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Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique. (English) Zbl 1253.93016
Summary: A novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order non-autonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then, an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/non-autonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/non-autonomous fractional-order dynamical systems in finite time.

MSC:
93B12 Variable structure systems
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations and fractional differential inclusions
93C41 Control/observation systems with incomplete information
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