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Enhanced Fractional Order Chapter | 20 617

simulation example, chaos synchronization of two fractional order systems,
is given to demonstrate the effectiveness of the proposed methodology. The
significance of the proposed control scheme in the simulation for different
values of q is manifest. Simulation results show that a fast synchronization
of drive and response can be achieved and as q is reduced the chaos is seen
reduced, i.e., the synchronization error is reduced, accordingly. The asymp-
totic stability of the overall control system is established and an illustrative
simulation example, chaos synchronization of two fractional order systems,
is realized with the Gru ¨nwald Letnikov numerical approximation approach
to demonstrate the effectiveness of the proposed methodology.
Future research efforts will concern observer-based nonlinear adaptive
control of uncertain or unknown fractional order systems. The problem of
online identification and parameters estimation for such systems is also a
good challenge. Another topic of interest is the design of new robust adap-
tive control laws for the class of fractional discrete nonlinear systems based
on various control configurations.

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