Abstract
To achieve synchronization of uncertain fractional-order chaotic systems with time-delays, an adaptive fuzzy controller with integer-order parameter adaptive laws, is established. Unknown nonlinear functions and uncertain external disturbances are approximated by fuzzy logic systems. Adaptive laws are designed to adjust corresponding parameters in the controller. The proposed controller guarantees that the synchronization error of the system converges to a small enough region of the origin by making use of quadratic Lyapunov functions in the stability analysis, and the boundedness of all signals in the closed-loop. Finally, simulation studies have been provided to verify the effectiveness of the proposed methods.
Highlights
Fractional calculus has a history as long as the integer-order calculus, it has received much attention only in recent several decades because it has been shown that the fractional calculus can provide real-world systems some useful properties, such as hereditary and memory [1,2,3,4,5,6,7,8,9,10,11,12]
Considering systems with unknown parameters and external disturbances, this paper studies the synchronization of unknown fractional-order chaotic systems with different structures and time-delays based on adaptive fuzzy control [37, 41,42,43]
6 Conclusions It can be seen that the designed adaptive feedback controller has strong anti-interference ability on the condition of not requiring an exact model and including time-delay state variables, unknown nonlinear terms and uncertain external disturbances
Summary
Fractional calculus has a history as long as the integer-order calculus, it has received much attention only in recent several decades because it has been shown that the fractional calculus can provide real-world systems some useful properties, such as hereditary and memory [1,2,3,4,5,6,7,8,9,10,11,12]. [29], the synchronization of fractional-order chaotic systems with time-delays was achieved by designing a sliding mode controller, where the external disturbances were not considered and one needed to known the exact upper bounds of unknown terms. To achieve the synchronization problem of unknown fractional-order chaotic systems with time-delays, this paper designs a controller that can be used to eliminate time-delay characteristics, nonlinear terms and external disturbances in nonlinear systems. Considering systems with unknown parameters and external disturbances, this paper studies the synchronization of unknown fractional-order chaotic systems with different structures and time-delays based on adaptive fuzzy control [37, 41,42,43].
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