Page 455 - Mathematical Techniques of Fractional Order Systems

440 Mathematical Techniques of Fractional Order Systems

nonlocality of these models and their memory dependency which have made
the realization more complex and the models more representative. The frac-
tional orders are extra parameters that can be used to increase the range of
system parameters at which the system shows chaotic response.
Most of the applications of FOCS have some sort of chaos control or syn-
chronization in their structure. Chaos control is used when chaotic behavior
is undesirable and needs to be annihilated or diminished while synchroniza-
tion is preferred when two systems needs to follow some aspects of each
other. The use of fractional models in either the model or the control or both
allowed more control over the convergence time. There are still unexplored
areas in nonlinear control of FOCS like back-stepping control.
The area of secure communications benefits from FOCS in two main
ways: the structure of the communication system itself and the encryption of
the transferred data. For example, in the first case, both chaotic systems at
the sender and receiver ends need to be in sync for successful transmission
of the message. In the second case, FOCS are used as pseudo-random num-
ber generators which can be used in either block chiper or stream cipher.
The possibilities are unlimited in this area and the output algorithms have to
be put to standardized tests to check their reliability. Biomedical applications
exploited the tools of control and synchronization and it can really benefit
from faster control algorithms that could help to avoid disasters like in epide-
miological modeling or making faster diagnosis.
Fractional order models of motors are nonlinear and the chaotic range of
operations needs to be avoided as it causes damage and total failure of the
system. If a change in system parameters occurs and the system moves into
the chaotic range, chaos control needs to act fast to stabilize the system back
to its safe operating conditions. So, fast identification of chaotic response is
an important topic to help this purpose. FPGA realizations of FOCS shorten
the gap between the theoretical study and market demand. Also, FOCS are
very sensitive to their implementation which allows for even more tuning to
achieve higher MLE and other desirable characteristics. Also, there will be
always a trade-off between generating an accurate response and system com-
plexity in FPGA design.

REFERENCES

AbdelAty, A.M., Radwan, A.G., Ahmed, W.A., Faied, M., 2016. Charging and discharging rc α
circuit under riemann-liouville and caputo fractional derivatives. In: Electrical Engineering/
Electronics, Computer, Telecommunications and Information Technology (ECTI-CON),
2016 13th International Conference on (pp. 1 4). IEEE.
AbdelAty, A.M., Soltan, A., Ahmed, W.A., Radwan, A.G., 2017. On the analysis and design of
fractional-order chebyshev complex filter. Circuits Systems Signal Processing 2017, 1 24.
AbdelAty, A.M., Radwan, A.G., Elwakil, A.S., Psychalinos, C., 2018. Transient and steady-state
response of a fractional-order dynamic pv model under different loads. J. Circuits Systems
Computers 27 (02), 1850023.