Page 316 - Mathematical Techniques of Fractional Order Systems

Sliding Mode Stabilization and Synchronization Chapter | 10 305

FIGURE 10.21 Real and imaginary components of the variable x(1).

10.7 CONCLUSION

Due to chaos and hyperchaos being a phenomenon found in many kind of
physical systems such as mechanical, electrical, chemical, and biological sys-
tems, in this book chapter the design of a terminal sliding mode controller
along with an adaptive terminal sliding mode technique is proposed for the
stabilization and synchronization of fractional order chaotic and hyperchaotic
systems. These control and synchronization strategies consist of dividing the
real and imaginary parts of the studied systems in order to obtain the desired
control and adaptive gain law. Suitable sliding surfaces were designed to
derive efficient control and synchronization strategies to obtain the desired
system response. As a future direction, the design of sliding mode techniques
for these kinds of systems could be considered, such as sliding mode back-
stepping control, to provide more contributions in this field.