Fractional calculus is about differentiation and
integration of non-integer orders. Using integer-order models and controllers
for complex natural or man-made systems is simply for our own convenience while
the nature runs in a fractional order dynamical way. Using integer order
traditional tools for modelling and control of dynamic systems may result in
suboptimum performance, that is, using fractional order calculus tools, we could
be ¡°more optimal¡± as already documented in the literature. An interesting remark
is that, using integer order traditional tools, more and more ¡°anomalous¡±
phenomena are being reported or perhaps complained but in applied fractional
calculus community, it is now more widely accepted that ¡°Anomalous is normal¡± in
nature. We believe, beneficial uses of fractional calculus from an engineering
point of view are possible and important. We also hope that fractional calculus
might become an enabler for new science discoveries. Bruce J. West just finished
a new book entitled ¡°The Fractional Dynamic View of Complexity - Tomorrow¡¯s
Science¡± (CRC Press, late 2015). We resonate that, with this special issue,
¡°Fractional Order Systems and Controls¡± will one day enable ¡°tomorrow¡¯s
sciences¡±.
Since 2012, several special issues were
published in some leading journals which showcase the active interference of
fractional calculus to control engineering. Clearly, there is a strong need to
have a special issue in an emerging leading control journal such as IEEE/CAA
Journal of Automatica Sinica (JAS). This focused special issue on control theory
and applications is yet another effort to bring forward the latest updates from
the applied fractional calculus community. For that we feel very excited and we
hope the readers will feel the same.
The aim of this special issue is to show the
control engineering research community the usefulness of the fractional order
tools from signals to systems to controls. It is our sincere hope that this
special issue will become a milestone of a significant trend in the future
development of classical and modern control theory. The contributions may
stimulate future industrial applications of the fractional order control leading
to simpler, more economical, more energy efficient, more reliable and versatile
systems with increasing complexities.
There is no doubt that with this special issue,
the emerging concepts of fractional calculus will have their mathematical
abstractness removed and become an attractive tool in the field of control
engineering with more "good consequence". We welcome any contribution within
the general scope of the Special Issue theme ¡°Fractional Order Systems and
Controls¡±.
IMPORTANT DATES: (tentative)
31 August 2015: Paper Submission
31 October 2015: First Review
30 November 2015: Paper Acceptance
Issue #1 of 2016: Publication online
SUBMISSION GUIDELINES:
Potential authors are encouraged to upload the
electronic file of their manuscript through the journal¡¯s online submission
website:
One of the most
well-known bioinspired optimization techniques is particle swarm
optimization (PSO), which has demonstrated remarkably high potential in
optimization problems wherein conventional optimization techniques
cannot find a satisfactory solution, due to nonlinearities and
discontinuities. The PSO technique consists of a number of particles
whose collective dynamics, resembling a biological ecosystem, allows
effectively exploring the search space to find the optimal solution. The
Darwinian PSO (DPSO) is an evolutionary optimization algorithm and an
extension of the original PSO that makes use of Darwin¡¯s
theory of natural selection to regulate the evolution of the particles
and of their collective dynamics,so that complex optimization of
functions exhibiting many local maxima/minima can be successfully
accomplished. The fractional order DPSO (FODPSO) incorporates in DPSO
the notion of fractional-order derivatives to attain memory of past
decisions and even better convergence properties.
This study suggests that the power law decay of prime number distribution can be considered a sub-diffusion process, one of typical anomalous diffusions, and could be described by the fractional derivative equation model, whose solution is the statistical density function of Mittag-Leffler distribution. It is observed that the Mittag-Leffler distribution of the fractional derivative diffusion equation agrees well with the prime number distribution and performs far better than the prime number theory. Compared with the Riemann¡¯s method, the fractional diffusion model is less accurate but has clear physical significance and appears more stable. We also find that the Shannon entropies of the Riemann¡¯s description and the fractional diffusion models are both very close to the original entropy of prime numbers. The proposed model appears an attractive physical description of the power law decay of prime number distribution and opens a new methodology in this field.
Publication information: Tsuneo Usuki.
Dispersion curves for 3D viscoelastic beams of solid circular cross
section with fractional derivatives.
Journal of Sound and Vibration, 2013, 332: 126-144.
The aim is to extend the theory to a viscoelastic beam that satisfies stress-free surface boundary conditions. A viscoelastic material (polyvinyl chloride) was used in the numerical calculation, and the phase and group velocity curves were derived for a viscoelastic beam from the case without damping to the case with damping proportional to the first-order derivative with respect to time. Based on the preliminary data, the phase and group velocity curves were derived for a beam of solid circular cross section. As a result, it was confirmed that, as earlier pointed out for elastic materials, these curves were controlled by the phase velocity inherent to the material. Finally, with the phase velocity and the group velocity of the beam, regularities were derived for the absolute value of the complex velocity on the complex plane.