2 research outputs found
Identification of unknown parameters and orders via cuckoo search oriented statistically by differential evolution for non-commensurate fractional order chaotic systems
Identification of the unknown parameters and orders of fractional chaotic
systems is of vital significance in controlling and synchronization of
fractional-order chaotic systems. In this paper, a non-Lyapunov novel approach
is proposed to estimate the unknown parameters and orders together for
non-commensurate and hyper fractional chaotic systems based on cuckoo search
oriented statistically the differential evolution (CSODE). Firstly, a novel
Gao's mathematical model is put and analysed in three sub-models, not only for
the unknown orders and parameters' identification but also for systems'
reconstruction of fractional chaos systems with time-delays or not. Then the
problems of fractional-order chaos' identification are converted into a
multiple modal non-negative functions' minimization through a proper
translation, which takes fractional-orders and parameters as its particular
independent variables. And the objective is to find best combinations of
fractional-orders and systematic parameters of fractional order chaotic systems
as special independent variables such that the objective function is minimized.
Simulations are done to estimate a series of non-commensurate and hyper
fractional chaotic systems with the new approaches based on CSODE, the cuckoo
search and differential evolution respectively. The experiments' results show
that the proposed identification mechanism based on CSODE for fractional-orders
and parameters is a successful methods for fractional-order chaotic systems,
with the advantages of high precision and robustness.Comment: 53 pages, 12 figures. arXiv admin note: text overlap with
arXiv:1207.735
Reconstruction mechanism with self-growing equations for hyper, improper and proper fractional chaotic systems through a novel non-Lyapunov approach
Identification of the unknown parameters and orders of fractional chaotic
systems is of vital significance in controlling and synchronization of
fractional-order chaotic systems. However there exist basic hypotheses in
traditional estimation methods, that is, the parameters and fractional orders
are partially known or the known data series coincide with definite forms of
fractional chaotic differential equations except some uncertain parameters and
fractional orders. What should I do when these hypotheses do not exist?
In this paper, a non-Lyapunov novel approach with a novel united mathematical
model is proposed to reconstruct fractional chaotic systems, through the
fractional-order differential equations self-growing mechanism by some genetic
operations ideas independent of these hypotheses. And the cases of identifying
the unknown parameters and fractional orders of fractional chaotic systems can
be thought as special cases of the proposed united mathematical reconstruction
method in non-Lyapunov way. The problems of fractional-order chaos
reconstruction are converted into a multiple modal non-negative special
functions' minimization through a proper translation, which takes
fractional-order differential equations as its particular independent variables
instead of the unknown parameters and fractional orders. And the objective is
to find best form of fractional-order differential equations such that the
objective function is minimized. Simulations are done to reconstruct a series
of hyper and normal fractional chaotic systems. The experiments' results show
that the proposed self-growing mechanism of fractional-order differential
equations with genetic operations is a successful methods for fractional-order
chaotic systems' reconstruction, with the advantages of high precision and
robustness.Comment: 50 pages, 12 figure