IEEE Systems, Man and Cybernetics Magazine - July 2018 - 27

Prof. Karl J. Åström has called the hidden technology:
automatic control [27].
Before the 19th century, automata were purely decorative objects of fantasy-in conception and function-that
imitated human beings or animals in their form and
actions. Often, these sophisticated devices were able to
sing, dance, and play music. But after the birth of control
theory, and especially with the advent of cybernetics, the
model for the ideal machine (the human being) included not
only material elements (hardware) but also computational
ones (software) to deal with the emerging concepts of selfregulation and information processing. Self-regulation or
homeostasis is also the basis of life, just as feedback control is the foundation of our most sophisticated machines.
So, to the extent that memory and nonlocal phenomena
affect performance, new mathematical tools are needed to
describe and model the behavior of human subjects.
When Wiener joined the MIT faculty in 1920, the general
approach taken to analyze nonlinear circuits was the
direct generalization of impedance and transfer functions
to include both linear and nonlinear systems [28]. The consequence was that, according to Wiener [3]:
The study of non-linear was getting into a state comparable with that of the last stages of the Ptolemaic
system of astronomy in which epicycle was piled on
epicycle, correction upon correction, until a vast
patchwork structure ultimately broke down under its
own weight.
In a similar manner, when considering feedback control
in complex systems (machines, animals, or humans), the
classical derivatives and integrals of integer order lead to
stacking operators until the structure breaks down under
its own redundancy. A new starting point is to consider
noninteger derivatives and integrals. The nature of fractional operators allows not only a renewed consideration of
the past (and, because of this, a new form of predicting the
future) but a richer way of perceiving the instant and therefore time: from time-based sampling to duration-based
sampling, or, as has been pointed out before, extending the
models from Newtonian time to Bergsonian time [13].
Future Directions
Cybernetics played a key role in the birth of automatic control, artificial intelligence, and robotics in the mid-20th
century. Its scope now includes cyberphysical systems
[29]-[32], and its fundamental definition has recently been
discussed by Zhao et al. [32] and Magin [34]. We suggest
that fractional calculus can be applied more extensively in
cybernetics as it continues to develop new methods to
solve the complex, interconnected, and multiscale problems of the natural world.
For example, in the field of bioengineering, fractional
calculus has been used by Anastasio [35] to improve the
neuronal model of the vestibuloocular reflex and by Landolt
and Correia [36] to model the neurodynamic response of the
semicircular canal, while Ionescu and colleagues [37], [38]

have used it to describe a wide range of biological phenomena. In the cybernetics arena, Liu et al. [39] and Ono and
Deng [40] have applied fractional calculus to neural networks and to nonlinear control problems, respectively.
Hence, we believe that now is a good time to build on such
studies and for the cybernetics and fractional calculus communities to seek more ways to cooperate and work together.
To quote Gerhard Werner [41]:
Neural Dynamics must take into account the [noninteger] nature of phase transitions and criticality in
complex systems, requiring the mathematical tools of
Fractional Calculus and its physical models of Random Walks with long-term memory.
Perhaps, if we asked the brain to speak for itself, the
answer would be, "Fractional calculus is spoken here!"
Acknowledgments
We wish to acknowledge support from the Slovak Academic Information Agency for a two-month grant to Prof. Richard Magin under the National Scholarship Program that
was hosted by Prof. Igor Podlubny and Prof. Ivo Petras at
the Technical University of Kosice, Slovakia. Prof. Podlubny's efforts were partially supported by grants VEGA
1/0908/15, APVV-14-0892, and Army Research Office
WF911NF-15-1-0228.
About the Authors
Richard Magin (rmagin@uic.edu) earned his B.S. and M.S.
degrees in physics from the Georgia Institute of Technology,
Atlanta, in 1969 and 1972, respectively, and his Ph.D. degree
in biophysics from the University of Rochester, New York, in
1976. Until 1999, he was an assistant, associate, and full professor of electrical and computer engineering at the University of Illinois, Urbana-Champaign. From 1999 to 2009, he
was head of the Department of Bioengineering at the University of Illinois, Chicago (UIC). Currently, he is a distinguished
professor in the Richard and Loan Hill Department of Bioengineering at UIC. His research interests focus on the application of magnetic resonance imaging in science and engineering. He is a fellow of the American Institute for Medical and
Biological Engineering and a Fellow of the IEEE.
Blas Vinagre (bvinagre@unex.es) earned his M.S.
degree in telecommunications engineering from the Technical University of Madrid, Spain, in 1985 and his Ph.D. degree
from the National University of Distant Learning, Madrid,
Spain, in 2001. He worked in industry from 1985 to 1994,
mainly in communications, automation, and electronic warfare. In 1994, he joined the University of Extremadura,
Spain, as an assistant professor. From 2001 to 2016, he was
an associate professor in the Department of Electric, Electronic, and Automation Engineering at the University of
Extremadura, where he is now a full professor of automatic
control. His research interests focus on the application of
fractional calculus in automatic control and robotics,
including microrobotics for medical applications. He is a
Member of the IEEE.
Ju ly 2018

IEEE SyStEmS, man, & CybErnEtICS magazInE

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