too strong gain coefficients are used, whils parameters can not be estimated exactly if too weak gain coefficients are used. Therefore, appropriate gain coefficients are critical to achieve the shortest transient period for parameter identification and complete synchronization of chaotic systems, and the optimization of gain coefficients depends on the model being studied. Furthermore, it is confirmed by our numerical results that this scheme is effective and reliable to estimate the parameters even if some parameters jump suddenly.

Adaptive synchronization of chaos in permanent magnet synchronous motors based on passivity theory

“…The control law u can also be designed by using the Lyapunov stability theory. [12,21] Compared with the original Lyapunov stability theory, the passivity theory, which is considered as an alternative tool for analysing the stability of nonlinear systems and designing controllers, has superior features, such as having a distinct physical meaning and a positive definite storage function.…”