Page 314 - Mathematical Techniques of Fractional Order Systems

Sliding Mode Stabilization and Synchronization Chapter | 10 303

(A) 20

0
REAL (U(1)) –20

–40

–60
0 0.5 1 1.5 2 2.5 3
Time (s)
(B)
20

0

IMAG (U(1)) –20

–40

–60
0 0.5 1 1.5 2 2.5 3
Time (s)
FIGURE 10.18 Real and imaginary components of the input u(1).

hyperchaotic systems, this study provides a deep analysis and theoretical
framework in which the terminal sliding mode control strategy stabilizes
effectively the two studied systems to reach the equilibrium point. The
results obtained by the proposed control strategy provide more accurate and
faster outcomes than other control techniques found in literature. In the syn-
chronization case, the sliding mode technique along with its variation have
not been studied deeply in recent years considering the capability of this
kind of controller to deal with uncertainties. Therefore, a strong theoretical
study is provided in this chapter where the synchronization by an adaptive
terminal sliding mode controller is done effectively for fractional order com-
plex chaotic and hyperchaotic systems in the identical and nonidentical syn-
chronization cases.